Abstract:

As the span of cable-stayed bridges increases, these structures become more susceptible to vibration under various complex loads. To investigate the dynamic behavior of cable-stayed bridges under vehicle loads, this study establishes a cable-stayed shallow arch model subjected to the equivalent sustained moving-force excitation, with the initial configuration of the bridge deck and cable vibration considered. First, the governing equations are derived based on Hamilton’s principle, in which the initial configuration of the shallow arch is characterized by a non-dimensional rise. Subsequently, the governing equations are reduced to ordinary differential equations (ODEs) by the Galerkin discretization, and the method of multiple time scales is used to derive the modulation equations. On this basis, the steady-state frequency-response and force-response curves are obtained. Numerical analysis indicates that the variations in the initial configuration have a significant effect on the nonlinear behavior of the system. Specifically, as the non-dimensional rise increases within the considered parameter range, the response curves exhibit more complex nonlinear characteristics, with new branches emerging alongside more stable solutions, unstable solutions, and bifurcation points.

Key words: cable-stayed shallow arch, continuous traffic loading, nonlinear vibration, primary resonance, internal resonance