Chebyshev finite element method for dynamic analysis of functionally graded sandwich plates lying on an elastic foundation subjected to harmonic loading

Abstract

This study presents a Chebyshev finite element method (C-FEM) for the dynamic analysis of functionally graded sandwich (FGS) plates lying on an elastic foundation (EF) and subjected to harmonic loading (HL). The FGS plate consists of two functionally graded (FG) face sheets and either a hard-core (Type 1) or a soft-core (Type 2). Based on the first-order shear deformation theory (FSDT) and Hamilton’s principle, the governing equations are formulated and discretized using Chebyshev-based shape functions. The proposed formulation accounts for both free and forced vibrations. The EF includes two parameters: the spring and shear layer stiffnesses. The accuracy and convergence of the C-FEM formulation are verified through comparisons with available reference solutions. Parametric investigations are then performed to examine the effects of material gradation, sandwich configuration, foundation stiffness, boundary conditions (BCs), and excitation frequency on the dynamic characteristics of the FGS plates. Particular attention is given to the resonance and beat phenomena under harmonic excitation. The results demonstrate that the material gradient and core configuration have opposite effects on the dynamic response of Type 1 and Type 2 plates, while the EF generally increases the natural frequencies and suppresses the vibration amplitude. The proposed C-FEM framework provides an efficient computational tool for analyzing and designing FGS structures with tailored material and core configurations under dynamic loading.