Application of the Tail-Equivalent Linearization Method for Stochastic Dynamic Analysis with Asymmetric Hysteresis

The tail-equivalent linearization method (TELM) is used to investigate the stationary response of a system having a highly asymmetric hysteretic behavior and subjected to a discretized white-noise excitation. The equivalent linear system is defined by equating its tail probability with the first-order approximation of the tail probability of the nonlinear response. The equivalent linear system is determined in a non-parametric form in terms of its impulse response function, which depends on the response threshold of interest. The method is able to capture the non-Gaussian and asymmetric distribution of both the point-in-time response and the extreme response over a time interval (the first-passage probability) for large thresholds (small exceedance probabilities), which are of interest in reliability analysis.