Linear 2017 - Nonlinear (edit).xlsx
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SAMPLE 1 Actual Temp. (°C)
15
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 172267 138942 129144 103374 88833 63569
12.8515501 14.90658 15.8472872 20.1137123 22.1495304 25.2703648
Actual Temp. (°C)
15
SAMPLE 1 Actual Temp. (°C)
25
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 142037 107802 94789 63578 53503 37837
28.4355869 31.1378937 33.8276901 39.0176506 38.4435081 36.6759071
Actual Temp. (°C)
25
SAMPLE 1 Actual Temp. (°C)
40
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 75250 57579 48393 33102 28454 22713
36.4389572 36.4631805 34.6970024 34.5666733 32.8909607 30.9623127
Actual Temp. (°C)
40
SAMPLE 3
Actual Temp. (°C)
55
Frequency (Hz)
Angle |E*| (Mpa) Phase (Deg)
25 44212.4667 10 31218 5 25935.6 1 19736.4333 0.5 17879.4 0.1 15754.0667
34.5670776 33.6047058 31.824297 27.9230499 24.6654949 17.3788319
Actual Temp. (°C)
55
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
15
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
SAMPLE 3
|E*| (Mpa)
25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
25
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
Frequency (Hz)
Frequency (Hz)
|E*| (Mpa)
25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
40
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3
|E*| (Mpa)
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
Actual Temp. (°C)
Frequency (Hz)
|E*| (Mpa)
25 10 5 1 0.5 0.1
55
1000000
1000000
100000 100000
1000 10000
100 10 1 0.1
1
10
100
1000
log E*
log E*
10000
1000
log frequency ω 100
10
1 0.001
0.
conversion angle in degree = angle in radian *180°/PI() Hz (cycle/sec) = 2*PI() angular freq (rad/s) TOTAL Phase Angle (Deg)
Actual Temp. (°C)
15
Angle θ Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 172266.667 12.851550102 10 138942.1 14.906579971 5 129143.5 15.847287178 1 103374 20.113712311 0.5 88833.0333 22.149530411 0.1 63568.7333 25.270364761
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
25
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 142036.667 28.435586929 10 107801.567 31.137893677 5 94788.8667 33.827690125 1 63577.5667 39.017650604 0.5 53503.1333 38.443508148 0.1 37837.1333 36.675907135
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
40
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 75250.2667 36.438957214 10 57579.0533 36.463180542 5 48393.2667 34.697002411 1 33102.4333 34.566673279 0.5 28453.9333 32.890960693 0.1 22713.3667 30.962312698
TOTAL
Phase Angle (Deg)
Actual Temp. (°C)
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 44212.4667 34.567077637 10 31218 33.604705811 5 25935.6 31.824296951 1 19736.4333 27.923049927 0.5 17879.4 24.665494919 0.1 15754.0667 17.378831863
55
1000000
1
100000
0.1
0.01
1000
log J*
log E*
10000
100
0.0001
10
1 0.001
0.001
0.00001
0.01
0.1
1
10
log frequency ω
100
1000
10000
0.000001 0.001
Phase Angle θ (Rad)
|J*| (1/E*)
0.2243018633 0.2601689007 0.2765873388 0.3510505046 0.3865822334 0.4410510683
0.000005805 7.19724259E-06 7.74332429E-06 9.67361232E-06 1.12570737E-05 0.000015731
Phase Angle (Rad)
|J*| (1/E*)
0.4962946166 0.5434587668 0.590404571 0.6809864694 0.6709657932 0.6401153357
7.04043557E-06 9.27630303E-06 1.05497622E-05 1.57288184E-05 1.86904941E-05 2.64290635E-05
Phase Angle (Rad)
|J*| (1/E*)
0.6359797794 0.6364025562 0.6055769326 0.6033022602 0.5740555582 0.5403943006
0.000013289 1.73674269E-05 0.000020664 3.02092595E-05 3.5144526E-05 4.40269386E-05
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Actual Temp. (°C)
Frequency (ω)
J*
15
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
5.8E-06 7.2E-06 7.7E-06 9.7E-06 1.1E-05 1.6E-05
Actual Temp. (°C)
Frequency (ω)
J*
25
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
7E-06 9.3E-06 1.1E-05 1.6E-05 1.9E-05 2.6E-05
Actual Temp. (°C)
Frequency (ω)
J*
40
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
1.3E-05 1.7E-05 2.1E-05 3E-05 3.5E-05 4.4E-05
Phase Angle (Rad)
|J*| (1/E*)
0.6033093176 0.5865127606 0.5554387639 0.4873491584 0.430494098 0.3033178362
2.26180549E-05 3.20328016E-05 0.000038557 5.06677161E-05 5.59302885E-05 6.3475674E-05
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Actual Temp. (°C)
Frequency (ω)
J*
55
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
2.3E-05 3.2E-05 3.9E-05 5.1E-05 5.6E-05 6.3E-05
1
0.1
log J*
0.01
0.001
0.0001
0.00001
10000
0.000001 0.001
0.01
0.1
1
log frequency ω
10
100
1000
10000
Log (reduced ω) (reduced ω) 3.196119877 2.7981798684 2.4971498727 1.7981798684 1.4971498727 0.7981798684
1570.79633 628.318531 314.159265 62.8318531 31.4159265 6.28318531
Actual Temp. (°C) 15 25 40 55
aT
log (aT) 0.1 -1 1 0 15 1.176091 225 2.352183
15
25
Log (reduced ω) (reduced ω) 2.196119877 1.7981798684 1.4971498727 0.7981798684 0.4971498727 -0.2018201316
157.079633 62.8318531 31.4159265 6.28318531 3.14159265 0.62831853
40
55
Log (reduced ω) (reduced ω) 1.020028618 0.6220886093 0.3210586136 -0.3779113907 -0.6789413864 -1.3779113907
10.4719755 4.1887902 2.0943951 0.41887902 0.20943951 0.0418879
Log (reduced ω) (reduced ω) -0.1560626411 -0.5540026498 -0.8550326454 -1.5540026498 -1.8550326454 -2.5540026498
0.6981317 0.27925268 0.13962634 0.02792527 0.01396263 0.00279253
1
15 25 40 55
0.1
log J*
0.01 0.001
15 25 40 55
0.0001 0.00001 1000
10000
0.000001 0.1
1
10
log frequency ω
100
1000
Frequency (ω) J* (ω) [CALCULATION] [EXP]
Phase Angle θ (Rad) [EXP]
J'
[EXP]
157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
0.000005805 7.19724259242E-06 7.74332428655E-06 9.67361232031E-06 1.12570736637E-05 0.000015731 7.04043556828E-06 9.27630303456E-06 1.05497621732E-05 1.57288183935E-05 1.86904941393E-05 2.64290635126E-05
0.2243018633 0.2601689007 0.2765873388 0.3510505046 0.3865822334 0.4410510683 0.4962946166 0.5434587668 0.590404571 0.6809864694 0.6709657932 0.6401153357
5.65953731568516E-06 0.000006955 0.000007449 9.08363784756019E-06 1.04263359680341E-05 1.42256015602625E-05 0.000006191 7.93982225368962E-06 8.76385120706946E-06 1.22205377801094E-05 1.4638797909155E-05 2.11968192080711E-05
157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
0.000013289 1.73674269046E-05 0.000020664 3.02092595408E-05 3.51445260058E-05 4.40269386162E-05 2.26180549377E-05 3.20328015888E-05 0.000038557 5.06677160514E-05 5.59302884884E-05 6.34756740059E-05
0.6359797794 0.6364025562 0.6055769326 0.6033022602 0.5740555582 0.5403943006 0.6033093176 0.5865127606 0.5554387639 0.4873491584 0.430494098 0.3033178362
1.06908608126649E-05 1.39675610057686E-05 1.69894260087798E-05 2.48763138813546E-05 2.95110534817307E-05 3.77533592065868E-05 1.86251204646853E-05 2.66793448268219E-05 3.27607286801382E-05 4.47688443417948E-05 5.08271901580398E-05 6.05780567839882E-05
15 25 40 55
1000
J"
[EXP]
J'
J"
[MODEL]
[MODEL]
Error
Time
1.29117125527063E-06 1.85144583372375E-06 2.1145027743446E-06 3.32660469218643E-06 4.24419907059311E-06 6.71541122474738E-06 3.35244754882657E-06 4.79677189042242E-06 0.000005873 9.90223128493299E-06 1.16206784201926E-05 1.57857611033318E-05
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
3.36975E-11 5.18003E-11 5.99591E-11 9.35788E-11 1.26722E-10 2.47464E-10 4.95677E-11 8.60498E-11 1.11297E-10 2.47396E-10 3.49335E-10 6.98495E-10
0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943 0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943
7.89320820337851E-06 1.03215675570675E-05 1.1762721326648E-05 1.713967239133E-05 0.000019085 2.26507216779253E-05 1.28328210788949E-05 1.77288729828122E-05 2.03317507643716E-05 2.3726947257533E-05 2.33408207018787E-05 1.8959436351716E-05
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
1.76597E-10 3.01628E-10 4.27002E-10 9.12599E-10 1.23514E-09 1.93837E-09 5.11576E-10 1.0261E-09 1.48665E-09 2.56722E-09 3.1282E-09 4.02916E-09
0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943 0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943
sum of error =
1.98956E-08
J*(t)
tau 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Jn
0.001 0.01 0.1 1 10 100 1000
lamda 1000 100 10 1 0.1 0.01 0.001
J0
SAMPLE 1 Actual Temp. (°C)
15
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 172267 138942 129144 103374 88833 63569
12.8515501 14.90658 15.8472872 20.1137123 22.1495304 25.2703648
Actual Temp. (°C)
15
SAMPLE 1 Actual Temp. (°C)
25
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 142037 107802 94789 63578 53503 37837
28.4355869 31.1378937 33.8276901 39.0176506 38.4435081 36.6759071
Actual Temp. (°C)
25
SAMPLE 1 Actual Temp. (°C)
40
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 75250 57579 48393 33102 28454 22713
36.4389572 36.4631805 34.6970024 34.5666733 32.8909607 30.9623127
Actual Temp. (°C)
40
SAMPLE 1 Actual Temp. (°C)
1000000
Angle |E*| (Mpa) Phase (Deg)
25 44212.4667 10 31218 5 25935.6 1 19736.4333 0.5 17879.4 0.1 15754.0667
Actual Temp. (°C)
34.5670776 33.6047058 31.824297 27.9230499 24.6654949 17.3788319
55
log E*
55
Frequency (Hz)
SAMPLE 3
100000
10000 0.0001
0.001
0.01
0.1
log frequency ω
1
10
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
15
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
|E*| (Mpa)
25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
25
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
Frequency (Hz)
Frequency (Hz)
|E*| (Mpa)
25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
40
Frequency (Hz) 25 10 5 1 0.5 0.1
|E*| (Mpa)
ency ω
SAMPLE 3
SAMPLE 3
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
Actual Temp. (°C)
Frequency (Hz) 25 10 5 1 0.5 0.1
55
1000000 100000
log E*
10000 1000 100 10 1 0.001
0.01
0.1
log frequency ω
1
10
100
1000
1
10
|E*| (Mpa)
conversion angle in degree = angle in radian *180°/PI() Hz (cycle/sec) = 2*PI() angular freq (rad/s) TOTAL Phase Angle (Deg)
Actual Temp. (°C)
15
Angle θ Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 172266.667 10 138942.1 5 129143.5 1 103374 0.5 88833.0333 0.1 63568.7333
12.851550102 14.906579971 15.847287178 20.113712311 22.149530411 25.270364761
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
25
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 142036.667 28.435586929 10 107801.567 31.137893677 5 94788.8667 33.827690125 1 63577.5667 39.017650604 0.5 53503.1333 38.443508148 0.1 37837.1333 36.675907135
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
40
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 75250.2667 36.438957214 10 57579.0533 36.463180542 5 48393.2667 34.697002411 1 33102.4333 34.566673279 0.5 28453.9333 32.890960693 0.1 22713.3667 30.962312698
TOTAL Actual Temp. (°C)
55
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 44212.4667 34.567077637 10 31218 33.604705811 5 25935.6 31.824296951 1 19736.4333 27.923049927 0.5 17879.4 24.665494919 0.1 15754.0667 17.378831863 1
0.1
0.01
log J*
Phase Angle (Deg)
0.001
0.0001
0.00001
0.000001 0.0001
Phase Angle θ (Rad)
|J*| (1/E*)
