A Three-Dimensional Finite Element Analysis of a Two-Axially Pre-Loaded Plate Exposed to a Dynamic Force

Abstract

In this paper, the forced vibration analysis by a harmonically time-dependent force of an elastic plate covered rigidly by a rigid half-plane is given. The plate layer is subjected to bi-axial normal initial force, into lateral sides separately. Here, the preloading state is exactly static and homogeneous. To eliminate the disadvantage of such a nonlinear model, the problem formulation is modeled in terms of the fundamental consideration of the theory of linearized wave in elastic solids under a pre-loaded state (TLWESPS) in a plane-stress case. For this purpose, considering Hamilton’s principles, the system of the partial equations of motion and the boundary-contact conditions are found. Based on the virtual work and the fundamental theorem of the calculus of variation, the three-dimensional finite element method (3D-FEM) is used to understand the dynamic behavior of the plate. A numerical validation process is established based on error norm functions. Next, influences of certain problem parameters such as Young’s modulus, aspect ratio, thickness ratio, pre-loaded parameter, etc. on the frequency mode of the pre-stressed system are given. The numerical investigations show that higher values of Poisson's ratio promote the resonant mode of the plate while increasing the influence of the preloaded parameter on the dynamic response of the plate.