摘 要：复杂耦合动力系统是一种常见的工程力学系统，本文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，应用本文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。

Abstract: The statistical characteristics of vibrational response to coupled dynamical system were analyzed in this paper. At first, the equation of energy balance on random dynamical system was gained based on statistical energy analysis (SEA). Then, the statistical estimated expression was proposed on vibrational response of coupled dynamical system. It mainly analyses the influence to the statistical estimation of all kinds of inputs forms and the confirming method of the loading parameters when analysis the statistical characteristics of vibrational response of complicated coupled dynamical system. Its show that the condition of independent- excitations was a special case of correlated-excitations, they could be expressed by uniform expression. Experimental sample was designed to validate the correctness of the method based on the estimated expression. The experimental results show that the proposed statistical analysis method was of more accuracy than the existent result, and it can reduce the relatively deviation of vibrational response effectively.