PLANAR AND NONPLANAR NONLINEAR DYNAMICS OF SUSPENDED CABLES UNDER RANDOM INPLANE LOADING .1. SINGLE INTERNAL RESONANCE

The non-linear interaction of the in-plane and out-of-plane motions of a suspended cable in the neighbourhood of 2:1 internal resonance unde r random loading is studied. The random loading acts externally on the in-plane mode, while the out-of-plane mode is non-linearly coupled wi th the in-plane mode. Any non-trivial motion of the out-of-plane mode is mainly due to this non-linear coupling, which becomes significant i n the neighbourhood of internal resonance. The response statistics are estimated by employing the Fokker-Planck equation together with Gauss ian and non-Gaussian closures. Monte-Carlo simulation is also used for numerical verification. Away from the internal resonance condition, t he response is governed by the inplane motion, and the non-Gaussian cl osure solution is found to be in good agreement with numerical simulat ion results. The stochastic bifurcation of the out-of-plane mode is pr edicted by Gaussian and non-Gaussian closures, and by Monte-Carlo simu lation. The non-Gaussian closure can only predict bounded solutions wi thin a limited region. The on-off intermittency of the second mode is observed in the Monte-Carlo simulation over a small range of excitatio n level. The influence on response statistics of excitation level and cable parameters, such as internal detuning, damping ratios, and sag-t o-span ratio, is reported. Copyright (C) 1996 Published by Elsevier Sc ience Ltd.