Abstract
In this study, a unified solution method to obtain the natural frequencies of the functionally graded rectangular plate (FGRP) with general elastic restraints by using ultraspherical polynomials and the Ritz method is presented. It is supposed that the material distribution properties of the FGRP depend on four different parameters. Based on the first order shear deformation plate theory, the displacement fields of the FGRP are set and boundary and continuity conditions are modeled by adopting the virtual spring technique. All displacement functions of the FGRP including boundary and continuity conditions are expressed by ultraspherical polynomials, and the natural frequencies of the FGRP are obtained by applying the Ritz method. The accuracy of the proposed method is verified by comparison with the results of the previous literature and finite element method. Finally, the effects of several parameters on the natural frequencies of the FGRP with various classical and elastic restraints are also discussed, which can be helpful to the further development of the same topic.
Highlights
It is an important problem to analyze accurately and quickly the vibration characteristics of plates, which are widely being used in various engineering applications
All displacement functions of the functionally graded rectangular plate (FGRP) including boundary and continuity conditions are expressed by ultraspherical polynomials, and the natural frequencies of the FGRP are obtained by applying the Ritz method
Various plate theories such as classical plate theory (CPT), first-order shear deformation plate theory (FSDPT), higher-order deformation plate theory (HSDPT), exponential shear deformation plate theory (ESDPT), hyperbolic shear deformation plate theory, and trigonometric shear deformation plate theory have been reported in the study of free vibration of functionally graded material (FGM) plates
Summary
It is an important problem to analyze accurately and quickly the vibration characteristics of plates, which are widely being used in various engineering applications. Research on the vibration analysis of FGM plates has been developed by many researchers. Kumar et al. to investigate the free vibration behavior of the thin functionally graded rectangular plate (FGRP) used the dynamic stiffness method (DSM), solved the dynamic stiffness matrix by the Wittrick–Williams algorithm, and obtained the natural frequencies. In this study, they set the displacement field of the FGRP by using
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