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Nonlinear longitudinal/transversal modal interactions in highly extensible suspended cables

Srinil, N. and Rega, G. (2008) Nonlinear longitudinal/transversal modal interactions in highly extensible suspended cables. Journal of Sound and Vibration, 310 (1-2). pp. 230-242. ISSN 0022-460X

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Recent research literature mostly deals with nonlinear resonant dynamics of low-extensible cables involving transversal modes. Herein, we aim to investigate geometrically nonlinear longitudinal/transversal modal interactions in highly extensible suspended cables, whose material properties are assumed to be linearly elastic. Depending on cable elasto-geometric properties, the spectrum of low-order planar frequencies manifests primary and secondary frequency crossover phenomena of transversal/transversal and longitudinal/transversal modes, respectively. By focusing on 1:1 internal resonances, nonlinear equations of finite-amplitude, harmonically forced and damped, cable motion are considered, fully accounting for overall inertia and displacement coupling effects. Meaningful quadratic nonlinear contributions of non-resonant, higher-order, longitudinal modes are highlighted via a multimode-based, second-order multiple scales solution. Overall coupled/uncoupled dynamic responses, bifurcations, stability and space-time-varying displacements due to longitudinal/transversal (vs. transversal/transversal) modal interactions at secondary (vs. primary) crossovers are analytically and numerically evaluated, along with the resonant longitudinal mode-induced dynamic forces.