随机激励下滞迟系统的稳态响应闭合解

发布时间：2018-09-09 15:46

【摘要】：滞迟系统属于一类典型的强非线性系统,滞迟力不仅取决于系统的瞬时变形,还与变形历程有关.虽然滞迟系统的随机振动问题已被广泛研究,但至今尚未得到滞迟系统随机响应概率密度函数的精确闭合解.本文运用迭代加权残值法获得了高斯白噪声激励下Bouc-Wen滞迟系统稳态响应概率密度函数的近似闭合解.首先,运用等效线性化法求出系统的稳态高斯概率密度函数;然后以此构造权函数,应用加权残值法求得了系统指数多项式形式的非高斯概率密度函数;最后引入迭代的过程,逐步优化权函数,提高计算所得结果的精度.以随机地震激励下钢纤维陶粒混凝土结构的稳态响应作为算例,其中Bouc-Wen模型的参数是基于拟静力学试验数据,并应用最小二乘法辨识获得.与Monte Carlo模拟结果相比,等效线性化法得到的结果精度较差;由加权残值法得到的结果能够表现出非线性特征,但其精度依然无法令人满意;采用迭代加权残值法得到的近似闭合解与Monte Carlo模拟的结果吻合非常好;对于较强随机激励情形,采用渐进迭代加权残值法具有较高的求解效率,所获得的理论解析解具有较高的精度.结果表明,所获得的近似闭合解不仅对于土木工程领域具有重要的实际应用价值,而且还可作为检验其他非线性系统随机响应预测方法的精度的标准.
[Abstract]:Hysteretic system is a kind of typical strongly nonlinear system. The hysteresis force depends not only on the instantaneous deformation of the system, but also on the deformation history. Although the stochastic vibration of hysteretic systems has been widely studied, the exact closed solution of probability density function for stochastic response of hysteretic systems has not been obtained. In this paper, the approximate closed solution of probability density function of steady-state response of Bouc-Wen hysteretic system excited by Gao Si white noise is obtained by using iterative weighted residual method. First of all, we use the equivalent linearization method to calculate the steady state Gao Si probability density function of the system, then we construct the weight function and use the weighted residuals method to obtain the non-Gao Si probability density function in the form of exponential polynomial of the system. Finally, the iterative process is introduced. The weight function is optimized step by step to improve the accuracy of the calculated results. The steady-state response of steel fiber ceramsite concrete structure under random earthquake excitation is taken as an example. The parameters of Bouc-Wen model are based on quasi-static test data and are identified by least square method. Compared with the Monte Carlo simulation results, the accuracy of the results obtained by the equivalent linearization method is poor, the results obtained by the weighted residuals method can show nonlinear characteristics, but the accuracy is still not satisfactory. The approximate closed solution obtained by the iterative weighted residual method is in good agreement with the result of Monte Carlo simulation, and for the strong random excitation case, the incremental iterative weighted residual method has a higher efficiency. The theoretical analytical solutions obtained are of high accuracy. The results show that the obtained approximate closed solutions not only have important practical application value in the field of civil engineering, but also can be used as a standard to test the accuracy of other nonlinear system stochastic response prediction methods.
【作者单位】：华侨大学土木工程学院;加州大学Merced分校工程学院;
【基金】：国家自然科学基金(11172197,11332008,11572215,11672111,51608211) 福建省自然科学基金(2013J05080) 福建省高校杰出青年科研人才培育计划华侨大学优秀青年科技创新人才(ZQN-YX307)资助项目
【分类号】：O324

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