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 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. 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.
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