Equivalent viscous damping of bilinear hysteretic oscillators

An improved formula to determine the equivalent viscous damping ratio of a single-degree-of-freedom (SDOF) bilinear oscillator is proposed in this paper, which simultaneously considers the influence of the initial period, ductility ratio, and strain hardening ratio. A large number of parameters are considered in order to present comprehensive results. Based on the assumption of secant stiffness, several equivalent linearization approaches are evaluated through parametric analyses. Then, optimization analyses are performed using a genetic algorithm to identify the variation trend of optimal damping ratios. A new formula of an equivalent viscous damping ratio is proposed by nonlinear regression analyses of the optimal damping ratios. Finally, the proposed approach is validated and the results show that the proposed approach leads to better estimates of maximum inelastic displacement response in the entire parameter space considered in this study when compared with other equivalent linearization approaches.