An Exact Solution for the Differential Equation Governing the Lateral Motion of Thin Plates Subjected to Lateral and In-Plane Loadings

One of the powerful analytical methods to solve partial differential equations is the Adomian decomposition method (ADM). This paper presents a novel approach for the dynamic analysis of a flexible plate by using the ADM, which is a Boundary Value Problem (BVP). In this regard, a general approach based on the generalized Fourier series expansion is applied. The obtained analytical solution is simplified in terms of a given orthogonal basis functions that these functions satisfy the boundary conditions of plate. For the first time, we solved this equation using ADM and compared the results with those of the modal classical analysis in two cases to demonstrate the validity of the present study.