Analysis on In-Plane 2:2:1 Internal Resonance of a Complex Cable-Stayed Bridge System Under External Harmonic Excitation

Nonlinear dynamic analysis of a cable-stayed bridge has been a hot topic due to its structural flexibility. Based on integro-partial differential equations of a double-cable-stayed shallow-arch model, in-plane 2:2:1 internal resonance among three first in-plane modes of two cables and a shallow arch under external primary or subharmonic resonance is considered. Galerkin's method and the method of multiple scales are used to derive averaged equations of this cable-stayed bridge system. Nonlinear dynamic behaviors of the system are investigated via numerical simulation. Results show rich nonlinear phenomena of the cable-stayed bridge system and some new phenomena are observed. Two identical cables that are symmetrically located above the shallow arch can have different dynamic behaviors even when initial conditions of the system are symmetrically given. Two cables with some differences between their parameters can exhibit either softening or hardening characteristics.