Semi-analytical solutions for stationary response of a stay cable under combined Gaussian and Poisson excitations

Abstract

This paper studies nonlinear random vibrations of a stay cable subject to combined Gaussian and Poisson excitations. The Gaussian excitation is continuous stochastic process directly acting on the stay cable, while the Poisson excitation describes discrete random disturbances to the base of the system. The in-plane and out-of-plane coupled vibration of the stay cable is discretized and represented by a two-degree-of-freedom dynamical system with the help of the Galerkin method. Then, the stationary response of the stay cable is determined in terms of radial basis function neural networks (RBFNN) to minimize the residual error of the generalized-Fokker–Planck–Kolmogorov (GFPK) equation. A super-long stay cable in practice is taken as an engineering example to demonstrate the analysis. The influences of system parameters on the random vibration responses of the stay cable are examined to reveal the features of the vibration response. Extensive Monte Carlo simulations (MCS) are conducted to check the precision of the semi-analytical solutions. This research lays down a foundation for optimal design and vibration control design of the stay cable.