Dynamic Analysis of a Double-Cable-Stayed Shallow Arch Model Under Multi-Frequency Excitation by IHB Method

To reveal the dynamic properties of cable-stayed bridges under complex external excitations, a double-cable-stayed shallow arch model induced by multi-frequency harmonic excitations is established. The cable and shallow arch exhibit primary or subharmonic resonances by sweeping excitations simultaneously and asynchronously. Galerkin method, one/two time scales Incremental Harmonic Balance (IHB) method, and Runge–Kutta (RK) method are applied to explore the nonlinear dynamic responses. Research results demonstrate that both the cables and shallow arch present soft and hard spring properties, despite the very weak hard spring of the shallow arch; one-way dynamic interaction among the cables and the shallow arch is discovered when sweeping excitations asynchronously.