Nonlinear planar response of a cable under random excitation

Abstract

In this study, the nonlinear planar response of a cable in its first symmetric mode of oscillation under two types of random forcing is investigated. The forcing could be either a narrowband excitation or a periodic function plus a white noise. A single mode approximation is used; wherein the cable is represented by an oscillator with both quadratic and cubic nonlinear stiffness terms. The equivalent linearization technique in conjunction with a stochastic sample stability analysis is employed in the response analysis. In particular, the effect of sag on the cable response is studied. The validity of the theoretical solutions is examined through limited digital simulation results.