First-passage failure of Duhem hysteretic systems

Abstract

Mechanical and structural systems under dynamic loading always represent hysteresis behavior, which is a typical nonlinear phenomenon and lets the dynamic responses of the systems remarkably deviate from that of corresponding equivalent linear systems. The Duhem hysteretic model is versatile to cover most existing hysteresis models and to describe the hysteretic behavior more accurately, and the investigation and application of that are abundant. The combination of the equivalent nonlinearization technique, which transforms the hysteretic force into energy-depending damping and stiffness, and the stochastic averaging technique yields the best forecast for the dynamic responses. The first-passage failure of Duhem hysteretic systems, an important question in random vibration, however, remains open. The analysis of the backward Kolmogorov equation associated with the averaged Ito stochastic differential equation generates the reliability function and probability density function, and the effects of system parameters on first-passage failure are discussed concisely. The present work will guide the parameter design of the Duhem materials to decrease the probability of first-passage failure and make the Duhem systems safer.