Global and Local Nonlinear System Responses under Narrowband Random Excitations. II: Prediction, Simulation, and Comparison

Abstract

The response behavior of the single-degree-of-freedom (SDOF) nonlinear structural system subjected to narrowband stochastic excitations studied in Part I is investigated via simulations to verify the stochastic system characteristics assumed in the development of the semianalytical method. In addition, to demonstrate the accuracy of the method, predicted response–amplitude probability distributions are presented and compared to simulation results. Numerical simulations are conducted by directly integrating the SDOF system with the narrowband excitation modeled by the 1971 Shinozuka formulation. It is observed that the proposed semianalytical method is capable of accurately characterizing the stochastic response behavior of the nonlinear system by predicting the response–amplitude probability distribution and capturing the trends of variations in the response–amplitude statistical properties. In both the primary and the subharmonic resonance regions, good agreements between the response–amplitude probability distributions predicted by the semianalytical method and obtained from simulation results are observed both qualitatively and quantitatively. In addition, trends of the variations in the probability masses associated with the modes with variations in excitation parameters (bandwidth and variance) are captured.