Random vibration of hysteretic systems under Poisson white noise excitations

Hysteresis widely exists in civil structures, and dissipates the mechanical energy of systems. Research on the random vibration of hysteretic systems, however, is still insufficient, particularly when the excitation is non-Gaussian. In this paper, the radial basis function (RBF) neural network (RBF-NN) method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations. The solution to the reduced generalized Fokker-PlanckKolmogorov (GFPK) equation is expressed in terms of the RBF-NNs with the Gaussian activation functions, whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition. A steel fiber reinforced ceramsite concrete (SFRCC) column loaded by the Poisson white noise is studied as an example to illustrate the solution process. The effects of several important parameters of both the system and the excitation on the stochastic response are evaluated, and the obtained results are compared with those obtained by the Monte Carlo simulations (MCSs). The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency.