Legendre–Ritz solutions for vibration characteristics of three-dimensional double-layer lattice truss sandwich plates

Abstract

In this paper, Legendre–Ritz solutions for vibration characteristics of double-layer lattice truss sandwich plates are proposed based on three-dimensional (3-D) elasticity theory. Double-layer lattice truss sandwich plates consist of three face sheets and two cores. The face sheets are composed of fiber-reinforced composites and the cores are composed of pyramidal lattice trusses made of isotropic materials. The pyramidal lattice core is equated to a homogeneous plate according to equivalence principle. Based on 3-D elasticity theory and pseudo excitation method (PEM), each layer's energy expressions of double-layer lattice truss sandwich plates are constructed. After that, Legendre polynomials are adopted to describe displacement components in length, width and thickness directions. On this basis, the Rayleigh-Ritz method is used to solve energy functions to obtain motion equations of double-layer lattice truss sandwich plates. The accuracy and validity of the present method are corroborated by comparisons with references and finite element method (FEM). Additionally, in order to find out effects of relevant parameters on dynamical characteristics of double-layer lattice truss sandwich plates, parametric studies are carried out by means of some numerical examples.