This article presents a unified mathematical model to investigate free and forced vibration responses of perforated
thin and thick beams. Analytical models of the equivalent geometrical and material characteristics for regularly squared
perforated beam are developed. Because of the shear deformation regime increasing in perforated structures, the investigation of
dynamical behaviors of these structures becomes more complicated and effects of rotary inertia and shear deformation should be
considered. So, both Euler-Bernoulli and Timoshenko beam theories are proposed for thin and short (thick) beams, respectively.
Mathematical closed forms for the eigenvalues and the corresponding eigenvectors as well as the forced vibration time response
are derived. The validity of the developed analytical procedure is verified by comparing the obtained results with both analytical
and numerical analyses and good agreement is detected. Numerical studies are presented to illustrate effects of beam slenderness
ratio, filling ratio, as well as the number of holes on the dynamic behavior of perforated beams. The obtained results and
concluding remarks are helpful in mechanical design and industrial applications of large devices and small systems (MEMS)
based on perforated structure.
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