Nonlinear longitudinal/transversal modal interactions in highly extensible suspended cables

Tools

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 (https://doi.org/10.1016/j.jsv.2007.07.056)

[thumbnail of strathprints018549]
Preview
 Text. Filename: strathprints018549.pdf
Accepted Author Manuscript
Download (2MB)| Preview

Abstract

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.

CORE (COnnecting REpositories)