The impact of non-local elasticity factors on natural frequencies of a rectangular cantilever beam
Date
2020
Authors
Bouzaid, Ibrahim F., author
Heyliger, Paul, advisor
Chen, Suren, committee member
Weinberger, Chris, committee member
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Abstract
The natural frequencies of a structural element are important factors in attaining a safe design. Natural frequency is the frequency at which an element tends to vibrate in the absence of any driving or damping force. When an object vibrates at a frequency equivalent to its natural frequency, its vibration amplitude increases significantly, which could lead to severe damage. A safe design would thus require having a different natural frequency compared to the frequency of the vibrating element. In some cases, obtaining accurate natural frequencies is challenging. In cases in which non-local elasticity, where the stress at a point is a function of the strain at the close region around that point, provides a better solution to the mechanical problems compared to other theories, natural frequencies should be studied. The non-local elastic solution to the non-local elastic natural frequencies of a rectangular cantilever beam problem was developed using a Fortran code, and the finite elements of non-local mesh were generated using a MATLAB code. The eigenvalue problem was solved, and the mode shapes were plotted using another MATLAB code. The results indicate that the natural frequencies for the non-local solution have dropped 25–30 percent. The non-local factors, mesh size, and slenderness influenced the drop in the natural frequencies. The non-local natural frequencies tended to match the local natural frequencies up to the third frequency, then start diverged. The mode shapes are similar to the local elastic mode shapes in all cases.
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Subject
natural frequencies
in plane vibration
non local elasticity