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.
| Original language | English |
|---|---|
| Pages (from-to) | 230-242 |
| Number of pages | 13 |
| Journal | Journal of Sound and Vibration |
| Volume | 310 |
| Issue number | 1-2 |
| DOIs | |
| Publication status | Published - 5 Feb 2008 |
Keywords
- highly-extensible cable
- longitudinal mode
- modal interaction
- internal resonance
- non-linear forced vibration