An analysis of forced vibration by an inclined dynamic load of a bilayered plate with a two-axially preloaded case

Abstract

Presented herein is a novel approach to apply the finite element method (FEM) to the forced vibration analysis of a two-axially preloaded plate with two constituent materials standing on a rigid foundation under a time-variable angled force based on a piecewise homogeneous body model. The article is pioneering the application of the FEM to analyze the mentioned problem, marking a significant advancement in the understanding of multilayered composite structures in engineering dynamics. First, the geometry of the problem and the physical considerations are explained in detail. Next, a mathematical solution process is developed in the context of the theory of linearized waves in elastic solids under a preloaded state according to the variational calculus. The solution algorithm is validated by presenting an error analysis thanks to norm functions and the convergence analysis compared to the available studies. Next, a thorough numerical discussion is performed to highlight how various factors involving the initial deformation state, the angles of inclined force, and the resonance frequency, together with the thickness ratio and the frequency response of the system, affect its forced vibration behaviors. Numerical results demonstrate that while increasing the vertical length of the body exceeds the resonance frequency of the system, increasing the horizontal lengths promotes that mode. Also, it is shown that when the Young modulus of the lower layer is bigger than that of the upper layer, the stability of the system increases.