Stochastic excitation of suspended cables involving three simultaneous internal resonances using Monte Carlo simulation

In the neighborhood of three simultaneous internal resonance conditions amo ng four normal modes, the response behavior of a suspended cable to random Gaussian excitation is studied using computational simulations. The study i ncludes the interaction between the first two in-plane and the first two ou t-of-plane modes. When the first in-plane mode is externally excited its re sponse can act as a parametric excitation to the other three modes through nonlinear coupling. The governed modal equations of motion are numerically simulated using a double-precision, initial value problem server Adam-Moult on algorithm. The random excitation is generated numerically from a normal distribution using an inverse Cumulative Distribution Function (CDF) techni que. The numerical results are processed to estimate response statistics su ch as mean squares power spectra, probability density functions, and autoco rrelation functions. The modes, which are indirectly excited, exhibit the w ell-known phenomenon 'on-off intermittency' in the neighborhood of stochast ic bifurcation. Furthermore, in the neighborhood of internal resonances the directly excited mode is found to transfer energy to other modes. Under Ga ussian excitation the response coordinates of the four modes are essentiall y non-Gaussian narrow band random processes with a central frequency close to each mode natural frequency. (C) 1999 Elsevier Science S.A. All rights r eserved.