MARTIN_JEFFREY_LAB8

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University of Alabama *

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351

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Mechanical Engineering

Date

Dec 6, 2023

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4

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Jeffrey Martin ME 351-001 10/30/23 Lab 8: Buckling and Frequency Analysis 8a: Buckling Analysis of L-beam 1. Fill in table 1 with factor of safety that was obtained from each study (static and buckling) for both materials. Material Factor of Safety Static Buckling ASTM A36 Steel 3.397 5.417 Aluminum 6063-T83 3.216 1.7802 Table 1: Factors of safety of loaded L-beam resulting from different material and simulation analyses. 2. Is the change in the factor of safety (FOS) with respect to buckling expected? See slides 6-9 in background information. Due to the structure of the materials, buckling is more likely to occur at lower forces than yielding. Therefore, a lower factor of safety is expected with respect to buckling. 3. Fill in table 2 with the critical buckling loads obtained from the SWS buckling simulation for both materials. Material Buckling Load Factor Critical Buckling Load (N) ASTM A36 Steel 5.417 27.09 kN Aluminum 6063-T83 1.7802 8.901 kN Table 2: Critical buckling loads of L-beam resulting from buckling analyses. 4. Provide a screenshot of the buckling resultant amplitude (AMPRES) plot and the static von mises (VM) stress plot in “normal - to” view of the L-beam for both materials. Fig. 1. Static VM Stress plot of L-beam (ASTM A36 Steel)
Jeffrey Martin ME 351-001 10/30/23 Fig. 2. Static VM Stress plot of L-beam (Aluminum 6063-T83) Fig. 3. Buckling AMPRES plot of L-beam (ASTM A36 Steel) Fig. 4. Buckling AMPRES plot of L-beam (Aluminum 6063-T83)
Jeffrey Martin ME 351-001 10/30/23 8b: Frequency Analysis of Tuning Fork 1. Replicate the mode shape plot (Slide 11 Lab 8 PPT) which includes the first 4 mode shape plots of the tuning fork in a single image. Include a superimposed original shape on all four mode plots. Fig. 1. Mode shape plot from frequency analysis of tuning fork. 2. Re-create the image of the list of modes from the frequency study with no fixture. 11 mode shapes should be listed. Highlight the frequency which relates to the fundamental mode of vibration of the tuning fork. Fig. 2. Frequency mode list from non-fixed frequency analysis of tuning fork.
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Jeffrey Martin ME 351-001 10/30/23 3. Discuss why the non-fixed frequency analysis study required 6 modes before reaching the fundamental mode of frequency and discuss why the fixed tuning fork required at least 3 modes before reaching the fundamental mode of frequency. Reference the book (Ch. 6 page 6). The first 6 modes of vibration correspond to rigid body modes and because the tuning fork is not supported, it has 6 degrees of freedom with 3 being translational and 3 being rotational. The first eleastic mode of vibration occurs at mode 7 which is the first requiring the node to deform. Because a support is needed for the vibration to exist, therefore after the first three modes have ben damped out the tuning fork vibrates the way it is supposed to in mode 4.