0.2243018633 0.2601689007 0.2765873388 0.3510505046 0.3865822334 0.4410510683
0.000005805 7.19724259E-06 7.74332429E-06 9.67361232E-06 1.12570737E-05 0.000015731
Phase Angle (Rad)
|J*| (1/E*)
0.4962946166 0.5434587668 0.590404571 0.6809864694 0.6709657932 0.6401153357
7.04043557E-06 9.27630303E-06 1.05497622E-05 1.57288184E-05 1.86904941E-05 2.64290635E-05
Phase Angle (Rad)
|J*| (1/E*)
0.6359797794 0.6364025562 0.6055769326 0.6033022602 0.5740555582 0.5403943006
0.000013289 1.73674269E-05 0.000020664 3.02092595E-05 3.5144526E-05 4.40269386E-05
Time (sec) 0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
Frequency (ω) 0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
Frequency (ω) 0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
Actual Temp. (°C)
Time (sec)
15
0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
Actual Temp. (°C)
Frequency (ω)
25
0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
Actual Temp. (°C)
Frequency (ω)
40
0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
Phase Angle (Rad)
|J*| (1/E*)
0.6033093176 0.5865127606 0.5554387639 0.4873491584 0.430494098 0.3033178362
2.26180549E-05 3.20328016E-05 0.000038557 5.06677161E-05 5.59302885E-05 6.3475674E-05
Frequency (ω)
Actual Temp. (°C)
Frequency (ω)
55
0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
1
0.1
log J*
0.01
0.001
0.0001
0.00001
0.000001 0.0001
0.001
0.01
0.1
1
log time
10
100
J* 0.000005805 7.197243E-06 7.743324E-06 9.673612E-06 1.125707E-05 0.000015731
J* 7.040436E-06 9.276303E-06 1.054976E-05 1.572882E-05 1.869049E-05 2.642906E-05
J* 0.000013289 1.736743E-05 0.000020664 3.020926E-05 3.514453E-05 4.402694E-05
Log (time, sec) -3.196119877 -2.7981798684 -2.4971498727 -1.7981798684 -1.4971498727 -0.7981798684
Log (reduced ω) -2.196119877 -1.7981798684 -1.4971498727 -0.7981798684 -0.4971498727 0.2018201316
Log (reduced ω) -1.0221946797 -0.6242546711 -0.3232246754 0.3757453289 0.6767753246 1.3757453289
(reduced time, sec) 0.0006366198 0.0015915494 0.0031830989 0.0159154943 0.0318309886 0.1591549431
(reduced ω) 0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
(reduced ω) 0.0950178765 0.2375446912 0.4750893824 2.3754469118 4.7508938236 23.7544691182
Actual Temp. (°C) 15 25 40 55
aT
log (aT)
10 1 1 0 0.067 -1.173925 0.0044 -2.356547
J* 2.261805E-05 3.20328E-05 0.000038557 5.066772E-05 5.593029E-05 6.347567E-05
Log (reduced ω) 0.1604274465 0.5583674552 0.8593974508 1.5583674552 1.8593974508 2.5583674552
(reduced ω) 1.446863119 3.6171577975 7.2343155951 36.1715779754 72.3431559509 361.7157797543
1
15 25 40 55
0.1
log J*
0.01 0.001 0.0001 0.00001 10
100
1000
0.000001 0.001
0.01
0.1
log frequency ω
1
10
reduced Time J* (sec) (sec) [EXP] [CALCULATION]
15
25
40
55
Phase Angle θ (Rad) (reduced time, sec) [EXP] [CALCULATION]/[SORTED]
0.0006366198 0.0015915494 0.0031830989 0.0159154943 0.0318309886 0.1591549431 0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
0.000005805 7.19724259242E-06 7.74332428655E-06 9.67361232031E-06 1.12570736637E-05 0.000015731 7.04043556828E-06 9.27630303456E-06 1.05497621732E-05 1.57288183935E-05 1.86904941393E-05 2.64290635126E-05
0.2243018633 0.2601689007 0.2765873388 0.3510505046 0.3865822334 0.4410510683 0.4962946166 0.5434587668 0.590404571 0.6809864694 0.6709657932 0.6401153357
0.0006366198 0.0015915494 0.0031830989 0.0063661977 0.0159154943 0.0159154943 0.0318309886 0.0318309886 0.0950178765 0.1591549431 0.1591549431 0.2375446912
0.0950178765 0.2375446912 0.4750893824 2.3754469118 4.7508938236 23.7544691182 1.446863119 3.6171577975 7.2343155951 36.1715779754 72.3431559509 361.7157797543
0.000013289 1.73674269046E-05 0.000020664 3.02092595408E-05 3.51445260058E-05 4.40269386162E-05 2.26180549377E-05 3.20328015888E-05 0.000038557 5.06677160514E-05 5.59302884884E-05 6.34756740059E-05
0.6359797794 0.6364025562 0.6055769326 0.6033022602 0.5740555582 0.5403943006 0.6033093176 0.5865127606 0.5554387639 0.4873491584 0.430494098 0.3033178362
0.3183098862 0.4750893824 1.446863119 1.5915494309 2.3754469118 3.6171577975 4.7508938236 7.2343155951 23.7544691182 36.1715779754 72.3431559509 361.7157797543
15 25 40 55
0.1
requency ω
1
10
J* (sec) [EXP]/[SORTED]
Phase Angle (Rad) [SORTED]/[EXP]
J'
J"
[EXP]
[EXP]
0.000005805 7.19724259241799E-06 7.74332428654946E-06 7.04043556828049E-06 9.67361232031265E-06 9.27630303455701E-06 1.12570736636634E-05 1.05497621731947E-05 0.000013289 0.000015731 1.57288183934899E-05 1.73674269045526E-05
0.2243018633 0.2601689007 0.2765873388 0.4962946166 0.3510505046 0.5434587668 0.3865822334 0.590404571 0.6359797794 0.4410510683 0.6809864694 0.6364025562
5.65953731568516E-06 0.000006955 0.000007449 0.000006191 9.08363784756019E-06 7.93982225368962E-06 1.04263359680341E-05 8.76385120706946E-06 1.06908608126649E-05 1.42256015602625E-05 1.22205377801094E-05 1.39675610057686E-05
1.29117125527063E-06 1.85144583372375E-06 2.1145027743446E-06 3.35244754882657E-06 3.32660469218643E-06 4.79677189042242E-06 4.24419907059311E-06 0.000005873 7.89320820337851E-06 6.71541122474738E-06 9.90223128493299E-06 1.03215675570675E-05
1.86904941392841E-05 0.000020664 2.26180549377476E-05 2.64290635125635E-05 3.02092595408394E-05 3.2032801588827E-05 3.51445260057778E-05 0.000038557 4.40269386161746E-05 5.06677160513635E-05 5.5930288488428E-05 6.34756740058651E-05
0.6709657932 0.6055769326 0.6033093176 0.6401153357 0.6033022602 0.5865127606 0.5740555582 0.5554387639 0.5403943006 0.4873491584 0.430494098 0.3033178362
1.4638797909155E-05 1.69894260087798E-05 1.86251204646853E-05 2.11968192080711E-05 2.48763138813546E-05 2.66793448268219E-05 2.95110534817307E-05 3.27607286801382E-05 3.77533592065868E-05 4.47688443417948E-05 5.08271901580398E-05 6.05780567839882E-05
1.16206784201926E-05 1.1762721326648E-05 1.28328210788949E-05 1.57857611033318E-05 1.713967239133E-05 1.77288729828122E-05 0.000019085 2.03317507643716E-05 2.26507216779253E-05 2.3726947257533E-05 2.33408207018787E-05 1.8959436351716E-05
0.001
0.0001
0.00001
0.000001 0.001
0.01
0.1
1
10
100
1000
0.00001
0.000001 0.001
0.01
0.1
1
10
100
1000
J'
[MODEL]
J"
[MODEL]
Time
J*(t)
0.0001108073 0.0001006741 9.37303320060384E-05 8.42383431501753E-05 6.5822557074067E-05 6.5822557074067E-05 5.61014963376098E-05 5.61014963376098E-05 0.000042596 3.56566361328499E-05 3.56566361328499E-05 3.16795546567538E-05
1.25733349597594E-05 1.65186226606022E-05 1.88377723397909E-05 2.35153186577283E-05 2.40168117327762E-05 2.40168117327762E-05 2.04223863818031E-05 2.04223863818031E-05 1.90034938628489E-05 1.67376088401388E-05 1.67376088401388E-05 1.4317502310958E-05
421.52562 244.334062 196.713413 195.097017 77.6996132 69.2017317 33.7210488 35.3129567 10.8875674 4.49688754 4.1543115 1.75790911
0.1 10.1 10.2 10.3 10 6.28318531 157.079633 62.8318531 31.4159265 6.28318531 3.14159265 0.62831853
1.45715E-05 4.93189E-05 4.94543E-05 4.95887E-05 4.91825E-05 4.3279E-05 9.02488E-05 7.51284E-05 6.53714E-05 4.3279E-05 3.62334E-05 2.34616E-05
2.95447725550347E-05 2.70966268881988E-05 1.97692396034956E-05 1.9212124286523E-05 1.7283212331609E-05 1.58046880226369E-05 1.49381497750657E-05 1.34682617412943E-05 9.40612824662155E-06 8.58687143219525E-06 7.3576698862398E-06 4.88054690367681E-06
1.28205825133796E-05 1.14867133490324E-05 9.07348577116386E-06 8.76873511401952E-06 7.5030916820982E-06 6.53089251853093E-06 6.16874255151827E-06 5.84645599831823E-06 4.11605534181874E-06 3.53116299016657E-06 3.06948314354812E-06 1.75289721395131E-06
1.04749745 0.35447 0.08959139 0.20636152 0.40927985 0.56509131 0.70187379 0.85437221 1.23336514 1.37767864 1.48571791 1.6689961
10.5243354 4.20973416 2.10486708 0.42097342 0.21048671 0.04209734 0.69115038 0.27646015 0.13823008 0.02764602 0.01382301 0.0027646
4.98865E-05 0.000039 3.26909E-05 2.12144E-05 1.78781E-05 1.15719E-05 2.40585E-05 1.91528E-05 1.59611E-05 1.0436E-05 8.71873E-06 5.83495E-06
sum of error =
100
Error
1000
1304.89643
τn 0.001 0.01 0.1 1 10 100 1000
100
1000
Dn 1.77E-06 0.00000367 7.24785385E-06 1.25372543E-05 2.66140939E-05 4.06631052E-05 2.16706441E-05
λn 1000 100 10 1 0.1 0.01 0.001
J0 3.04707448E-06
t
w 10
0.1
SAMPLE 1 Actual Temp. (°C)
15
Frequency (Hz)
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg)
25 10 5 1 0.5 0.1
Actual Temp. (°C)
15
SAMPLE 1 Actual Temp. (°C)
25
Frequency (Hz)
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg)
25 10 5 1 0.5 0.1
Actual Temp. (°C)
25
SAMPLE 1 Actual Temp. (°C)
40
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg)
Actual Temp. (°C)
40
SAMPLE 3
Actual Temp. (°C)
55
Frequency (Hz) 25 10 5 1 0.5 0.1
Angle |E*| (Mpa) Phase (Deg)
Actual Temp. (°C)
55
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 172366.67 17.8515501 10 139042.1 19.90657997 5 129243.5 20.84728718 1 103474 25.11371231 0.5 89033.033 27.14953041 0.1 63768.733 30.27036476
SAMPLE 3 Actual Temp. (°C)
15
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 142336.67 33.43558693 10 108101.57 36.13789368 5 95088.867 38.82769013 1 64077.567 44.0176506 0.5 54003.133 43.44350815 0.1 38337.133 41.67590714
SAMPLE 3
|E*| (Mpa)
25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
25
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 76250.267 41.43895721 10 58579.053 41.46318054 5 49393.267 39.69700241 1 34102.433 39.56667328 0.5 29453.933 37.89096069 0.1 23713.367 35.9623127
Frequency (Hz)
Frequency (Hz)
|E*| (Mpa)
25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
40
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3
|E*| (Mpa)
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 45462.467 39.56707764 10 32468 38.60470581 5 27185.6 36.82429695 1 20986.433 32.92304993 0.5 19129.4 29.66549492 0.1 17004.067 22.37883186
Actual Temp. (°C)
55
Frequency (Hz) 25 10 5 1 0.5 0.1
|E*| (Mpa)
conversion angle in degree = angle in radian *180°/PI() Hz (cycle/sec) = 2*PI() angular freq (rad/s) TOTAL Phase Angle (Deg)
Actual Temp. (°C)
15
Angle θ Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 172366.667 17.851550102 10 139042.1 19.906579971 5 129243.5 20.847287178 1 103474 25.113712311 0.5 89033.0333 27.149530411 0.1 63768.7333 30.270364761
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
25
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 142336.667 33.435586929 10 108101.567 36.137893677 5 95088.8667 38.827690125 1 64077.5667 44.017650604 0.5 54003.1333 43.443508148 0.1 38337.1333 41.675907135
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
40
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 76250.2667 41.438957214 10 58579.0533 41.463180542 5 49393.2667 39.697002411 1 34102.4333 39.566673279 0.5 29453.9333 37.890960693 0.1 23713.3667 35.962312698
TOTAL
Phase Angle (Deg)
Actual Temp. (°C)
55
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 45462.4667 39.567077637 10 32468 38.604705811 5 27185.6 36.824296951 1 20986.4333 32.923049927 0.5 19129.4 29.665494919 0.1 17004.0667 22.378831863
1000000 100000
log E*
