To overcome complexities and shortcomings of previous studies, a new method is proposed to derive an equivalent linear model for predicting seismic hysteretic energy demand of bilinear single degree of freedom (SDOF) models. A new displacement spectrum is defined, which represents hysteretic energy. It is found that by increasing initial period and damping of a nonlinear system in the correct proportion and defining a linear model with these characteristics, the new developed displacement can be achieved. Error minimization is applied through an algorithm to find the optimum equivalent period corresponding to an equivalent damping utilizing two sets of far‐field and near‐field earthquakes. To analyze the effects of stiffness degradation, the proposed algorithm has been implemented on modified Clough hysteretic model as well. Comparing the results, effects of stiffness degradation on the ratio of equivalent to initial period is evident in the short period range, while with increasing initial period, the effect can almost be neglected at higher values of ductility. Nonlinear regression analysis is carried out to provide the equations for predicting equivalent linear parameters as a function of ductility. Despite the previous predictive equations, the proposed model is independent of earthquake characteristics and response‐related parameters, which has increased efficiency as well as simplicity.

中文翻译：

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关于考虑刚度衰减效应的地震滞回能量需求的等效线性化方法的建议

为了克服先前研究的复杂性和不足，提出了一种新的方法来推导等效线性模型，以预测双线性单自由度（SDOF）模型的地震滞回能量需求。定义了一个新的位移谱，它代表了滞回能。发现通过以适当的比例增加初始周期和非线性系统的阻尼并定义具有这些特征的线性模型，可以实现新开发的位移。通过算法应用误差最小化，以利用两组远场和近场地震来找到与等效阻尼相对应的最佳等效周期。为了分析刚度退化的影响，在改进的Clough滞回模型上也实现了该算法。比较结果 刚度降低对初始当量比的影响在短时期内很明显，而随着初始时期的增加，在较高的延性值下几乎可以忽略不计。进行了非线性回归分析，以提供等式来预测作为延展性函数的等效线性参数。尽管有先前的预测方程，但所提出的模型与地震特征和与响应有关的参数无关，从而提高了效率并简化了操作。进行了非线性回归分析，以提供等式来预测作为延展性函数的等效线性参数。尽管有先前的预测方程，但所提出的模型与地震特征和与响应有关的参数无关，从而提高了效率并简化了操作。进行了非线性回归分析，以提供方程来预测等效线性参数随延展性的变化。尽管有先前的预测方程，但所提出的模型与地震特征和与响应相关的参数无关，从而提高了效率并简化了操作。