A method for natural frequency calculation of the functionally graded rectangular plate with general elastic restraints

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.