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BYU Structural Dynamics Research Lab
PROJECT OBJECTIVE
PROJECT OBJECTIVE
Assisting a PhD student’s thesis in nonlinearities, my objective was to determine the natural frequencies and mode shapes of the first three bending modes for a slender, riveted steel beam—utilizing mathematical, analytical, and experimental methods.
MATHEMATICAL MODEL
MATHEMATICAL MODEL
Using the mode shape equation for a free-free beam, the mode shapes and frequencies were calculated and modeled in MATLAB
FINITE ELEMENT ANALYSIS (FEA)
FINITE ELEMENT ANALYSIS (FEA)
Additionally, the bending modes up to 4000 Hz were captured through FEA analysis in Abaqus
EXPERIMENTAL TESTING
EXPERIMENTAL TESTING
Using the mathematical and FEA results as a framework, a Roving Hammer Test was used on the beam to measure the frequency response of an impact. Two accelerometers captured the vibration frequencies, and Siemen’s Impact Testing software was used to extract the frequency-response function (FRF)—depicted on the bottom-left.
Data analysis of the FRF in MATLAB revealed the mode shape of the beam at each natural frequency—depicted on the bottom-right
RESULTS
RESULTS
The results of the Roving Hammer Test recorded the bending and torsional modes all the way up to mode 10. However, only the first three were of interest to the project:
Mode 1: 18.9 Hz
Mode 2: 52.0 Hz
Mode 3: 100.8 Hz
The results of this analysis was used by PhD students as the base dataset to compare nonlinear mode shapes to.
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