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MAE 456 David Walton Thomas Price 10-01-2007 Assignment #3
Introduction Assignment 3 of MAE 456 is accomplished by creating a 3 dimensional piping system subject to an internalized pressure. The 3-D model is created and analyzed in Ansys through the modal and harmonic methods available in the program. The piping system is capped off on each end and subjected to an internalized pressure of 1,000 psi. The first section of this design problem is to analyze the pipe with just the internalized pressure. A modal analysis is completed and images from the first three frequency modes are displayed in the report. The second part of this design problem is to examine the harmonic motion of the pipe system with a vertical excitation of .01 units of displacement and frequency range between 0 and 500 hertz. Isometric View The first figure is an isometric view of the piping system to be analyzed. The only affects on the system are the meshing and dimensions of the pipe.
Figure 1: Isometric view of piping system before any analysis
Internalized Pressure This image is a view of the system with an applied internal pressure of 1,000 psi. This is before the modal analysis is conducted and so the only source for the stress in the pipe is from the internalized pressure and not from the natural frequencies.
Figure 2: Piping system with internalized pressure of 1,000 psi.
The 12 natural frequencies This table shows the 12 natural frequencies of the pipe system. These natural frequencies occur as the name implies: naturally. It is of no consequence whether the internal pressure is figured into the analysis because it changes nothing. The 12 frequencies shown will occur under the natural conditions of the system.
Figure 3: Table of the 12 natural frequencies of the pipe system
Mode 1 The next image displays the system after the first natural frequency. The frequency has a value of 42.35 hz. The highest stress concentration is in the center of the pipe because both ends are fixed, creating the greatest deflection in the middle of the beam.
Figure 4: Modal analysis of the system during the first natural frequency.
Mode 2 The second mode of the natural frequency has more twist and a much higher deflection than the first mode. The frequency is 61.919 hz.
Figure 5: Modal analysis during the second natural frequency of the system
Mode 3
The final mode displayed in the report is for the 3rd mode of natural frequency. The twist and deflection of the system is still increasing under the natural frequencies. However, the change between the second and third mode is not nearly as significant as the change from the first natural frequency to the second one.
Figure 6: The 3rd mode of the natural frequency
Harmonic Analysis
The graph below illustrates the harmonic frequencies of the first 12 modes. The maximum displacement occurs at 200 hertz. This graph is produced from Ansys after a vertical excitation is produced on one end of the pipe system.
Figure 7: Harmonic frequencies of first 12 modes
Results The internal pressure that is applied to the pipe has no effect on the natural frequencies of the system. Doing the analysis with and without the internal pressure of 1,000 psi made no impact on the design. Figure 7 shows that the most important frequencies are at 100, 200, and 375 hertz. The frequency causing the most displacement is at 200 hertz, which is almost seven times greater than the displacement at 100 hertz. Looking at figures 4, and 5 the greatest displacement is located in the center portion of the pipe. Figure 6 further refines the ultimate stress location as being in the first bend of the middle section of pipe. A brace should be placed in the center of the pipe and would greatly reduce the vibrations of the pipe and help to steady the entire system. A brace would be very simple to add into the design and would greatly help to support the piping system. The brace should be made of steel just like the pipe to adequately sustain the piping system. After completing this design process Ansys has allowed for a greater understanding of how modal and harmonic analysis are used in determining how natural vibrations affect a structure.
Introduction Assignment 3 of MAE 456 is accomplished by creating a 3 dimensional piping system subject to an internalized pressure. The 3-D model is created and analyzed in Ansys through the modal and harmonic methods available in the program. The piping system is capped off on each end and subjected to an internalized pressure of 1,000 psi. The first section of this design problem is to analyze the pipe with just the internalized pressure. A modal analysis is completed and images from the first three frequency modes are displayed in the report. The second part of this design problem is to examine the harmonic motion of the pipe system with a vertical excitation of .01 units of displacement and frequency range between 0 and 500 hertz. Isometric View The first figure is an isometric view of the piping system to be analyzed. The only affects on the system are the meshing and dimensions of the pipe.
Figure 1: Isometric view of piping system before any analysis
Internalized Pressure This image is a view of the system with an applied internal pressure of 1,000 psi. This is before the modal analysis is conducted and so the only source for the stress in the pipe is from the internalized pressure and not from the natural frequencies.
Figure 2: Piping system with internalized pressure of 1,000 psi.
The 12 natural frequencies This table shows the 12 natural frequencies of the pipe system. These natural frequencies occur as the name implies: naturally. It is of no consequence whether the internal pressure is figured into the analysis because it changes nothing. The 12 frequencies shown will occur under the natural conditions of the system.
Figure 3: Table of the 12 natural frequencies of the pipe system
Mode 1 The next image displays the system after the first natural frequency. The frequency has a value of 42.35 hz. The highest stress concentration is in the center of the pipe because both ends are fixed, creating the greatest deflection in the middle of the beam.
Figure 4: Modal analysis of the system during the first natural frequency.
Mode 2 The second mode of the natural frequency has more twist and a much higher deflection than the first mode. The frequency is 61.919 hz.
Figure 5: Modal analysis during the second natural frequency of the system
Mode 3
The final mode displayed in the report is for the 3rd mode of natural frequency. The twist and deflection of the system is still increasing under the natural frequencies. However, the change between the second and third mode is not nearly as significant as the change from the first natural frequency to the second one.
Figure 6: The 3rd mode of the natural frequency
Harmonic Analysis
The graph below illustrates the harmonic frequencies of the first 12 modes. The maximum displacement occurs at 200 hertz. This graph is produced from Ansys after a vertical excitation is produced on one end of the pipe system.
Figure 7: Harmonic frequencies of first 12 modes
Results The internal pressure that is applied to the pipe has no effect on the natural frequencies of the system. Doing the analysis with and without the internal pressure of 1,000 psi made no impact on the design. Figure 7 shows that the most important frequencies are at 100, 200, and 375 hertz. The frequency causing the most displacement is at 200 hertz, which is almost seven times greater than the displacement at 100 hertz. Looking at figures 4, and 5 the greatest displacement is located in the center portion of the pipe. Figure 6 further refines the ultimate stress location as being in the first bend of the middle section of pipe. A brace should be placed in the center of the pipe and would greatly reduce the vibrations of the pipe and help to steady the entire system. A brace would be very simple to add into the design and would greatly help to support the piping system. The brace should be made of steel just like the pipe to adequately sustain the piping system. After completing this design process Ansys has allowed for a greater understanding of how modal and harmonic analysis are used in determining how natural vibrations affect a structure.
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