Modeling and Analysis of 1:3 Internal Resonance of Suspension Bridge Under Boundary Excitations

This study investigated the nonlinear dynamic behavior of suspension bridge subjected to multi-frequency boundary excitations. Firstly, the nonlinear dynamic model of the suspension bridge subjected to multi-frequency boundary excitations is established. The in-plane vibration equations are derived based on Hamilton's principle, taking into account the effects of geometric nonlinearity of the girder-deck and main cable as well as the stiffness of hangers. Secondly, the Galerkin method is used to solve for the frequencies and corresponding mode shape functions. Thirdly, the corresponding modulation equations are obtained based on the multiple scales method, and the 3:1 internal resonance between two symmetrical modes is analyzed. Combined with numerical analysis, the nonlinear dynamic behavior between modes of the suspension bridge is demonstrated through the frequency-response, force-response, and time history curves. The results indicate that the drift phenomenon appears when perturbing the amplitude and frequency of the different excitations, and the system exhibits intricate dynamic responses.