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

Abstract

In the neighborhood of three simultaneous internal resonance conditions among four normal modes, the response behavior of a suspended cable to random Gaussian excitation is studied using computational simulations. The study includes the interaction between the first two in-plane and the first two out-of-plane modes. When the first in-plane mode is externally excited its response 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 solver Adam-Moulton algorithm. The random excitation is generated numerically from a normal distribution using an inverse Cumulative Distribution Function (CDF) technique. The numerical results are processed to estimate response statistics such as mean squares power spectra, probability density functions, and autocorrelation functions. The modes, which are indirectly excited, exhibit the well-known phenomenon ‘on-off intermittency’ in the neighborhood of stochastic bifurcation. Furthermore, in the neighborhood of internal resonances the directly excited mode is found to transfer energy to other modes. Under Gaussian excitation the response coordinates of the four modes are essentially non-Gaussian narrow band random processes with a central frequency close to each mode natural frequency.