A semi-analytical method for dynamic analysis of a rectangular plate with general boundary conditions based on FSDT

Abstract

In this paper, the unified Jacobi–Ritz method (JRM) is utilized to analyze the dynamic response of rectangular plates with general boundary conditions. First, the structural energy functional is established in the framework of the first-order shear deformation theory, and the rectangular plate is divided into several equal parts according to the domain decomposition method. Then, the artificial springs are introduced to ensure the continuity of segments and diversified boundary conditions. The Jacobi orthogonal polynomials are expanded to represent the displacement field in one direction. Finally, the free and forced vibration characteristics of the rectangular plate can be obtained by utilizing the Rayleigh–Ritz method, where the Newmark-β integration method is adopted to realize the time-domain solutions for transient vibration response. The results for different structural scale parameters and various boundary conditions are presented, and the validity and accuracy of the presented method are verified by comparing the results from published literature and FEM. The results of the study can provide technical support for vibration control of the plate structure.

Keywords

• jacobi polynomials
• steady and transient vibration
• rectangular plate
• general boundary condition