Global and Local Nonlinear System Responses under Narrowband Random Excitations. I: Semianalytical Method

Abstract

A single-degree-of-freedom nonlinear structural system under narrowband random excitation can exhibit very complex global and local response behaviors. In order to develop a stochastic method to analyze the nonlinear responses, the system under deterministic excitation is first modeled and examined in the primary and subharmonic resonance regions. Typical response behaviors including coexistence of attractors and (global) jump phenomena are observed. Governing equations of the probability for the response–amplitude perturbations (a local transition) within an attraction domain and a jump between different attraction domains (a global transition) are derived under the assumption of a stationary Markov condition. The overall response–amplitude probability distribution is obtained by applying the Bayes formula to the two types of response transition probability distributions. In this study, we focus on understanding the physics of the transitions using the proposed probability method.