Dynamic modeling and in-plane 1:1:1 internal resonance analysis of cable-stayed bridge

A novel nonlinear dynamic double-cable-stayed shallow-arch model of cable-stayed bridge is established and the in-plane 1:1:1 internal resonance between three first modes of shallow arch and two cables under both external primary and subharmonic resonance is investigated, respectively. The Galerkin discretization and the method of multiple scales are applied to obtain the modulation equations of the dynamic system. The stable equilibrium solutions of the modulation equations are examined by Newton-Raphson method. Numerical simulations are carried out to investigate the dynamic behavior of the new dynamic system and Runge-kutta method is also used to solve the ordinary differential equations to verify the results. The results show the rich nonlinear phenomena and some new conclusions are also drawn.