Non-stationary non-Gaussian random vibration problems of structures are challenging and drawing increasing attention. In the present study, firstly, an explicit time-domain method (ETDM) is proposed to determine the higher-order response statistics of linear systems subjected to non-stationary non-Gaussian random excitations, in which the first four orders of cumulants of dynamic responses are directly formulated through the cumulant operation rule based on the explicit expressions of responses. Secondly, an equivalent linearization – explicit time-domain method (EL-ETDM) is further developed to solve the non-stationary non-Gaussian random vibration problems of Duffing systems, in which the equivalent linear system is derived discarding the assumption of Gaussian response, and the corresponding higher-order cumulant analyses of the linearized system are accomplished by the efficient ETDM. The present approach can account for non-Gaussian random excitations with arbitrary forms, and two specific applications to the Poisson white noise and the square form of Gaussian random process are investigated. Four numerical examples are presented to demonstrate the effectiveness of the proposed methods.

结构的非平稳非高斯随机振动问题具有挑战性并引起越来越多的关注。在本研究中，首先，提出了一种显式时域方法（ETDM）来确定非平稳非高斯随机激励下线性系统的高阶响应统计量，其中动态的前四阶累积量基于响应的显式表达式，通过累积运算规则直接制定响应。其次，进一步发展了等效线性化-显式时域方法（EL-ETDM）来解决Duffing系统的非平稳非高斯随机振动问题，其中放弃高斯响应的假设推导等效线性系统，并且通过高效的ETDM完成了线性化系统相应的高阶累积量分析。本方法可以解释任意形式的非高斯随机激励，并且研究了泊松白噪声和高斯随机过程的平方形式的两个具体应用。提出了四个数值例子来证明所提出方法的有效性。