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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]

Abstract This study investigated the internal resonance phenomenon of a suspended bridge structure with a 6-Degree-of-Freedom sectional model. The primary resonance of the second mode of the system under harmonic excitation is firstly studied. The one-to-two internal resonance between the second and third modes, and one-to-three internal resonance between the second and fourth modes may be induced if the corresponding natural frequency ratios are close to 2.0 and 3.0, respectively. Numerical analysis also shows that the two-to-one internal resonance between the third and second modes can be induced under different scenarios of excitation. The first one happens with the second mode being excited, resulting in two response peaks in the frequency response curves. The second one may occur when the third mode is excited with sufficient large excitation where most of the energy input will be transmitted to the second mode. Hopf bifurcation can also be found in the frequency response curve of the system. Lastly, the three-to-one internal resonance between the fourth and second modes is also found when the second mode is excited. The response of the second mode is slightly reduced with a distinct increase in the response of the fourth mode due to the internal resonance. All these behaviors of this dynamic system indicate the meaningful role played by a variety of internal resonances in the design of mega-scale cable-supported bridge structure. Highlights • The modal property of a 6-dof sectional model of suspension bridge is studied. • Primary resonance of the second mode is examined. • The one-to-two internal resonance between the second and third mode is studied. • The one-to-three internal resoance between the second and fourth mode is checked. [ABSTRACT FROM AUTHOR]