MULTIPLE INTERNAL RESONANCE IN SUSPENDED CABLES UNDER RANDOM INPLANE LOADING

The random excitation of a suspended cable with simultaneous internal resonances is considered. The internal resonances can take place among the first in-plane and the first two out-of-plane modes. The external loading is represented by a wide-band random process. The response st atistics are estimated using the Fokker-Planck-Kolmogorov (FPK) equati on, together with Gaussian and non-Gaussian closures. Monte Carlo simu lation is also used for numerical verification. The unimodal in-plane motion exists in regions away from the internal resonance condition. T he mixed mode interaction is manifested within a limited range of inte rnal detuning parameters, depending on the excitation power spectrum d ensity and damping ratios. The Gaussian closure scheme failed to predi ct bounded solutions of mixed mode interaction. The non-Gaussian closu re results are in good agreement with the Monte Carlo simulation. The on-off intermittency of the autoparametrically excited modes is observ ed in the Monte Carlo simulation over a small range of excitation leve ls. The influence of the cable parameters, such as damping ratios, sag -to-span ratio, internal detuning parameters, and excitation level on the autoparametric interaction, is studied. It is found that the inter nal detuning and excitation level are the two main parameters which af fect the autoparametric interaction among the three modes. Due to the system's nonlinearity, the response of the three modes is strongly non -Gaussian and the coupled modes experience irregular modulation.