A Nonlinear Mathematical Model of Thermoelastic Thin Plates with Voids and Its Applications

Abstract

Following the linear theory of thermoelastic materials with voids, a generalized Hamilton variational principle is extended to the thermoelastic plates with voids under the case of large deflection, and a 3D nonlinear mathematical model is presented. In this process, the balance equation of the entropy is converted to an equivalent form without the first-order time-derivative by integral, and the concept of the moments for the volume fraction of voids and temperature field is introduced. As application, the nonlinear dynamic and aerodynamic characteristics of simply-supported rectangular thermoelastic plates with voids for four different materials are studied and compared by using a Galerkin approach. The effects of the initial deflections and material parameters are considered in detail. In addition to providing a generalized Hamilton variational principle and a 3D nonlinear mathematical model, it is also provided a valuable numerical method to solve the dynamic problem directly in the paper. The theory and the method can be applied to solving various problems of the thermoelastic plates with voids easily.