Abstract The sensitivity analysis of hysteretic systems under nonstationary random excitations is of great concern to the stochastic optimal design and control of structures. The equivalent linear equation of motion is first constructed for the hysteretic system by the equivalent linearization method (ELM), and the sensitivity equation of the equivalent linear system is then derived by the direct differentiation technique. These two equations are further combined into an overall equivalent linear equation, which depends on the statistical moments and sensitivities of responses of the system and should be solved on an iterative basis. The analysis problem is thus transformed to a series of nonstationary random vibration analyses of the iterative linearized systems, which can be solved with the explicit time-domain method (ETDM) recently proposed for linear random vibration problems. The ETDM has high computational efficiency owing to the explicit formulations of statistical moments of responses. Therefore, a numerical algorithm is developed by combining ELM and ETDM for efficient stochastic sensitivity analysis of hysteretic systems. A 100-degree-of-freedom hysteretic system is investigated to illustrate the accuracy and efficiency of the proposed method, and a 10-degree-of-freedom base-isolated system is further analyzed to show the feasibility of the proposed method for stochastic structural optimization.

中文翻译：

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基于显式时域法的地震激励下滞回系统随机灵敏度分析的迭代等效线性化方法

摘要 非平稳随机激励下滞回系统的灵敏度分析是结构随机优化设计和控制的重要课题。首先通过等效线性化方法（ELM）为滞后系统构造等效线性运动方程，然后通过直接微分技术导出等效线性系统的灵敏度方程。这两个方程进一步组合成一个整体等效线性方程，该方程取决于系统的统计矩和响应灵敏度，应在迭代的基础上求解。因此，分析问题转化为一系列迭代线性化系统的非平稳随机振动分析，这可以通过最近为线性随机振动问题提出的显式时域方法 (ETDM) 解决。由于响应统计矩的显式公式，ETDM 具有很高的计算效率。因此，通过结合 ELM 和 ETDM 开发了一种数值算法，用于对滞后系统进行有效的随机灵敏度分析。研究了一个 100 自由度滞回系统来说明所提出方法的准确性和效率，并进一步分析了一个 10 自由度基础隔离系统，以表明所提出方法对随机结构的可行性。优化。通过结合 ELM 和 ETDM 开发了一种数值算法，用于对滞后系统进行有效的随机灵敏度分析。研究了一个 100 自由度滞回系统来说明所提出方法的准确性和效率，并进一步分析了一个 10 自由度基础隔离系统，以表明所提出方法对随机结构的可行性。优化。通过结合 ELM 和 ETDM 开发了一种数值算法，用于对滞后系统进行有效的随机灵敏度分析。研究了一个 100 自由度滞回系统来说明所提出方法的准确性和效率，并进一步分析了一个 10 自由度基础隔离系统，以表明所提出方法对随机结构的可行性。优化。