10000 1000 100 10 1 0.1
1
10
log frequency ω
100
1000
Phase Angle θ (Rad)
|J*| (1/E*)
0.3115683259 0.3474353633 0.3638538014 0.4383169672 0.473848696 0.5283175309
5.80158577E-06 7.19206629E-06 7.73733302E-06 9.66426349E-06 1.12317863E-05 1.56816664E-05
Phase Angle (Rad)
|J*| (1/E*)
0.5835610792 0.6307252294 0.6776710336 0.768252932 0.7582322558 0.7273817983
7.02559659E-06 9.25055974E-06 1.05164783E-05 1.56060857E-05 1.8517444E-05 2.60843708E-05
Phase Angle (Rad)
|J*| (1/E*)
0.723246242 0.7236690188 0.6928433952 0.6905687228 0.6613220208 0.6276607632
1.31147082E-05 1.70709485E-05 2.02456745E-05 2.93234207E-05 3.39513229E-05 4.2170309E-05
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Actual Temp. (°C)
Frequency (ω)
J*
15
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
5.8E-06 7.2E-06 7.7E-06 9.7E-06 1.1E-05 1.6E-05
Actual Temp. (°C)
Frequency (ω)
J*
25
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
7E-06 9.3E-06 1.1E-05 1.6E-05 1.9E-05 2.6E-05
Actual Temp. (°C)
Frequency (ω)
J*
40
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
1.3E-05 1.7E-05 2E-05 2.9E-05 3.4E-05 4.2E-05
Phase Angle (Rad)
|J*| (1/E*)
0.6905757802 0.6737792232 0.6427052265 0.574615621 0.5177605606 0.3905842988
2.19961668E-05 3.07995565E-05 3.67841799E-05 4.76498309E-05 5.22755549E-05 5.88094613E-05
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Actual Temp. (°C)
Frequency (ω)
J*
55
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
2.2E-05 3.1E-05 3.7E-05 4.8E-05 5.2E-05 5.9E-05
Log (reduced ω) (reduced ω) #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
Actual Temp. (°C)
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
aT
log (aT)
15 25 40 55
Err:502 Err:502 Err:502 Err:502
15
25
1 0.1
Log (reduced ω) (reduced ω) #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
log J*
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
0.01 0.001
40
0.0001 0.00001 0.000001 0.1
1
10
log frequency ω
Log (reduced ω) (reduced ω) #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
100
55
1000
Log (reduced ω) (reduced ω) #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
Frequency (ω) J* (ω) [CALCULATION] [EXP]
Phase Angle θ (Rad) [EXP]
J'
[EXP]
157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
5.80158576678E-06 7.19206628784E-06 7.73733301868E-06 9.66426348648E-06 1.12317862546E-05 1.56816663548E-05 7.02559659024E-06 9.25055973595E-06 1.05164782698E-05 1.56060857492E-05 1.85174440495E-05 2.60843707667E-05
0.3115683259 0.3474353633 0.3638538014 0.4383169672 0.473848696 0.5283175309 0.5835610792 0.6307252294 0.6776710336 0.768252932 0.7582322558 0.7273817983
5.52226243007492E-06 6.76233335721773E-06 7.23078748452949E-06 8.75067409747359E-06 9.99425308088338E-06 1.35435714030964E-05 5.86290105851906E-06 7.47075232727044E-06 8.19270513716874E-06 1.12227384146764E-05 1.34446405171975E-05 1.94828820146058E-05
157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307 157.0796326795 100 62.8318530718 1000 31.4159265359 6.2831853072 3.1415926536 0.6283185307
1.31147082327E-05 1.70709484551E-05 2.02456745116E-05 2.93234207139E-05 3.39513228567E-05 4.217030901E-05 2.19961668013E-05 3.07995564864E-05 3.67841798599E-05 4.76498309225E-05 5.2275554905E-05 5.88094612661E-05
0.723246242 0.7236690188 0.6928433952 0.6905687228 0.6613220208 0.6276607632 0.6905757802 0.6737792232 0.6427052265 0.574615621 0.5177605606 0.3905842988
9.83158855932412E-06 1.27926509029902E-05 1.55776895282488E-05 0.000022605 2.67937385203732E-05 3.41327934051E-05 1.69563914634771E-05 2.40689056723185E-05 2.94449000918833E-05 3.99973290243522E-05 4.54237841033102E-05 5.43803300994444E-05
J"
[EXP]
J'
J"
[MODEL]
Error
[MODEL]
Time
1.77848673389589E-06 2.44880890526303E-06 2.75354945398757E-06 4.10166936452824E-06 5.1252246608913E-06 7.90482974590439E-06 3.87109785808383E-06 5.45533821985403E-06 6.59362553794228E-06 1.08443559000565E-05 1.27333175367333E-05 1.73439242013125E-05
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943 0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943
8.67959897860457E-06 1.13033341996867E-05 1.2931470349221E-05 1.86783065656021E-05 2.08515682820837E-05 2.4764639637211E-05 1.40111435111252E-05 1.92171917692246E-05 2.20470802272406E-05 2.58982636070863E-05 0.000025873 2.23904540527371E-05
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943 0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943
sum of error =
#DIV/0!
J*(t)
tau 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Jn
0.001 0.01 0.1 1 10 100 1000
lamda 1000 100 10 1 0.1 0.01 0.001
J0
SAMPLE 1 Actual Temp. (°C)
15
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 178367 145042 135244 109474 98033 72769
17.8515501 19.90658 20.8472872 25.1137123 27.1495304 30.2703648
Actual Temp. (°C)
15
SAMPLE 1 Actual Temp. (°C)
25
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 151337 117102 107089 79078 69003 53337
33.4355869 36.1378937 38.8276901 44.0176506 43.4435081 41.6759071
Actual Temp. (°C)
25
SAMPLE 1 Actual Temp. (°C)
40
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 98250 80579 71393 56102 54454 45713
41.4389572 41.4631805 39.6970024 39.5666733 37.8909607 35.9623127
Actual Temp. (°C)
40
SAMPLE 1 Actual Temp. (°C)
55
Frequency (Hz)
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg)
25 78462.4667 10 65468 5 60185.6 1 43986.4333 0.5 42129.4 0.1 40004.0667
39.5670776 38.6047058 36.824297 32.9230499 29.6654949 22.3788319
Actual Temp. (°C)
55
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
15
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
|E*| (Mpa)
25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
25
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
Frequency (Hz)
Frequency (Hz)
|E*| (Mpa)
25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
40
Frequency (Hz) 25 10 5 1 0.5 0.1
|E*| (Mpa)
SAMPLE 3
SAMPLE 3
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 73462 10 60468 5 55186 1 38986 0.5 37129 0.1 35004
Actual Temp. (°C)
Frequency (Hz) 25 10 5 1 0.5 0.1
55
1000000 100000
log E*
10000 1000 100 10 1 0.1
1
10
log frequency ω
100
1000
|E*| (Mpa)
conversion angle in degree = angle in radian *180°/PI() Hz (cycle/sec) = 2*PI() angular freq (rad/s) TOTAL Phase Angle (Deg)
Actual Temp. (°C)
15
Angle θ Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 178366.667 10 145042.1 5 135243.5 1 109474 0.5 98033.0333 0.1 72768.7333
17.851550102 19.906579971 20.847287178 25.113712311 27.149530411 30.270364761
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
25
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 151336.667 33.435586929 10 117101.567 36.137893677 5 107088.867 38.827690125 1 79077.5667 44.017650604 0.5 69003.1333 43.443508148 0.1 53337.1333 41.675907135
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
40
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 98250.2667 41.438957214 10 80579.0533 41.463180542 5 71393.2667 39.697002411 1 56102.4333 39.566673279 0.5 54453.9333 37.890960693 0.1 45713.3667 35.962312698
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
55
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 75962.4667 39.567077637 10 62968 38.604705811 5 57685.6 36.824296951 1 41486.4333 32.923049927 0.5 39629.4 29.665494919 0.1 37504.0667 22.378831863
Phase Angle θ (Rad)
|J*| (1/E*)
0.3115683259 0.3474353633 0.3638538014 0.4383169672 0.473848696 0.5283175309
5.6064287E-06 6.89454993E-06 7.39407069E-06 9.13458903E-06 1.02006433E-05 1.37421658E-05
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Actual Temp. (°C)
Frequency (ω)
J*
15
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
5.6E-06 6.9E-06 7.4E-06 9.1E-06 1E-05 1.4E-05
1000000
|J*| (1/E*)
0.5835610792 0.6307252294 0.6776710336 0.768252932 0.7582322558 0.7273817983
6.60778397E-06 8.5395954E-06 0.000009338 1.26458115E-05 1.44920955E-05 1.87486642E-05
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Actual Temp. (°C)
Frequency (ω)
J*
25
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
6.6E-06 8.5E-06 9.3E-06 1.3E-05 1.4E-05 1.9E-05
log E*
Phase Angle (Rad)
|J*| (1/E*)
0.723246242 0.7236690188 0.6928433952 0.6905687228 0.6613220208 0.6276607632
1.01780894E-05 1.24101731E-05 1.40069232E-05 1.78245388E-05 1.83641463E-05 2.18754398E-05
Frequency (ω)
Actual Temp. (°C)
Frequency (ω)
400.1
157.07963268 62.831853072 31.415926536 6.2831853072 10000 0.01 3.1415926536 0.6283185307
1
157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
0.01
log J*
Phase Angle (Rad)
100000
0.001
0.0001
J* 1E-05 1.2E-05 1.4E-05 1.8E-05 1.8E-05 0.1 2.2E-05
1
lo
log J*
Phase Angle (Rad)
|J*| (1/E*)
0.6905757802 0.6737792232 0.6427052265 0.574615621 0.5177605606 0.3905842988
1.31643961E-05 1.58810825E-05 1.73353489E-05 2.41042654E-05 2.52337911E-05 2.66637751E-05
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
0.001
Actual Temp. (°C)
Frequency (ω)
J*
55 0.00001
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
1.3E-05 1.6E-05 1.7E-05 2.4E-05 2.5E-05 2.7E-05
0.0001
0.000001 0.01
0.1
1
log freq
Actual Temp. (°C)
Log (reduced ω) (reduced ω) 2.9919998944 2.5940598857 2.29302989 1.5940598857 1.29302989 0.5940598857
981.747704 392.699082 196.349541 39.2699082 19.6349541 3.92699082
15 25 40 55
aT
log (aT)
0.16 -0.79588 1 0 8.5 0.929419 35 1.544068
15
25
Log (reduced ω) (reduced ω) 2.196119877 1.7981798684 1.4971498727 0.7981798684 0.4971498727 -0.2018201316
157.079633 62.8318531 31.4159265 6.28318531 3.14159265 0.62831853
40
55
Log (reduced ω) (reduced ω) 1.2667009513 18.4799568 0.8687609426 7.39198271 0.567730947 3.69599136 -0.1312390574 0.73919827 0.1-0.432269053 0.36959914 1 -1.1312390574 log 0.07391983 frequency ω
10
100
1000
15 25 40 55
15 25 40 55
Log (reduced ω) (reduced ω) 0.6520518327 0.254111824 -0.0469181717 -0.745888176 -1.0469181717 -1.745888176 1
10
100
1000
log frequency ω
1 0.1 0.01
log J*
0.1
4.48798951 1.7951958 0.8975979 0.17951958 0.08975979 0.01795196
0.001
15 25 40 55
0.0001 0.00001 0.000001 0.1
1
10
log frequency ω
100
1000
reduced Frequency (ω) J* (ω) [EXP] [CALCULATION]
Phase Angle θ (Rad) (reduced ω) [EXP] [CALCULATION]/[SORTED]
981.7477042468 392.6990816987 196.3495408494 39.2699081699 19.6349540849 3.926990817 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
5.60642870491E-06 6.89454992723E-06 7.39407069471E-06 9.13458903484E-06 1.02006432526E-05 1.37421658203E-05 6.60778396952E-06 8.53959539966E-06 0.000009338 1.26458114754E-05 1.4492095528E-05 1.87486641577E-05
0.3115683259 0.3474353633 0.3638538014 0.4383169672 0.473848696 0.5283175309 0.5835610792 0.6307252294 0.6776710336 0.768252932 0.7582322558 0.7273817983
0.017951958 0.0739198271 0.0897597901 0.1795195802 0.3695991357 0.6283185307 0.7391982714 0.897597901 1.7951958021 3.1415926536 3.6959913572 3.926990817
18.4799567858 7.3919827143 3.6959913572 0.7391982714 0.3695991357 0.0739198271 4.4879895051 1.7951958021 0.897597901 0.1795195802 0.0897597901 0.017951958
