The nonlinear dynamic model of a shallow arch with multiple cables is developed to model a long-span cable-stayed bridge. Based on the veering phenomenon of cable-stayed bridges, the in-plane modal internal resonance between the first mode of the shallow arch and the first mode of the cable is investigated under both primary resonance and subharmonic resonance. Modulation equations of the dynamic system are obtained by Galerkin discretization and the multiple scales method, in which the equilibrium solution of modulation equations is obtained by the Newton–Raphson method. Meanwhile, the Runge–Kutta method is applied to directly solve the ordinary differential equations to verify the accuracy of the perturbation analysis. Numerical analysis shows that the internal resonance occurs in adjacent cables; the energy transfer mechanism and the dynamic behavior of system become more complex.


Civil, Architectural and Environmental Engineering


National Natural Science Foundation of China, Grant 11872176

Keywords and Phrases

Cable-stayed bridge; Internal resonance; Modeling; Nonlinear behaviors

International Standard Serial Number (ISSN)

1573-269X; 0924-090X

Document Type

Article - Journal

Document Version

Final Version

File Type





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Publication Date

01 Jan 2022