Internal resonance of generalized suspension bridge model considering torsional-vertical vibration

Abstract

Non-linear vibration is a crucial issue for suspension bridge due to its slenderness and low damping. This study proposes a fully mathematical model of a suspension bridge considering arbitrary inclined angle of main cables by using principle of Hamilton. This is the first mathematical model that is capable of analyzing the nonlinear coupled vertical-torsional vibration of generalized bridge configurations with independently considering the motion of main cables and girder. Galerkin method is adopted for the discretization of the model, and the multi-scale method is employed to acquire modulation equations. The accuracy of the non-linear vibration obtained from proposed mathematical model are validated by a FE model. The internal resonance analysis for such a suspension bridge with spatial layout of main cables between vertical and torsional modes with frequency ratio of 2:1, and between two torsional modes respectively dominated by deck and main cables with frequency ratio of 1:1 are successively investigated in the first time within a narrow detuning frequency domain. The phenomenon of nonlinear resonance was discussed with different inclination angle of main cables and detuning parameters. Some novel and practical conclusions were obtained. Results show that 2:1 internal resonance between vertical and torsional modes may be induced only when two forces with frequencies corresponding to involved modes are applied simultaneously. In addition, significant 1:1 internal resonance is observed, with inducing Hopf bifurcation. Understanding such possible situations is favorable to the design of bridge structure.