1.01780894233E-05 1.24101730987E-05 1.40069231552E-05 1.78245388049E-05 1.83641463304E-05 2.18754397875E-05 1.31643961009E-05 1.58810824546E-05 1.73353488566E-05 2.41042654105E-05 2.52337910743E-05 2.66637751284E-05
0.723246242 0.7236690188 0.6928433952 0.6905687228 0.6613220208 0.6276607632 0.6905757802 0.6737792232 0.6427052265 0.574615621 0.5177605606 0.3905842988
4.4879895051 6.2831853072 7.3919827143 18.4799567858 19.6349540849 31.4159265359 39.2699081699 62.8318530718 157.0796326795 196.3495408494 392.6990816987 981.7477042468
15 25 40 55
1000
J* (ω) [EXP]/[SORTED]
Phase Angle (Rad) [SORTED]/[EXP]
J'
[EXP]
J"
[EXP]
2.66637751283861E-05 2.18754397874874E-05 2.52337910743034E-05 2.41042654104595E-05 1.83641463304151E-05 1.87486641576788E-05 1.78245388049122E-05 1.73353488565604E-05 1.58810824545801E-05 1.44920955280292E-05 1.40069231552182E-05 1.37421658203019E-05
0.3905842988 0.6276607632 0.5177605606 0.574615621 0.6613220208 0.7273817983 0.6905687228 0.6427052265 0.6737792232 0.7582322558 0.6928433952 0.5283175309
2.46556397892751E-05 1.77060563330358E-05 2.19263914070327E-05 2.02331512168468E-05 1.44926351471979E-05 1.4003711838873E-05 1.37406495813269E-05 1.38765528301327E-05 1.24105772673237E-05 0.000010522 1.07773885247722E-05 1.18685093669124E-05
1.01516663991019E-05 1.28464172058731E-05 1.24890981198482E-05 0.000013101 1.1278537003313E-05 1.24662930509128E-05 1.13537981614525E-05 1.0390168503503E-05 9.90890265473229E-06 9.96533072476731E-06 8.94660789697952E-06 6.92716441555913E-06
1.31643961008814E-05 1.26458114753995E-05 1.24101730987491E-05 1.01780894233366E-05 1.02006432525635E-05 0.000009338 9.13458903483932E-06 8.53959539966303E-06 6.60778396951609E-06 7.39407069470991E-06 6.89454992722803E-06 5.60642870491496E-06
0.6905757802 0.768252932 0.7236690188 0.723246242 0.473848696 0.6776710336 0.4383169672 0.6307252294 0.5835610792 0.3638538014 0.3474353633 0.3115683259
1.01481615266392E-05 9.09392890123059E-06 0.0000093 7.63011923365853E-06 9.07672278859806E-06 7.27465954843317E-06 8.27107122752418E-06 6.89657750741661E-06 5.51423400585499E-06 0.00000691 6.48259388748235E-06 5.33650140645065E-06
8.38547209941944E-06 8.78732069579277E-06 8.21725485144198E-06 6.73608081821993E-06 4.65469936569637E-06 5.85476715874593E-06 3.8768669805177E-06 5.03606078936119E-06 3.64088345274416E-06 2.63138981804258E-06 2.34750829370557E-06 1.71866097943854E-06
J'
[MODEL]
J"
[MODEL]
Error
Time
J*(t)
3.59439339402798E-05 3.07900769722348E-05 2.94123257823711E-05 2.45904821555202E-05 2.13185851019507E-05 1.91724139493902E-05 1.84186112057225E-05 0.000017466 1.42853528257307E-05 1.26032377856081E-05 1.22155905653184E-05 1.20742810926395E-05
1.1087289211475E-05 0.000009689 9.75708010908519E-06 8.70650636515078E-06 7.26989978733592E-06 6.9998875980441E-06 6.95605442289078E-06 6.85440111200218E-06 5.804074769199E-06 4.81786382421652E-06 4.6312674150516E-06 4.57514274109774E-06
0.21811012 0.60646713 0.16441473 0.15889149 0.34816033 0.32850897 0.26593388 0.18271428 0.19442844 0.30593416 0.2504634 0.11558529
0.00101859 0.00254648 0.00509296 0.02546479 0.05092958 0.25464791 0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943
2.96037E-06 4.33257E-06 5.26344E-06 8.08719E-06 9.51751E-06 1.42804E-05 5.58171E-06 7.17381E-06 8.52749E-06 1.27415E-05 1.50186E-05 2.19395E-05
1.1762339799721E-05 1.09244858997578E-05 1.04789491378617E-05 7.99287837112937E-06 7.86638693295366E-06 7.07149144964196E-06 6.76135464981087E-06 6.08505449137286E-06 4.55975192536632E-06 4.25188577516009E-06 3.48673387888492E-06 2.22280489105947E-06
0.000004475 4.32216261477562E-06 4.26352216452159E-06 3.45258408175524E-06 3.37851271311549E-06 2.89443748275898E-06 2.752885438891E-06 2.61826183545141E-06 2.30944373960301E-06 2.18505922067755E-06 1.96684802389336E-06 1.92494667745243E-06
0.24277069 0.2987221 0.24757715 0.239867 0.092951 0.25643888 0.11737076 0.2443397 0.1636918 0.17674602 0.23986679 0.35484548
0.05411268 0.1352817 0.2705634 1.35281702 2.70563403 13.5281702 0.22281692 0.5570423 1.1140846 5.57042301 11.140846 55.7042301
9.65684E-06 1.22189E-05 0.00001448 2.10989E-05 2.46711E-05 3.42173E-05 1.38416E-05 1.7012E-05 2.01145E-05 2.84364E-05 3.2851E-05 4.40645E-05
sum of error =
5.81479958
tau 0.001 0.01 0.1 1 10 100 1000
Jn
lamda
3.08E-06 3.15E-06 5.37E-06 9.22E-06 1.45E-05 0 0.000151
1000 100 10 1 0.1 0.01 0.001
J0 6.2E-07
Chart Title 1 0.1 0.01 0.001 0.0001 0.00001 0.000001 0.001
0.01
0.1
1
10
100
aged result Frequency (ω) J* (ω) [CALCULATION] [EXP]
15
25
40
55
Phase Angle θ (Rad) (reduced ω) [EXP] [CALCULATION]/[SORTED]
981.7477042468 392.6990816987 196.3495408494 39.2699081699 19.6349540849 3.926990817 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
5.60642870491E-06 6.89454992723E-06 7.39407069471E-06 9.13458903484E-06 1.02006432526E-05 1.37421658203E-05 6.60778396952E-06 8.53959539966E-06 0.000009338 1.26458114754E-05 1.4492095528E-05 1.87486641577E-05
0.3115683259 0.3474353633 0.3638538014 0.4383169672 0.473848696 0.5283175309 0.5835610792 0.6307252294 0.6776710336 0.768252932 0.7582322558 0.7273817983
0.017951958 0.0739198271 0.0897597901 0.1795195802 0.3695991357 0.6283185307 0.7391982714 0.897597901 1.7951958021 3.1415926536 3.6959913572 3.926990817
18.4799567858 7.3919827143 3.6959913572 0.7391982714 0.3695991357 0.0739198271 4.4879895051 1.7951958021 0.897597901 0.1795195802 0.0897597901 0.017951958
1.01780894233E-05 1.24101730987E-05 1.40069231552E-05 1.78245388049E-05 1.83641463304E-05 2.18754397875E-05 1.31643961009E-05 1.58810824546E-05 1.73353488566E-05 2.41042654105E-05 2.52337910743E-05 2.66637751284E-05
0.723246242 0.7236690188 0.6928433952 0.6905687228 0.6613220208 0.6276607632 0.6905757802 0.6737792232 0.6427052265 0.574615621 0.5177605606 0.3905842988
4.4879895051 6.2831853072 7.3919827143 18.4799567858 19.6349540849 31.4159265359 39.2699081699 62.8318530718 157.0796326795 196.3495408494 392.6990816987 981.7477042468
aged result J* (ω) [EXP]/[SORTED]
Phase Angle (Rad) [SORTED]/[EXP]
J'
[EXP]
J"
[EXP]
2.66637751283861E-05 2.18754397874874E-05 2.52337910743034E-05 2.41042654104595E-05 1.83641463304151E-05 1.87486641576788E-05 1.78245388049122E-05 1.73353488565604E-05 1.58810824545801E-05 1.44920955280292E-05 1.40069231552182E-05 1.37421658203019E-05
0.3905842988 0.6276607632 0.5177605606 0.574615621 0.6613220208 0.7273817983 0.6905687228 0.6427052265 0.6737792232 0.7582322558 0.6928433952 0.5283175309
2.46556397892751E-05 1.77060563330358E-05 2.19263914070327E-05 2.02331512168468E-05 1.44926351471979E-05 1.4003711838873E-05 1.37406495813269E-05 1.38765528301327E-05 1.24105772673237E-05 0.000010522 1.07773885247722E-05 1.18685093669124E-05
1.01516663991019E-05 1.28464172058731E-05 1.24890981198482E-05 0.000013101 1.1278537003313E-05 1.24662930509128E-05 1.13537981614525E-05 1.0390168503503E-05 9.90890265473229E-06 9.96533072476731E-06 8.94660789697951E-06 6.92716441555913E-06
1.31643961008814E-05 1.26458114753995E-05 1.24101730987491E-05 1.01780894233366E-05 1.02006432525635E-05 0.000009338 9.13458903483932E-06 8.53959539966303E-06 6.60778396951609E-06 7.39407069470991E-06 6.89454992722803E-06 5.60642870491496E-06
0.6905757802 0.768252932 0.7236690188 0.723246242 0.473848696 0.6776710336 0.4383169672 0.6307252294 0.5835610792 0.3638538014 0.3474353633 0.3115683259
1.01481615266392E-05 9.09392890123059E-06 0.0000093 7.63011923365853E-06 9.07672278859806E-06 7.27465954843317E-06 8.27107122752418E-06 6.89657750741661E-06 5.51423400585499E-06 0.00000691 6.48259388748235E-06 5.33650140645065E-06
8.38547209941944E-06 8.78732069579277E-06 8.21725485144198E-06 6.73608081821993E-06 4.65469936569637E-06 5.85476715874593E-06 3.8768669805177E-06 5.03606078936119E-06 3.64088345274416E-06 2.63138981804258E-06 2.34750829370557E-06 1.71866097943854E-06
J'
[MODEL]
aging model J"
unaged [MODEL]
Error
Time
J*(t)
9.68E-06 1.40E-05 1.85E-05 3.11E-05 3.98E-05 6.24E-05 1.98E-05 2.59E-05 3.39E-05 5.33E-05 6.74E-05 1.04E-04
6.24E-06 9.09E-06 1.05E-05 1.76E-05 1.97E-05 3.19E-05 1.09E-05 1.49E-05 1.85E-05 2.70E-05 3.37E-05 5.17E-05
2.78605433 0.24108571 0.07239175 0.18653145 0.58843652 0.97209109 0.09548265 0.30665903 0.61845819 1.04271457 1.24501694 1.53515565
0.00101859 0.00254648 0.00509296 0.02546479 0.05092958 0.25464791 0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943
4.62418E-06 5.72756E-06 6.71245E-06 1.0225E-05 1.21389E-05 1.87659E-05 7.09089E-06 9.05567E-06 1.08042E-05 1.65945E-05 1.98247E-05 3.03142E-05
4.05E-05 5.09E-05 6.37E-05 9.92E-05 1.26E-04 1.92E-04 5.95E-05 7.97E-05 9.41E-05 1.58E-04 1.84E-04 2.80E-04
1.99E-05 2.53E-05 3.24E-05 4.84E-05 6.11E-05 7.29E-05 3.06E-05 3.70E-05 4.48E-05 6.45E-05 6.96E-05 7.41E-05
0.89640284 1.10118308 1.28653514 1.59320374 1.7143215 1.77164914 1.50401267 1.58061111 1.73041562 1.83469633 1.86450491 1.91636499
0.05411268 0.1352817 0.2705634 1.35281702 2.70563403 13.5281702 0.22281692 0.5570423 1.1140846 5.57042301 11.140846 55.7042301
1.23291E-05 1.58655E-05 1.9051E-05 2.89767E-05 3.48896E-05 5.34449E-05 1.81424E-05 2.27442E-05 0.00002744 4.19172E-05 5.06803E-05 7.33285E-05
sum of error =
28.4839789
tau 0.001 0.01 0.1 1 10 100 1000
D unaged Jn
lamda
1.7723124E-06 0.00000367 7.2478539E-06 1.2537254E-05 2.6614094E-05 4.0663105E-05 2.1670644E-05
Z
1000 100 10 1 0.1 0.01 0.001
A
k
3.301562 -2.30156
1
J0 3.0470745E-06
0.001
0.0001
0.00001
0.000001 0.001
0.01
0.1
1
10
100
1000
15
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 172267 138942 129144 103374 88833 63569
12.8515501 14.90658 15.8472872 20.1137123 22.1495304 25.2703648
Actual Temp. (°C)
15
SAMPLE 1 Actual Temp. (°C)
25
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 142037 107802 94789 63578 53503 37837
28.4355869 31.1378937 33.8276901 39.0176506 38.4435081 36.6759071
Actual Temp. (°C)
25
SAMPLE 1 Actual Temp. (°C)
40
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 75250 57579 48393 33102 28454 22713
36.4389572 36.4631805 34.6970024 34.5666733 32.8909607 30.9623127
Actual Temp. (°C)
40
SAMPLE 3
Actual Temp. (°C)
55
Frequency (Hz)
Angle |E*| (Mpa) Phase (Deg)
25 44212.4667 10 31218 5 25935.6 1 19736.4333 0.5 17879.4 0.1 15754.0667
34.5670776 33.6047058 31.824297 27.9230499 24.6654949 17.3788319
Actual Temp. (°C)
55
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
15
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
SAMPLE 3
|E*| (Mpa)
25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
25
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
Frequency (Hz)
Frequency (Hz)
|E*| (Mpa)
25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
40
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3
|E*| (Mpa)
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
Actual Temp. (°C)
Frequency (Hz)
|E*| (Mpa)
25 10 5 1 0.5 0.1
55
1000000
1000000
100000 100000
1000 10000
100 10 1 0.1
1
10
100
1000
log E*
log E*
10000
1000
log frequency ω 100
10
1 0.001
0.
