Dynamics of Elastic Cable under Parametric and External Resonances

Abstract

Nonlinear dynamics of a heavy elastic suspended cable were investigated for application to a stack/wire system. Small oscillations of the cable at the support attached to the stack, the result of bending motion of the stack due to vortex shedding, lead to parametric and external excitation. Numerical analysis was used to predict the parametric and external resonances of the elastic suspended cable, which contained cubic nonlinearities due to cable stretching and quadratic nonlinearities due to equilibrium cable curvature in a tilted configuration. Numerical results agree well with the original stack/wire response. Additional parametric analyses were pursued to distinguish between parametric and external resonances and their couplings. It was found that excitation amplitudes and tilted angles play very important roles in parametric and external resonances.