Natural Frequencies of Functionally Graded Sandwich Plates Resting on an Elastic Foundation Using Chebyshev Finite Element Method

In this study, the article uses a finite element method based on Chebyshev polynomials to calculate the natural frequencies of functionally graded sandwich (FGS) plates with hard-core (HC) or soft-core (SC) resting on an elastic foundation. Chebyshev polynomials are a series of orthogonal polynomials defined recursively, and the value of them belongs to the range [-1, 1] as well as vanishes at Gauss points. More clearly, the novelty of this article is to use the high-order shape functions that satisfy the interpolation condition at the points based on Chebyshev polynomials to build the flat quadrilateral element for analysis of FGS plates. On the other hand, these plates are composed of two functionally graded skins and a hard or soft core. The elastic foundation with a two-parameter as a spring stiffness (α₁) and a shear layer stiffness (α₂) are used. Comparative examples are presented to validate the effectiveness of the current approach.