conversion angle in degree = angle in radian *180°/PI() Hz (cycle/sec) = 2*PI() angular freq (rad/s) TOTAL Phase Angle (Deg)
Actual Temp. (°C)
15
Angle θ Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 172266.667 12.851550102 10 138942.1 14.906579971 5 129143.5 15.847287178 1 103374 20.113712311 0.5 88833.0333 22.149530411 0.1 63568.7333 25.270364761
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
25
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 142036.667 28.435586929 10 107801.567 31.137893677 5 94788.8667 33.827690125 1 63577.5667 39.017650604 0.5 53503.1333 38.443508148 0.1 37837.1333 36.675907135
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
40
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 75250.2667 36.438957214 10 57579.0533 36.463180542 5 48393.2667 34.697002411 1 33102.4333 34.566673279 0.5 28453.9333 32.890960693 0.1 22713.3667 30.962312698
TOTAL
Phase Angle (Deg)
Actual Temp. (°C)
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 44212.4667 34.567077637 10 31218 33.604705811 5 25935.6 31.824296951 1 19736.4333 27.923049927 0.5 17879.4 24.665494919 0.1 15754.0667 17.378831863
55
1000000
1
100000
0.1
0.01
1000
log J*
log E*
10000
100
0.0001
10
1 0.001
0.001
0.00001
0.01
0.1
1
10
log frequency ω
100
1000
10000
0.000001 0.001
Phase Angle θ (Rad)
|J*| (1/E*)
0.2243018633 0.2601689007 0.2765873388 0.3510505046 0.3865822334 0.4410510683
0.000005805 7.19724259E-06 7.74332429E-06 9.67361232E-06 1.12570737E-05 0.000015731
Phase Angle (Rad)
|J*| (1/E*)
0.4962946166 0.5434587668 0.590404571 0.6809864694 0.6709657932 0.6401153357
7.04043557E-06 9.27630303E-06 1.05497622E-05 1.57288184E-05 1.86904941E-05 2.64290635E-05
Phase Angle (Rad)
|J*| (1/E*)
0.6359797794 0.6364025562 0.6055769326 0.6033022602 0.5740555582 0.5403943006
0.000013289 1.73674269E-05 0.000020664 3.02092595E-05 3.5144526E-05 4.40269386E-05
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Actual Temp. (°C)
Frequency (ω)
J*
15
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
5.8E-06 7.2E-06 7.7E-06 9.7E-06 1.1E-05 1.6E-05
Actual Temp. (°C)
Frequency (ω)
J*
25
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
7E-06 9.3E-06 1.1E-05 1.6E-05 1.9E-05 2.6E-05
Actual Temp. (°C)
Frequency (ω)
J*
40
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
1.3E-05 1.7E-05 2.1E-05 3E-05 3.5E-05 4.4E-05
Phase Angle (Rad)
|J*| (1/E*)
0.6033093176 0.5865127606 0.5554387639 0.4873491584 0.430494098 0.3033178362
2.26180549E-05 3.20328016E-05 0.000038557 5.06677161E-05 5.59302885E-05 6.3475674E-05
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Actual Temp. (°C)
Frequency (ω)
J*
55
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
2.3E-05 3.2E-05 3.9E-05 5.1E-05 5.6E-05 6.3E-05
1
0.1
log J*
0.01
0.001
0.0001
0.00001
10000
0.000001 0.001
0.01
0.1
1
log frequency ω
10
100
1000
10000
Log (reduced ω) (reduced ω) 3.196119877 2.7981798684 2.4971498727 1.7981798684 1.4971498727 0.7981798684
1570.79633 628.318531 314.159265 62.8318531 31.4159265 6.28318531
Actual Temp. (°C) 15 25 40 55
aT
log (aT) 0.1 -1 1 0 15 1.176091 225 2.352183
15
25
Log (reduced ω) (reduced ω) 2.196119877 1.7981798684 1.4971498727 0.7981798684 0.4971498727 -0.2018201316
157.079633 62.8318531 31.4159265 6.28318531 3.14159265 0.62831853
40
55
Log (reduced ω) (reduced ω) 1.020028618 0.6220886093 0.3210586136 -0.3779113907 -0.6789413864 -1.3779113907
10.4719755 4.1887902 2.0943951 0.41887902 0.20943951 0.0418879
Log (reduced ω) (reduced ω) -0.1560626411 -0.5540026498 -0.8550326454 -1.5540026498 -1.8550326454 -2.5540026498
0.6981317 0.27925268 0.13962634 0.02792527 0.01396263 0.00279253
1
15 25 40 55
0.1
log J*
0.01 0.001
15 25 40 55
0.0001 0.00001 1000
10000
0.000001 0.1
1
10
log frequency ω
100
1000
Frequency (ω) J* (ω) [CALCULATION] [EXP]
Phase Angle θ (Rad) [EXP]
J'
[EXP]
157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
0.000005805 7.19724259242E-06 7.74332428655E-06 9.67361232031E-06 1.12570736637E-05 0.000015731 7.04043556828E-06 9.27630303456E-06 1.05497621732E-05 1.57288183935E-05 1.86904941393E-05 2.64290635126E-05
0.2243018633 0.2601689007 0.2765873388 0.3510505046 0.3865822334 0.4410510683 0.4962946166 0.5434587668 0.590404571 0.6809864694 0.6709657932 0.6401153357
5.65953731568516E-06 0.000006955 0.000007449 9.08363784756019E-06 1.04263359680341E-05 1.42256015602625E-05 0.000006191 7.93982225368962E-06 8.76385120706946E-06 1.22205377801094E-05 1.4638797909155E-05 2.11968192080711E-05
157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
0.000013289 1.73674269046E-05 0.000020664 3.02092595408E-05 3.51445260058E-05 4.40269386162E-05 2.26180549377E-05 3.20328015888E-05 0.000038557 5.06677160514E-05 5.59302884884E-05 6.34756740059E-05
0.6359797794 0.6364025562 0.6055769326 0.6033022602 0.5740555582 0.5403943006 0.6033093176 0.5865127606 0.5554387639 0.4873491584 0.430494098 0.3033178362
1.06908608126649E-05 1.39675610057686E-05 1.69894260087798E-05 2.48763138813546E-05 2.95110534817307E-05 3.77533592065868E-05 1.86251204646853E-05 2.66793448268219E-05 3.27607286801382E-05 4.47688443417948E-05 5.08271901580398E-05 6.05780567839882E-05
15 25 40 55
1000
J"
[EXP]
J'
J"
[MODEL]
[MODEL]
Error
Time
1.29117125527063E-06 1.85144583372375E-06 2.1145027743446E-06 3.32660469218643E-06 4.24419907059311E-06 6.71541122474738E-06 3.35244754882657E-06 4.79677189042242E-06 0.000005873 9.90223128493299E-06 1.16206784201926E-05 1.57857611033318E-05
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
3.36975E-11 5.18003E-11 5.99591E-11 9.35788E-11 1.26722E-10 2.47464E-10 4.95677E-11 8.60498E-11 1.11297E-10 2.47396E-10 3.49335E-10 6.98495E-10
0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943 0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943
7.89320820337851E-06 1.03215675570675E-05 1.1762721326648E-05 1.713967239133E-05 0.000019085 2.26507216779253E-05 1.28328210788949E-05 1.77288729828122E-05 2.03317507643716E-05 2.3726947257533E-05 2.33408207018787E-05 1.8959436351716E-05
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
1.76597E-10 3.01628E-10 4.27002E-10 9.12599E-10 1.23514E-09 1.93837E-09 5.11576E-10 1.0261E-09 1.48665E-09 2.56722E-09 3.1282E-09 4.02916E-09
0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943 0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943
sum of error =
1.98956E-08
J*(t)
tau 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Jn
0.001 0.01 0.1 1 10 100 1000
lamda 1000 100 10 1 0.1 0.01 0.001
J0
SAMPLE 1 Actual Temp. (°C)
15
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 172267 138942 129144 103374 88833 63569
12.8515501 14.90658 15.8472872 20.1137123 22.1495304 25.2703648
Actual Temp. (°C)
15
SAMPLE 1 Actual Temp. (°C)
25
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 142037 107802 94789 63578 53503 37837
28.4355869 31.1378937 33.8276901 39.0176506 38.4435081 36.6759071
Actual Temp. (°C)
25
SAMPLE 1 Actual Temp. (°C)
40
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 75250 57579 48393 33102 28454 22713
36.4389572 36.4631805 34.6970024 34.5666733 32.8909607 30.9623127
Actual Temp. (°C)
40
SAMPLE 1 Actual Temp. (°C)
1000000
Angle |E*| (Mpa) Phase (Deg)
25 44212.4667 10 31218 5 25935.6 1 19736.4333 0.5 17879.4 0.1 15754.0667
Actual Temp. (°C)
34.5670776 33.6047058 31.824297 27.9230499 24.6654949 17.3788319
55
log E*
55
Frequency (Hz)
SAMPLE 3
100000
10000 0.0001
0.001
0.01
0.1
log frequency ω
1
10
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
15
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
|E*| (Mpa)
25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
25
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
Frequency (Hz)
Frequency (Hz)
|E*| (Mpa)
25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
40
Frequency (Hz) 25 10 5 1 0.5 0.1
|E*| (Mpa)
ency ω
SAMPLE 3
SAMPLE 3
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
Actual Temp. (°C)
Frequency (Hz) 25 10 5 1 0.5 0.1
55
1000000 100000
log E*
10000 1000 100 10 1 0.001
0.01
0.1
log frequency ω
1
10
100
1000
1
10
|E*| (Mpa)
conversion angle in degree = angle in radian *180°/PI() Hz (cycle/sec) = 2*PI() angular freq (rad/s) TOTAL Phase Angle (Deg)
Actual Temp. (°C)
15
Angle θ Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 172266.667 10 138942.1 5 129143.5 1 103374 0.5 88833.0333 0.1 63568.7333
12.851550102 14.906579971 15.847287178 20.113712311 22.149530411 25.270364761
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
25
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 142036.667 28.435586929 10 107801.567 31.137893677 5 94788.8667 33.827690125 1 63577.5667 39.017650604 0.5 53503.1333 38.443508148 0.1 37837.1333 36.675907135
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
40
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 75250.2667 36.438957214 10 57579.0533 36.463180542 5 48393.2667 34.697002411 1 33102.4333 34.566673279 0.5 28453.9333 32.890960693 0.1 22713.3667 30.962312698
TOTAL Actual Temp. (°C)
55
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 44212.4667 34.567077637 10 31218 33.604705811 5 25935.6 31.824296951 1 19736.4333 27.923049927 0.5 17879.4 24.665494919 0.1 15754.0667 17.378831863 1
0.1
0.01
log J*
Phase Angle (Deg)
0.001
0.0001
0.00001
0.000001 0.0001
Phase Angle θ (Rad)
|J*| (1/E*)
0.2243018633 0.2601689007 0.2765873388 0.3510505046 0.3865822334 0.4410510683
0.000005805 7.19724259E-06 7.74332429E-06 9.67361232E-06 1.12570737E-05 0.000015731
Phase Angle (Rad)
|J*| (1/E*)
0.4962946166 0.5434587668 0.590404571 0.6809864694 0.6709657932 0.6401153357
7.04043557E-06 9.27630303E-06 1.05497622E-05 1.57288184E-05 1.86904941E-05 2.64290635E-05
Phase Angle (Rad)
|J*| (1/E*)
0.6359797794 0.6364025562 0.6055769326 0.6033022602 0.5740555582 0.5403943006
0.000013289 1.73674269E-05 0.000020664 3.02092595E-05 3.5144526E-05 4.40269386E-05
Time (sec) 0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
Frequency (ω) 0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
Frequency (ω) 0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
Actual Temp. (°C)
Time (sec)
15
0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
Actual Temp. (°C)
Frequency (ω)
25
