53126-mt----stress Analysis & Vibration

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Code No: 53126/MT M.Tech. – I Semester Supplementary Examinations, September, 2008 STRESS ANALYSIS & VIBRATION (CAD/CAM) Time: 3hours

Max. Marks:60 Answer any FIVE questions All questions carry equal marks ---

1.a) b)

2.a) b)

Define the plane stress and plane strain problems with suitable examples. Investigate what problem of plane stress is solved by the stress 3F  xy − xy 3  p 2 function φ =  + y . 4c  3c 2  2 Show clearly the stress distribution and sketch of the structural member. Briefly explain the contact stresses A hollow rectangular thin wall steel torsion member has the c/s shown in fig below. The steel has a yield stress of 360Mpa and G = 77.5 Gpa. Determine the maximum torque that may be applied to the torsion member based on a factor of safety of 2.00 for the octahedral shearing stress criterion of failure. What is the unit angle of twist when the maximum torque is applied?

Contd…2.,

Code No: 53126/M

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3.

In a single degree damped vibration system, a suspended mass of 8kg. Makes 30 oscillations in 18 sec. The amplitude decreases to ¼ of its initial value after 5 cycles. Find a) Stiffness of spring b) Logarithmic decrement c) damping factor d) damping coefficient

4.a)

A cylinder of mass ‘m’ and radius ‘r’ rolls without slipping on a cylindrical surface of radius ‘R’. Find the natural frequency. A vibration pick up has a natural frequency of 6Hz and damping factor 0.6. What is the lowest frequency beyond which the amplitude can be measured with 1% error.

b)

5.

Find the natural frequencies and mode shapes of a double pendulum. Mass of each pendulum is ‘m’ and length of each pendilum is l.

6.a) b)

What is the principle of an undamped vibration absorber. A section of pipe pertaining to a certain machine vibrates with large amplitude at a compressor speed of 200 rpm. For analyzing this system, a spring mass system was suspended from the pipe to act as an absorber. A 1 kg absorber mass tuned to 200 cpm resulted in two resonant frequencies of 180 cpm and 240 cpm. What must be the mass and spring stiffness of the absorber if the resonant frequencies are to lie outside the range of 150 and 300 cpm?

7.

Using matrix iteration method, find the natural frequencies of the system shown in figure (equal masses are equally spaced on strings)

8.

A bar fixed at one end is pulled at the other end with a force P. The force is suddenly released. Investigate the vibration of the bar.