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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. [ABSTRACT FROM AUTHOR]

This paper reports a systematic investigation on the linear and nonlinear dynamics of a suspended cable, taking bending stiffness into account. Firstly, the linear dynamics features, for example, eigen frequencies and modes for in-plane and out-of-plane motions, are formulated. Secondly, parametrical studies are conducted to explore the effect of bending stiffness on the natural frequencies and mode shapes of the symmetrical/antisymmetrical in-plane and out-of-plane modes. Then, the three-to-one internal resonance between the first- and third-order in-plane symmetrical modes is analyzed by applying directly the method of multiple scales dealing with the nonlinear partial differential equation and boundary conditions. Finally, the frequency-response curves and force-response curves are obtained through solving the modulation equations using the Newton–Raphson method and the pseudo-arclength scheme. The results show that the bending stiffness plays a considerable role in changing the natural frequencies and mode shapes, shifting the conditions for the occurring of nonlinear interaction, saddle-node bifurcation and Hopf bifurcation of suspended cables. [ABSTRACT FROM PUBLISHER]