0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
Actual Temp. (°C)
Frequency (ω)
40
0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
Phase Angle (Rad)
|J*| (1/E*)
0.6033093176 0.5865127606 0.5554387639 0.4873491584 0.430494098 0.3033178362
2.26180549E-05 3.20328016E-05 0.000038557 5.06677161E-05 5.59302885E-05 6.3475674E-05
Frequency (ω)
Actual Temp. (°C)
Frequency (ω)
55
0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
1
0.1
log J*
0.01
0.001
0.0001
0.00001
0.000001 0.0001
0.001
0.01
0.1
1
log time
10
100
J* 0.000005805 7.197243E-06 7.743324E-06 9.673612E-06 1.125707E-05 0.000015731
J* 7.040436E-06 9.276303E-06 1.054976E-05 1.572882E-05 1.869049E-05 2.642906E-05
J* 0.000013289 1.736743E-05 0.000020664 3.020926E-05 3.514453E-05 4.402694E-05
Log (time, sec) -3.196119877 -2.7981798684 -2.4971498727 -1.7981798684 -1.4971498727 -0.7981798684
Log (reduced ω) -2.196119877 -1.7981798684 -1.4971498727 -0.7981798684 -0.4971498727 0.2018201316
Log (reduced ω) -1.0221946797 -0.6242546711 -0.3232246754 0.3757453289 0.6767753246 1.3757453289
(reduced time, sec) 0.0006366198 0.0015915494 0.0031830989 0.0159154943 0.0318309886 0.1591549431
(reduced ω) 0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
(reduced ω) 0.0950178765 0.2375446912 0.4750893824 2.3754469118 4.7508938236 23.7544691182
Actual Temp. (°C) 15 25 40 55
aT
log (aT)
10 1 1 0 0.067 -1.173925 0.0044 -2.356547
J* 2.261805E-05 3.20328E-05 0.000038557 5.066772E-05 5.593029E-05 6.347567E-05
Log (reduced ω) 0.1604274465 0.5583674552 0.8593974508 1.5583674552 1.8593974508 2.5583674552
(reduced ω) 1.446863119 3.6171577975 7.2343155951 36.1715779754 72.3431559509 361.7157797543
1
15 25 40 55
0.1
log J*
0.01 0.001 0.0001 0.00001 10
100
1000
0.000001 0.001
0.01
0.1
log frequency ω
1
10
reduced Time J* (sec) (sec) [EXP] [CALCULATION]
15
25
40
55
Phase Angle θ (Rad) (reduced time, sec) [EXP] [CALCULATION]/[SORTED]
0.0006366198 0.0015915494 0.0031830989 0.0159154943 0.0318309886 0.1591549431 0.0063661977 0.0159154943 0.0318309886 0.1591549431 0.3183098862 1.5915494309
0.000005805 7.19724259242E-06 7.74332428655E-06 9.67361232031E-06 1.12570736637E-05 0.000015731 7.04043556828E-06 9.27630303456E-06 1.05497621732E-05 1.57288183935E-05 1.86904941393E-05 2.64290635126E-05
0.2243018633 0.2601689007 0.2765873388 0.3510505046 0.3865822334 0.4410510683 0.4962946166 0.5434587668 0.590404571 0.6809864694 0.6709657932 0.6401153357
0.0006366198 0.0015915494 0.0031830989 0.0063661977 0.0159154943 0.0159154943 0.0318309886 0.0318309886 0.0950178765 0.1591549431 0.1591549431 0.2375446912
0.0950178765 0.2375446912 0.4750893824 2.3754469118 4.7508938236 23.7544691182 1.446863119 3.6171577975 7.2343155951 36.1715779754 72.3431559509 361.7157797543
0.000013289 1.73674269046E-05 0.000020664 3.02092595408E-05 3.51445260058E-05 4.40269386162E-05 2.26180549377E-05 3.20328015888E-05 0.000038557 5.06677160514E-05 5.59302884884E-05 6.34756740059E-05
0.6359797794 0.6364025562 0.6055769326 0.6033022602 0.5740555582 0.5403943006 0.6033093176 0.5865127606 0.5554387639 0.4873491584 0.430494098 0.3033178362
0.3183098862 0.4750893824 1.446863119 1.5915494309 2.3754469118 3.6171577975 4.7508938236 7.2343155951 23.7544691182 36.1715779754 72.3431559509 361.7157797543
15 25 40 55
0.1
requency ω
1
10
J* (sec) [EXP]/[SORTED]
Phase Angle (Rad) [SORTED]/[EXP]
J'
J"
[EXP]
[EXP]
0.000005805 7.19724259241799E-06 7.74332428654946E-06 7.04043556828049E-06 9.67361232031265E-06 9.27630303455701E-06 1.12570736636634E-05 1.05497621731947E-05 0.000013289 0.000015731 1.57288183934899E-05 1.73674269045526E-05
0.2243018633 0.2601689007 0.2765873388 0.4962946166 0.3510505046 0.5434587668 0.3865822334 0.590404571 0.6359797794 0.4410510683 0.6809864694 0.6364025562
5.65953731568516E-06 0.000006955 0.000007449 0.000006191 9.08363784756019E-06 7.93982225368962E-06 1.04263359680341E-05 8.76385120706946E-06 1.06908608126649E-05 1.42256015602625E-05 1.22205377801094E-05 1.39675610057686E-05
1.29117125527063E-06 1.85144583372375E-06 2.1145027743446E-06 3.35244754882657E-06 3.32660469218643E-06 4.79677189042242E-06 4.24419907059311E-06 0.000005873 7.89320820337851E-06 6.71541122474738E-06 9.90223128493299E-06 1.03215675570675E-05
1.86904941392841E-05 0.000020664 2.26180549377476E-05 2.64290635125635E-05 3.02092595408394E-05 3.2032801588827E-05 3.51445260057778E-05 0.000038557 4.40269386161746E-05 5.06677160513635E-05 5.5930288488428E-05 6.34756740058651E-05
0.6709657932 0.6055769326 0.6033093176 0.6401153357 0.6033022602 0.5865127606 0.5740555582 0.5554387639 0.5403943006 0.4873491584 0.430494098 0.3033178362
1.4638797909155E-05 1.69894260087798E-05 1.86251204646853E-05 2.11968192080711E-05 2.48763138813546E-05 2.66793448268219E-05 2.95110534817307E-05 3.27607286801382E-05 3.77533592065868E-05 4.47688443417948E-05 5.08271901580398E-05 6.05780567839882E-05
1.16206784201926E-05 1.1762721326648E-05 1.28328210788949E-05 1.57857611033318E-05 1.713967239133E-05 1.77288729828122E-05 0.000019085 2.03317507643716E-05 2.26507216779253E-05 2.3726947257533E-05 2.33408207018787E-05 1.8959436351716E-05
0.001
0.0001
0.00001
0.000001 0.001
0.01
0.1
1
10
100
1000
0.00001
0.000001 0.001
0.01
0.1
1
10
100
1000
J'
[MODEL]
J"
[MODEL]
Time
J*(t)
0.0001108073 0.0001006741 9.37303320060384E-05 8.42383431501753E-05 6.5822557074067E-05 6.5822557074067E-05 5.61014963376098E-05 5.61014963376098E-05 0.000042596 3.56566361328499E-05 3.56566361328499E-05 3.16795546567538E-05
1.25733349597594E-05 1.65186226606022E-05 1.88377723397909E-05 2.35153186577283E-05 2.40168117327762E-05 2.40168117327762E-05 2.04223863818031E-05 2.04223863818031E-05 1.90034938628489E-05 1.67376088401388E-05 1.67376088401388E-05 1.4317502310958E-05
421.52562 244.334062 196.713413 195.097017 77.6996132 69.2017317 33.7210488 35.3129567 10.8875674 4.49688754 4.1543115 1.75790911
0.1 10.1 10.2 10.3 10 6.28318531 157.079633 62.8318531 31.4159265 6.28318531 3.14159265 0.62831853
1.45715E-05 4.93189E-05 4.94543E-05 4.95887E-05 4.91825E-05 4.3279E-05 9.02488E-05 7.51284E-05 6.53714E-05 4.3279E-05 3.62334E-05 2.34616E-05
2.95447725550347E-05 2.70966268881988E-05 1.97692396034956E-05 1.9212124286523E-05 1.7283212331609E-05 1.58046880226369E-05 1.49381497750657E-05 1.34682617412943E-05 9.40612824662155E-06 8.58687143219525E-06 7.3576698862398E-06 4.88054690367681E-06
1.28205825133796E-05 1.14867133490324E-05 9.07348577116386E-06 8.76873511401952E-06 7.5030916820982E-06 6.53089251853093E-06 6.16874255151827E-06 5.84645599831823E-06 4.11605534181874E-06 3.53116299016657E-06 3.06948314354812E-06 1.75289721395131E-06
1.04749745 0.35447 0.08959139 0.20636152 0.40927985 0.56509131 0.70187379 0.85437221 1.23336514 1.37767864 1.48571791 1.6689961
10.5243354 4.20973416 2.10486708 0.42097342 0.21048671 0.04209734 0.69115038 0.27646015 0.13823008 0.02764602 0.01382301 0.0027646
4.98865E-05 0.000039 3.26909E-05 2.12144E-05 1.78781E-05 1.15719E-05 2.40585E-05 1.91528E-05 1.59611E-05 1.0436E-05 8.71873E-06 5.83495E-06
sum of error =
100
Error
1000
1304.89643
τn 0.001 0.01 0.1 1 10 100 1000
100
1000
Dn 1.77E-06 0.00000367 7.24785385E-06 1.25372543E-05 2.66140939E-05 4.06631052E-05 2.16706441E-05
λn 1000 100 10 1 0.1 0.01 0.001
J0 3.04707448E-06
t
w 10
0.1
SAMPLE 1 Actual Temp. (°C)
15
Frequency (Hz)
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg)
25 10 5 1 0.5 0.1
Actual Temp. (°C)
15
SAMPLE 1 Actual Temp. (°C)
25
Frequency (Hz)
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg)
25 10 5 1 0.5 0.1
Actual Temp. (°C)
25
SAMPLE 1 Actual Temp. (°C)
40
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg)
Actual Temp. (°C)
40
SAMPLE 3
Actual Temp. (°C)
55
Frequency (Hz) 25 10 5 1 0.5 0.1
Angle |E*| (Mpa) Phase (Deg)
Actual Temp. (°C)
55
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 172366.67 17.8515501 10 139042.1 19.90657997 5 129243.5 20.84728718 1 103474 25.11371231 0.5 89033.033 27.14953041 0.1 63768.733 30.27036476
SAMPLE 3 Actual Temp. (°C)
15
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 142336.67 33.43558693 10 108101.57 36.13789368 5 95088.867 38.82769013 1 64077.567 44.0176506 0.5 54003.133 43.44350815 0.1 38337.133 41.67590714
SAMPLE 3
|E*| (Mpa)
25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
25
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 76250.267 41.43895721 10 58579.053 41.46318054 5 49393.267 39.69700241 1 34102.433 39.56667328 0.5 29453.933 37.89096069 0.1 23713.367 35.9623127
Frequency (Hz)
Frequency (Hz)
|E*| (Mpa)
25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
40
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3
|E*| (Mpa)
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 45462.467 39.56707764 10 32468 38.60470581 5 27185.6 36.82429695 1 20986.433 32.92304993 0.5 19129.4 29.66549492 0.1 17004.067 22.37883186
Actual Temp. (°C)
55
Frequency (Hz) 25 10 5 1 0.5 0.1
|E*| (Mpa)
conversion angle in degree = angle in radian *180°/PI() Hz (cycle/sec) = 2*PI() angular freq (rad/s) TOTAL Phase Angle (Deg)
Actual Temp. (°C)
15
Angle θ Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 172366.667 17.851550102 10 139042.1 19.906579971 5 129243.5 20.847287178 1 103474 25.113712311 0.5 89033.0333 27.149530411 0.1 63768.7333 30.270364761
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
25
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 142336.667 33.435586929 10 108101.567 36.137893677 5 95088.8667 38.827690125 1 64077.5667 44.017650604 0.5 54003.1333 43.443508148 0.1 38337.1333 41.675907135
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
40
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 76250.2667 41.438957214 10 58579.0533 41.463180542 5 49393.2667 39.697002411 1 34102.4333 39.566673279 0.5 29453.9333 37.890960693 0.1 23713.3667 35.962312698
TOTAL
Phase Angle (Deg)
Actual Temp. (°C)
55
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 45462.4667 39.567077637 10 32468 38.604705811 5 27185.6 36.824296951 1 20986.4333 32.923049927 0.5 19129.4 29.665494919 0.1 17004.0667 22.378831863
1000000 100000
log E*
10000 1000 100 10 1 0.1
1
10
log frequency ω
100
1000
Phase Angle θ (Rad)
|J*| (1/E*)
