Multimodal interaction analysis of a cable-stayed bridge with consideration of spatial motion of cables

Abstract

The multi-cable-stayed shallow arch model and its related dynamic theory and behavior of a cable-stayed bridge are proposed and investigated. The partial differential equations that govern the motion of the system are derived according to the classic dynamic equations of cables and the shallow arch. Galerkin’s integral is used to obtain the corresponding ordinary differential equations of the system. Its linear eigenvalue problem is firstly analyzed. The perturbation method of multiple scales is used to derive the modulation equations of the system subjected to boundary forced and parametric excitation, respectively. Then, the multimodal interaction among the lowest in-plane and out-of-plane modes of cables and the lowest mode of the shallow arch is investigated by analyzing the frequency–response and force–response curves of the system. The influence of excitation frequency and amplitude, and the difference between different cables on dynamic behaviors of the system are discussed.