The classical random vibration theory has been well developed with broad applications, and the efficiency of analysis for random vibration has been improved by the pseudo-excitation method. However, random analysis for structural vibration under non-Gaussian excitation remains a substantial challenge. In this work, higher-order statistics for the response of the multiple-degree-of-freedom linear structure under stationary non-Gaussian excitation is analyzed, and a novel high-order analysis method is presented. Firstly, an analytical solution for the higher-order statistics of response is derived based on the mode superposition method, which is named the complete high-order combination method. Secondly, the expression for calculating higher-order moment spectrum of response is theoretically deduced. In contrast, the conventional pseudo-excitation method is just a particular case of the proposed method. Meanwhile, a novel and practical response analysis method is presented on the basis of the time-domain explicit formulation method. The higher-order moment spectrum of response can readily be achieved by the known response. Finally, two examples are investigated to demonstrate the effectiveness of the proposed method.

经典的随机振动理论得到了很好的发展和广泛的应用，伪激励方法提高了对随机振动的分析效率。然而，非高斯激励下结构振动的随机分析仍然是一个巨大的挑战。在这项工作中，分析了多自由度线性结构在平稳非高斯激励下的响应的高阶统计量，并提出了一种新的高阶分析方法。首先，基于模态叠加法推导出响应高阶统计量的解析解，称为完全高阶组合法。其次，从理论上推导出响应高阶矩谱的计算表达式。相比之下，传统的伪激励方法只是所提出方法的一个特例。同时，在时域显式公式的基础上，提出了一种新颖实用的响应分析方法。响应的高阶矩谱可以很容易地通过已知的响应来实现。最后，研究了两个例子来证明所提出方法的有效性。