Study on nonlinear dynamic behaviors of the cable-stayed functionally graded beam under extreme temperature environments

Abstract

This paper combines functionally graded materials (FGMs) with the cable-stayed beam to propose a cable-stayed functionally graded beam (CSFGB) model. The influences of temperatures on nonlinear behaviors of the model are analyzed when one-to-two internal resonance of the global mode (FGB) and the local mode (cable) is triggered. First, the governing equations, which consider thermal effects, are derived through the extended Hamilton's principle. Thereafter, the modal functions are obtained based on the boundary conditions. On this basis, the governing equations are discretized by employing Galerkin discretization, resulting in a set of ordinary differential equations (ODEs). The method of multiple time scales is then applied to solve these ODEs and derive the modulation equations. Finally, nonlinear dynamic behaviors of the CSFGB at three different temperatures are analyzed. The results show that as the temperature decreases, the response increases, making chaotic motion more likely to occur. Moreover, the distribution of FGMs has a significant impact on nonlinear responses of the system.