Planar multimodal 1:2:2 internal resonance analysis of cable-stayed bridge

Abstract

Abstract This study focuses on the analysis of the linear and nonlinear dynamics of a reduced nonlinear coupling model of cable-stayed bridge consisting of two cables and a shallow arch, considering the effect of geometric nonlinearity of cables and the shallow arch. The planar 1:2:2 internal resonance among three first modes of cables and the shallow arch is firstly investigated with the external harmonic excitation applied on the shallow arch. Partial differential equations that govern motion of the system are derived. The piecewise mode function of the shallow arch, satisfying continuous and mechanical conditions simultaneously, is newly derived and chosen as the trial function in Galerkin’s method rather than commonly trigonometric function. Moreover, Galerkin’s method is applied to get the corresponding ordinary differential equations of the system and the method of multiple scales is used to obtain modulation equations for exploring the nonlinear dynamic behaviors. Lastly, the frequency- and force-response curves are given to investigate the planar dynamic behaviors of the system. Some interesting and novel conclusions have been obtained.