0.3115683259 0.3474353633 0.3638538014 0.4383169672 0.473848696 0.5283175309
5.80158577E-06 7.19206629E-06 7.73733302E-06 9.66426349E-06 1.12317863E-05 1.56816664E-05
Phase Angle (Rad)
|J*| (1/E*)
0.5835610792 0.6307252294 0.6776710336 0.768252932 0.7582322558 0.7273817983
7.02559659E-06 9.25055974E-06 1.05164783E-05 1.56060857E-05 1.8517444E-05 2.60843708E-05
Phase Angle (Rad)
|J*| (1/E*)
0.723246242 0.7236690188 0.6928433952 0.6905687228 0.6613220208 0.6276607632
1.31147082E-05 1.70709485E-05 2.02456745E-05 2.93234207E-05 3.39513229E-05 4.2170309E-05
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Actual Temp. (°C)
Frequency (ω)
J*
15
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
5.8E-06 7.2E-06 7.7E-06 9.7E-06 1.1E-05 1.6E-05
Actual Temp. (°C)
Frequency (ω)
J*
25
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
7E-06 9.3E-06 1.1E-05 1.6E-05 1.9E-05 2.6E-05
Actual Temp. (°C)
Frequency (ω)
J*
40
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
1.3E-05 1.7E-05 2E-05 2.9E-05 3.4E-05 4.2E-05
Phase Angle (Rad)
|J*| (1/E*)
0.6905757802 0.6737792232 0.6427052265 0.574615621 0.5177605606 0.3905842988
2.19961668E-05 3.07995565E-05 3.67841799E-05 4.76498309E-05 5.22755549E-05 5.88094613E-05
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Actual Temp. (°C)
Frequency (ω)
J*
55
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
2.2E-05 3.1E-05 3.7E-05 4.8E-05 5.2E-05 5.9E-05
Log (reduced ω) (reduced ω) #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
Actual Temp. (°C)
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
aT
log (aT)
15 25 40 55
Err:502 Err:502 Err:502 Err:502
15
25
1 0.1
Log (reduced ω) (reduced ω) #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
log J*
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
0.01 0.001
40
0.0001 0.00001 0.000001 0.1
1
10
log frequency ω
Log (reduced ω) (reduced ω) #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
100
55
1000
Log (reduced ω) (reduced ω) #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
Frequency (ω) J* (ω) [CALCULATION] [EXP]
Phase Angle θ (Rad) [EXP]
J'
[EXP]
157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
5.80158576678E-06 7.19206628784E-06 7.73733301868E-06 9.66426348648E-06 1.12317862546E-05 1.56816663548E-05 7.02559659024E-06 9.25055973595E-06 1.05164782698E-05 1.56060857492E-05 1.85174440495E-05 2.60843707667E-05
0.3115683259 0.3474353633 0.3638538014 0.4383169672 0.473848696 0.5283175309 0.5835610792 0.6307252294 0.6776710336 0.768252932 0.7582322558 0.7273817983
5.52226243007492E-06 6.76233335721773E-06 7.23078748452949E-06 8.75067409747359E-06 9.99425308088338E-06 1.35435714030964E-05 5.86290105851906E-06 7.47075232727044E-06 8.19270513716874E-06 1.12227384146764E-05 1.34446405171975E-05 1.94828820146058E-05
157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307 157.0796326795 100 62.8318530718 1000 31.4159265359 6.2831853072 3.1415926536 0.6283185307
1.31147082327E-05 1.70709484551E-05 2.02456745116E-05 2.93234207139E-05 3.39513228567E-05 4.217030901E-05 2.19961668013E-05 3.07995564864E-05 3.67841798599E-05 4.76498309225E-05 5.2275554905E-05 5.88094612661E-05
0.723246242 0.7236690188 0.6928433952 0.6905687228 0.6613220208 0.6276607632 0.6905757802 0.6737792232 0.6427052265 0.574615621 0.5177605606 0.3905842988
9.83158855932412E-06 1.27926509029902E-05 1.55776895282488E-05 0.000022605 2.67937385203732E-05 3.41327934051E-05 1.69563914634771E-05 2.40689056723185E-05 2.94449000918833E-05 3.99973290243522E-05 4.54237841033102E-05 5.43803300994444E-05
J"
[EXP]
J'
J"
[MODEL]
Error
[MODEL]
Time
1.77848673389589E-06 2.44880890526303E-06 2.75354945398757E-06 4.10166936452824E-06 5.1252246608913E-06 7.90482974590439E-06 3.87109785808383E-06 5.45533821985403E-06 6.59362553794228E-06 1.08443559000565E-05 1.27333175367333E-05 1.73439242013125E-05
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943 0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943
8.67959897860457E-06 1.13033341996867E-05 1.2931470349221E-05 1.86783065656021E-05 2.08515682820837E-05 2.4764639637211E-05 1.40111435111252E-05 1.92171917692246E-05 2.20470802272406E-05 2.58982636070863E-05 0.000025873 2.23904540527371E-05
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943 0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943
sum of error =
#DIV/0!
J*(t)
tau 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Jn
0.001 0.01 0.1 1 10 100 1000
lamda 1000 100 10 1 0.1 0.01 0.001
J0
SAMPLE 1 Actual Temp. (°C)
15
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 178367 145042 135244 109474 98033 72769
17.8515501 19.90658 20.8472872 25.1137123 27.1495304 30.2703648
Actual Temp. (°C)
15
SAMPLE 1 Actual Temp. (°C)
25
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 151337 117102 107089 79078 69003 53337
33.4355869 36.1378937 38.8276901 44.0176506 43.4435081 41.6759071
Actual Temp. (°C)
25
SAMPLE 1 Actual Temp. (°C)
40
Frequency (Hz) 25 10 5 1 0.5 0.1
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg) 98250 80579 71393 56102 54454 45713
41.4389572 41.4631805 39.6970024 39.5666733 37.8909607 35.9623127
Actual Temp. (°C)
40
SAMPLE 1 Actual Temp. (°C)
55
Frequency (Hz)
SAMPLE 3 Angle |E*| (Mpa) Phase (Deg)
25 78462.4667 10 65468 5 60185.6 1 43986.4333 0.5 42129.4 0.1 40004.0667
39.5670776 38.6047058 36.824297 32.9230499 29.6654949 22.3788319
Actual Temp. (°C)
55
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
15
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
|E*| (Mpa)
25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
25
SAMPLE 3 Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 10 5 1 0.5 0.1
Frequency (Hz)
Frequency (Hz)
|E*| (Mpa)
25 10 5 1 0.5 0.1
SAMPLE 3 Actual Temp. (°C)
40
Frequency (Hz) 25 10 5 1 0.5 0.1
|E*| (Mpa)
SAMPLE 3
SAMPLE 3
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 73462 10 60468 5 55186 1 38986 0.5 37129 0.1 35004
Actual Temp. (°C)
Frequency (Hz) 25 10 5 1 0.5 0.1
55
1000000 100000
log E*
10000 1000 100 10 1 0.1
1
10
log frequency ω
100
1000
|E*| (Mpa)
conversion angle in degree = angle in radian *180°/PI() Hz (cycle/sec) = 2*PI() angular freq (rad/s) TOTAL Phase Angle (Deg)
Actual Temp. (°C)
15
Angle θ Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 178366.667 10 145042.1 5 135243.5 1 109474 0.5 98033.0333 0.1 72768.7333
17.851550102 19.906579971 20.847287178 25.113712311 27.149530411 30.270364761
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
25
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 151336.667 33.435586929 10 117101.567 36.137893677 5 107088.867 38.827690125 1 79077.5667 44.017650604 0.5 69003.1333 43.443508148 0.1 53337.1333 41.675907135
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
40
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 98250.2667 41.438957214 10 80579.0533 41.463180542 5 71393.2667 39.697002411 1 56102.4333 39.566673279 0.5 54453.9333 37.890960693 0.1 45713.3667 35.962312698
TOTAL Phase Angle (Deg)
Actual Temp. (°C)
55
Angle Frequency (Hz) |E*| (Mpa) Phase (Deg) 25 75962.4667 39.567077637 10 62968 38.604705811 5 57685.6 36.824296951 1 41486.4333 32.923049927 0.5 39629.4 29.665494919 0.1 37504.0667 22.378831863
Phase Angle θ (Rad)
|J*| (1/E*)
0.3115683259 0.3474353633 0.3638538014 0.4383169672 0.473848696 0.5283175309
5.6064287E-06 6.89454993E-06 7.39407069E-06 9.13458903E-06 1.02006433E-05 1.37421658E-05
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Actual Temp. (°C)
Frequency (ω)
J*
15
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
5.6E-06 6.9E-06 7.4E-06 9.1E-06 1E-05 1.4E-05
1000000
|J*| (1/E*)
0.5835610792 0.6307252294 0.6776710336 0.768252932 0.7582322558 0.7273817983
6.60778397E-06 8.5395954E-06 0.000009338 1.26458115E-05 1.44920955E-05 1.87486642E-05
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
Actual Temp. (°C)
Frequency (ω)
J*
25
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
6.6E-06 8.5E-06 9.3E-06 1.3E-05 1.4E-05 1.9E-05
log E*
Phase Angle (Rad)
|J*| (1/E*)
0.723246242 0.7236690188 0.6928433952 0.6905687228 0.6613220208 0.6276607632
1.01780894E-05 1.24101731E-05 1.40069232E-05 1.78245388E-05 1.83641463E-05 2.18754398E-05
Frequency (ω)
Actual Temp. (°C)
Frequency (ω)
400.1
157.07963268 62.831853072 31.415926536 6.2831853072 10000 0.01 3.1415926536 0.6283185307
1
157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
0.01
log J*
Phase Angle (Rad)
100000
0.001
0.0001
J* 1E-05 1.2E-05 1.4E-05 1.8E-05 1.8E-05 0.1 2.2E-05
1
lo
log J*
Phase Angle (Rad)
|J*| (1/E*)
0.6905757802 0.6737792232 0.6427052265 0.574615621 0.5177605606 0.3905842988
1.31643961E-05 1.58810825E-05 1.73353489E-05 2.41042654E-05 2.52337911E-05 2.66637751E-05
Frequency (ω) 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
0.001
Actual Temp. (°C)
Frequency (ω)
J*
55 0.00001
157.07963268 62.831853072 31.415926536 6.2831853072 3.1415926536 0.6283185307
1.3E-05 1.6E-05 1.7E-05 2.4E-05 2.5E-05 2.7E-05
0.0001
0.000001 0.01
0.1
1
log freq
Actual Temp. (°C)
Log (reduced ω) (reduced ω) 2.9919998944 2.5940598857 2.29302989 1.5940598857 1.29302989 0.5940598857
981.747704 392.699082 196.349541 39.2699082 19.6349541 3.92699082
15 25 40 55
aT
log (aT)
0.16 -0.79588 1 0 8.5 0.929419 35 1.544068
15
25
Log (reduced ω) (reduced ω) 2.196119877 1.7981798684 1.4971498727 0.7981798684 0.4971498727 -0.2018201316
157.079633 62.8318531 31.4159265 6.28318531 3.14159265 0.62831853
40
55
Log (reduced ω) (reduced ω) 1.2667009513 18.4799568 0.8687609426 7.39198271 0.567730947 3.69599136 -0.1312390574 0.73919827 0.1-0.432269053 0.36959914 1 -1.1312390574 log 0.07391983 frequency ω
10
100
1000
15 25 40 55
15 25 40 55
Log (reduced ω) (reduced ω) 0.6520518327 0.254111824 -0.0469181717 -0.745888176 -1.0469181717 -1.745888176 1
10
100
1000
log frequency ω
1 0.1 0.01
log J*
0.1
4.48798951 1.7951958 0.8975979 0.17951958 0.08975979 0.01795196
0.001
15 25 40 55
0.0001 0.00001 0.000001 0.1
1
10
log frequency ω
100
1000
reduced Frequency (ω) J* (ω) [EXP] [CALCULATION]
Phase Angle θ (Rad) (reduced ω) [EXP] [CALCULATION]/[SORTED]
981.7477042468 392.6990816987 196.3495408494 39.2699081699 19.6349540849 3.926990817 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
