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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]

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]