The Scheme to Determine the Convergence Term of the Galerkin Method for Dynamic Analysis of Sandwich Plates on Nonlinear Foundations

Abstract

The vibration of a plate resting on elastic foundations under a moving load is of great significance in the design of many engineering fields, such as the vehicle-pavement system and the aircraft-runway system. Pavements or runways are always laminated structures. The Galerkin truncation method is widely used in the research of vibration. The number of truncation terms directly affects the convergence and accuracy of the response results. However, the selection of the number of truncation terms has not been clearly stated. A nonlinear viscoelastic foundation model under a moving load is established. Based on the natural frequency of linear undisturbed derivative systems, the truncation terms are used to determine the convergence of vibration response. The criterion for the convergence of the Galerkin truncation term is presented. The scheme is related to the natural frequency with high efficiency and practicability. Through the dynamic response of the sandwich beam under a moving load, the feasibility of the scheme is verified. The effects of different system parameters on the scheme and the truncation convergence of dynamic response are presented. The research in this paper can be used as a reference for the study of the vibration of elastic foundation plates. Especially, the model established and the truncation analysis method proposed are helpful for studying the vibration of vehicle-pavement system and related systems.