Dynamic Behavior of Nonlinear Cable System. III

Abstract

The dynamic behavior of a geometrically nonlinear cable system is studied. Vector‐valued, nonwhite, correlated, stationary random excitation is used. The excitation has both additive and parametric components. The equations for the statistical moments of response are solved by numerical integration and by continuation. Simulation results are presented to assess the accuracy of the analytically predicted moments. The mean‐square response of the dominant coordinate decreases with increasing positive correlation between the excitation components. Increasing the prestrain of the system increases the linearized fundamental frequency and lowers responses. For some values of the parameters, the system has multiple stable and unstable mean‐square responses. Digital simulation shows that the system switches randomly in time from one stable branch to the other. The responses remain finite, so that the system can function safely in such regions. In general, the analytical predicted moments and those computed from simulation agree very well. Moreover, the multiple stable mean‐square responses predicted using Gaussian closure also match simulation results.