Orthogonal Polynomials-Ritz Method for Dynamic Response of Functionally Graded Porous Plates Using FSDT

Abstract

This work focuses on the dynamic response of the functionally graded porous (FGP) plates. To construct the FGP plate model, the material-distributed profiles of the FGP plates are given first. In addition, the relations between the stress and strain are given by means of the first-order shear deformation theory (FSDT). Furthermore, the boundary conditions are defined based on the virtual spring technique. Moreover, the third kind of Chebyshev orthogonal polynomials are employed to construct the displacement components of the FGP plate, and the energy expressions of the FGP plate are constructed and then changed into the Lagrange equation form. Ultimately, the FGP plate energy expressions are solved by means of the Rayleigh–Ritz method. On this basis, the verification of the proposed method is conducted, and then, a series of investigations are given with respect to diverse influence factors.