Convergent term of the Galerkin truncation for dynamic response of sandwich beams on nonlinear foundations

Abstract

Dynamic response of beams on elastic foundations is of great theoretical significance in the field of engineering. Galerkin truncation method is the most commonly used powerful method to study the vibration of these structures. The number of truncation terms affects the convergence of the analysis and determines the accuracy of the dynamic responses. However, there is still no basis for how to choose the appropriate number of truncation terms. In this paper, two effective schemes based on the natural frequency of the corresponding linear conservative system are proposed to determine the convergent terms of the Galerkin truncation. Since determining the natural frequencies of the corresponding linear conservative system are much easier, the convergence determination method is convenient for application. Based on the dynamic response of the sandwich beam on nonlinear foundations under a moving load, the feasibility of the two schemes for determining the convergent term is confirmed. Moreover, the effects of system parameters on the two schemes are presented. In short, this paper provides two simple and easy schemes for selecting the Galerkin truncation terms in the research of the dynamic response of elastic structures resting on elastic foundations.