Dynamic Behavior of Nonlinear Cable System. IV

A suitable filter response is defined that allows studies of the effects of excitation bandwidth on the responses of geometrically nonlinear dynamic systems. For such a random excitation, as the bandwidth approaches zero, the mean square displacement response of a linear single-degree-of-freedom (SDOF) system approaches the mean square response to harmonic excitation. Studies of mean square responses of a nonlinear SDOF model of a cable system are presented. The set of nonlinear equations for the response moments are truncated using Gaussian closure and solved using continuation techniques as implemented in the program AUTO. Surfaces of turning point loci are computed in the parameter space of excitation bandwidth, excitation central frequency, and system damping. These surfaces provide values of the three parameters that separate regions with multiple mean square responses from regions with unique mean square responses. Response time histories are computed by simulation to illustrate system behavior in regions with multiple stable mean square responses.