5.60642870491E-06 6.89454992723E-06 7.39407069471E-06 9.13458903484E-06 1.02006432526E-05 1.37421658203E-05 6.60778396952E-06 8.53959539966E-06 0.000009338 1.26458114754E-05 1.4492095528E-05 1.87486641577E-05
0.3115683259 0.3474353633 0.3638538014 0.4383169672 0.473848696 0.5283175309 0.5835610792 0.6307252294 0.6776710336 0.768252932 0.7582322558 0.7273817983
0.017951958 0.0739198271 0.0897597901 0.1795195802 0.3695991357 0.6283185307 0.7391982714 0.897597901 1.7951958021 3.1415926536 3.6959913572 3.926990817
18.4799567858 7.3919827143 3.6959913572 0.7391982714 0.3695991357 0.0739198271 4.4879895051 1.7951958021 0.897597901 0.1795195802 0.0897597901 0.017951958
1.01780894233E-05 1.24101730987E-05 1.40069231552E-05 1.78245388049E-05 1.83641463304E-05 2.18754397875E-05 1.31643961009E-05 1.58810824546E-05 1.73353488566E-05 2.41042654105E-05 2.52337910743E-05 2.66637751284E-05
0.723246242 0.7236690188 0.6928433952 0.6905687228 0.6613220208 0.6276607632 0.6905757802 0.6737792232 0.6427052265 0.574615621 0.5177605606 0.3905842988
4.4879895051 6.2831853072 7.3919827143 18.4799567858 19.6349540849 31.4159265359 39.2699081699 62.8318530718 157.0796326795 196.3495408494 392.6990816987 981.7477042468
15 25 40 55
1000
J* (ω) [EXP]/[SORTED]
Phase Angle (Rad) [SORTED]/[EXP]
J'
[EXP]
J"
[EXP]
2.66637751283861E-05 2.18754397874874E-05 2.52337910743034E-05 2.41042654104595E-05 1.83641463304151E-05 1.87486641576788E-05 1.78245388049122E-05 1.73353488565604E-05 1.58810824545801E-05 1.44920955280292E-05 1.40069231552182E-05 1.37421658203019E-05
0.3905842988 0.6276607632 0.5177605606 0.574615621 0.6613220208 0.7273817983 0.6905687228 0.6427052265 0.6737792232 0.7582322558 0.6928433952 0.5283175309
2.46556397892751E-05 1.77060563330358E-05 2.19263914070327E-05 2.02331512168468E-05 1.44926351471979E-05 1.4003711838873E-05 1.37406495813269E-05 1.38765528301327E-05 1.24105772673237E-05 0.000010522 1.07773885247722E-05 1.18685093669124E-05
1.01516663991019E-05 1.28464172058731E-05 1.24890981198482E-05 0.000013101 1.1278537003313E-05 1.24662930509128E-05 1.13537981614525E-05 1.0390168503503E-05 9.90890265473229E-06 9.96533072476731E-06 8.94660789697952E-06 6.92716441555913E-06
1.31643961008814E-05 1.26458114753995E-05 1.24101730987491E-05 1.01780894233366E-05 1.02006432525635E-05 0.000009338 9.13458903483932E-06 8.53959539966303E-06 6.60778396951609E-06 7.39407069470991E-06 6.89454992722803E-06 5.60642870491496E-06
0.6905757802 0.768252932 0.7236690188 0.723246242 0.473848696 0.6776710336 0.4383169672 0.6307252294 0.5835610792 0.3638538014 0.3474353633 0.3115683259
1.01481615266392E-05 9.09392890123059E-06 0.0000093 7.63011923365853E-06 9.07672278859806E-06 7.27465954843317E-06 8.27107122752418E-06 6.89657750741661E-06 5.51423400585499E-06 0.00000691 6.48259388748235E-06 5.33650140645065E-06
8.38547209941944E-06 8.78732069579277E-06 8.21725485144198E-06 6.73608081821993E-06 4.65469936569637E-06 5.85476715874593E-06 3.8768669805177E-06 5.03606078936119E-06 3.64088345274416E-06 2.63138981804258E-06 2.34750829370557E-06 1.71866097943854E-06
J'
[MODEL]
J"
[MODEL]
Error
Time
J*(t)
3.59439339402798E-05 3.07900769722348E-05 2.94123257823711E-05 2.45904821555202E-05 2.13185851019507E-05 1.91724139493902E-05 1.84186112057225E-05 0.000017466 1.42853528257307E-05 1.26032377856081E-05 1.22155905653184E-05 1.20742810926395E-05
1.1087289211475E-05 0.000009689 9.75708010908519E-06 8.70650636515078E-06 7.26989978733592E-06 6.9998875980441E-06 6.95605442289078E-06 6.85440111200218E-06 5.804074769199E-06 4.81786382421652E-06 4.6312674150516E-06 4.57514274109774E-06
0.21811012 0.60646713 0.16441473 0.15889149 0.34816033 0.32850897 0.26593388 0.18271428 0.19442844 0.30593416 0.2504634 0.11558529
0.00101859 0.00254648 0.00509296 0.02546479 0.05092958 0.25464791 0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943
2.96037E-06 4.33257E-06 5.26344E-06 8.08719E-06 9.51751E-06 1.42804E-05 5.58171E-06 7.17381E-06 8.52749E-06 1.27415E-05 1.50186E-05 2.19395E-05
1.1762339799721E-05 1.09244858997578E-05 1.04789491378617E-05 7.99287837112937E-06 7.86638693295366E-06 7.07149144964196E-06 6.76135464981087E-06 6.08505449137286E-06 4.55975192536632E-06 4.25188577516009E-06 3.48673387888492E-06 2.22280489105947E-06
0.000004475 4.32216261477562E-06 4.26352216452159E-06 3.45258408175524E-06 3.37851271311549E-06 2.89443748275898E-06 2.752885438891E-06 2.61826183545141E-06 2.30944373960301E-06 2.18505922067755E-06 1.96684802389336E-06 1.92494667745243E-06
0.24277069 0.2987221 0.24757715 0.239867 0.092951 0.25643888 0.11737076 0.2443397 0.1636918 0.17674602 0.23986679 0.35484548
0.05411268 0.1352817 0.2705634 1.35281702 2.70563403 13.5281702 0.22281692 0.5570423 1.1140846 5.57042301 11.140846 55.7042301
9.65684E-06 1.22189E-05 0.00001448 2.10989E-05 2.46711E-05 3.42173E-05 1.38416E-05 1.7012E-05 2.01145E-05 2.84364E-05 3.2851E-05 4.40645E-05
sum of error =
5.81479958
tau 0.001 0.01 0.1 1 10 100 1000
Jn
lamda
3.08E-06 3.15E-06 5.37E-06 9.22E-06 1.45E-05 0 0.000151
1000 100 10 1 0.1 0.01 0.001
J0 6.2E-07
Chart Title 1 0.1 0.01 0.001 0.0001 0.00001 0.000001 0.001
0.01
0.1
1
10
100
aged result Frequency (ω) J* (ω) [CALCULATION] [EXP]
15
25
40
55
Phase Angle θ (Rad) (reduced ω) [EXP] [CALCULATION]/[SORTED]
981.7477042468 392.6990816987 196.3495408494 39.2699081699 19.6349540849 3.926990817 157.0796326795 62.8318530718 31.4159265359 6.2831853072 3.1415926536 0.6283185307
5.60642870491E-06 6.89454992723E-06 7.39407069471E-06 9.13458903484E-06 1.02006432526E-05 1.37421658203E-05 6.60778396952E-06 8.53959539966E-06 0.000009338 1.26458114754E-05 1.4492095528E-05 1.87486641577E-05
0.3115683259 0.3474353633 0.3638538014 0.4383169672 0.473848696 0.5283175309 0.5835610792 0.6307252294 0.6776710336 0.768252932 0.7582322558 0.7273817983
0.017951958 0.0739198271 0.0897597901 0.1795195802 0.3695991357 0.6283185307 0.7391982714 0.897597901 1.7951958021 3.1415926536 3.6959913572 3.926990817
18.4799567858 7.3919827143 3.6959913572 0.7391982714 0.3695991357 0.0739198271 4.4879895051 1.7951958021 0.897597901 0.1795195802 0.0897597901 0.017951958
1.01780894233E-05 1.24101730987E-05 1.40069231552E-05 1.78245388049E-05 1.83641463304E-05 2.18754397875E-05 1.31643961009E-05 1.58810824546E-05 1.73353488566E-05 2.41042654105E-05 2.52337910743E-05 2.66637751284E-05
0.723246242 0.7236690188 0.6928433952 0.6905687228 0.6613220208 0.6276607632 0.6905757802 0.6737792232 0.6427052265 0.574615621 0.5177605606 0.3905842988
4.4879895051 6.2831853072 7.3919827143 18.4799567858 19.6349540849 31.4159265359 39.2699081699 62.8318530718 157.0796326795 196.3495408494 392.6990816987 981.7477042468
aged result J* (ω) [EXP]/[SORTED]
Phase Angle (Rad) [SORTED]/[EXP]
J'
[EXP]
J"
[EXP]
2.66637751283861E-05 2.18754397874874E-05 2.52337910743034E-05 2.41042654104595E-05 1.83641463304151E-05 1.87486641576788E-05 1.78245388049122E-05 1.73353488565604E-05 1.58810824545801E-05 1.44920955280292E-05 1.40069231552182E-05 1.37421658203019E-05
0.3905842988 0.6276607632 0.5177605606 0.574615621 0.6613220208 0.7273817983 0.6905687228 0.6427052265 0.6737792232 0.7582322558 0.6928433952 0.5283175309
2.46556397892751E-05 1.77060563330358E-05 2.19263914070327E-05 2.02331512168468E-05 1.44926351471979E-05 1.4003711838873E-05 1.37406495813269E-05 1.38765528301327E-05 1.24105772673237E-05 0.000010522 1.07773885247722E-05 1.18685093669124E-05
1.01516663991019E-05 1.28464172058731E-05 1.24890981198482E-05 0.000013101 1.1278537003313E-05 1.24662930509128E-05 1.13537981614525E-05 1.0390168503503E-05 9.90890265473229E-06 9.96533072476731E-06 8.94660789697951E-06 6.92716441555913E-06
1.31643961008814E-05 1.26458114753995E-05 1.24101730987491E-05 1.01780894233366E-05 1.02006432525635E-05 0.000009338 9.13458903483932E-06 8.53959539966303E-06 6.60778396951609E-06 7.39407069470991E-06 6.89454992722803E-06 5.60642870491496E-06
0.6905757802 0.768252932 0.7236690188 0.723246242 0.473848696 0.6776710336 0.4383169672 0.6307252294 0.5835610792 0.3638538014 0.3474353633 0.3115683259
1.01481615266392E-05 9.09392890123059E-06 0.0000093 7.63011923365853E-06 9.07672278859806E-06 7.27465954843317E-06 8.27107122752418E-06 6.89657750741661E-06 5.51423400585499E-06 0.00000691 6.48259388748235E-06 5.33650140645065E-06
8.38547209941944E-06 8.78732069579277E-06 8.21725485144198E-06 6.73608081821993E-06 4.65469936569637E-06 5.85476715874593E-06 3.8768669805177E-06 5.03606078936119E-06 3.64088345274416E-06 2.63138981804258E-06 2.34750829370557E-06 1.71866097943854E-06
J'
[MODEL]
aging model J"
unaged [MODEL]
Error
Time
J*(t)
9.68E-06 1.40E-05 1.85E-05 3.11E-05 3.98E-05 6.24E-05 1.98E-05 2.59E-05 3.39E-05 5.33E-05 6.74E-05 1.04E-04
6.24E-06 9.09E-06 1.05E-05 1.76E-05 1.97E-05 3.19E-05 1.09E-05 1.49E-05 1.85E-05 2.70E-05 3.37E-05 5.17E-05
2.78605433 0.24108571 0.07239175 0.18653145 0.58843652 0.97209109 0.09548265 0.30665903 0.61845819 1.04271457 1.24501694 1.53515565
0.00101859 0.00254648 0.00509296 0.02546479 0.05092958 0.25464791 0.0063662 0.01591549 0.03183099 0.15915494 0.31830989 1.59154943
4.62418E-06 5.72756E-06 6.71245E-06 1.0225E-05 1.21389E-05 1.87659E-05 7.09089E-06 9.05567E-06 1.08042E-05 1.65945E-05 1.98247E-05 3.03142E-05
4.05E-05 5.09E-05 6.37E-05 9.92E-05 1.26E-04 1.92E-04 5.95E-05 7.97E-05 9.41E-05 1.58E-04 1.84E-04 2.80E-04
1.99E-05 2.53E-05 3.24E-05 4.84E-05 6.11E-05 7.29E-05 3.06E-05 3.70E-05 4.48E-05 6.45E-05 6.96E-05 7.41E-05
0.89640284 1.10118308 1.28653514 1.59320374 1.7143215 1.77164914 1.50401267 1.58061111 1.73041562 1.83469633 1.86450491 1.91636499
0.05411268 0.1352817 0.2705634 1.35281702 2.70563403 13.5281702 0.22281692 0.5570423 1.1140846 5.57042301 11.140846 55.7042301
1.23291E-05 1.58655E-05 1.9051E-05 2.89767E-05 3.48896E-05 5.34449E-05 1.81424E-05 2.27442E-05 0.00002744 4.19172E-05 5.06803E-05 7.33285E-05
sum of error =
28.4839789
tau 0.001 0.01 0.1 1 10 100 1000
D unaged Jn
lamda
1.7723124E-06 0.00000367 7.2478539E-06 1.2537254E-05 2.6614094E-05 4.0663105E-05 2.1670644E-05
Z
1000 100 10 1 0.1 0.01 0.001
A
k
3.301562 -2.30156
1
J0 3.0470745E-06
0.001
0.0001
0.00001
0.000001 0.001
0.01
0.1
1
10
100
1000
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