Convergence of the Galerkin Method for Nonlinear Dynamics of the Continuous Structure

Abstract

The Galerkin truncation method is a powerful method for nonlinear dynamics analysis, and has been widely used to discretize the spatial differential operator. Due to more and more new fields of application, the research interest on the Galerkin method is still high today. In this paper, research on the convergence of Galerkin method for nonlinear dynamics of the continuous structure is thoroughly reviewed. At the beginning, the Galerkin method is briefly introduced. Then, the paper reviews the application of the truncation method. This paper also sums up the comparative study on the Galerkin method with other methods, such as the finite difference method (FDM), the finite element method (FEM), and the multiple time scales method. In the investigations concerning the convergence of the Galerkin method, this paper summarizes recent studies on nonlinear dynamics of the axially moving systems, the continua on the nonlinear foundation, and the belt-pulley systems. Finally, the truncation terms of Galerkin method for the continuous structure's nonlinear dynamics analysis is suggested for the future research applications.