复杂耦合动力系统振动响应的统计估计方法研究

摘要

复杂耦合动力系统是一种常见的工程力学系统,分析了复杂耦合动力系统振动响应的统计估计问题.首先通过动态系统的统计能量分析(SEA)方程,应用扰动法推导随机系统的能量平衡方程,进而推导复杂耦合系统响应的统计估计公式.在分析复杂耦合系统的响应统计估计时,重点分析各种形式激励对系统响应统计估计的影响以及载荷参数的确定方法.分析表明,相互独立的载荷作用是相关载荷作用时的一种特殊情况,它们可以应用统一的计算公式来表达.根据建立的响应统计估计方法,设计了相应的试验件,验证其正确性,试验结果表明,应用该推导得到的理论公式,系统响应的相对偏差能有效的减小,得到的能量平均值能够与试验值较好地吻合.%The statistical characteristics of vibrational response of a coupled dynamical system were analyzed here.At first, the equation of energy balance of a random dynamical system was gained based on statistical energy analysis (SEA).Then, the statistical estimation expression was deduced for the vibrational response of the coupled dynamical system.the influence of all kinds of excitation on the statistical estimation and the method of determining loading parameters were analyzed.It was shown that the independent excitation is a special case of correlated-excitations, they can be expressed with an uniform expression.Test samples were designed to validate the correctness of the method based on the estimation expression.The experimental results showed that the statistical analysis method proposed is more accurate than the existing ones, it can reduce the relative deviation of vibrational response effectively.