Abstract This paper presents a novel time-domain method for non-stationary random vibration analysis of linear structures. Specifically, using the well-known spectral representation method, the stochastic excitation process is first decomposed into a set of trigonometric basis functions (TBFs) modulated by a series of orthogonal basis random variables (BRVs). Next, each TBF is used as a deterministic excitation input for the structural model, and the induced structural responses are derived analytically using the modal superposition method. After superposition of each TBF-induced deterministic responses, an explicit closed-form expression between the structural stochastic responses and the BRVs is derived, based on which the response statistics of structures at any time instant can be evaluated easily. Furthermore, the accuracy of the solution is independent of the time step used. Finally, several numerical examples in civil engineering, including a Euler beam under stochastic moving load and a shear frame structure subjected to uniformly modulated or fully non-stationary seismic motions, are studied to illustrate the performance of the proposed method. The obtained structural response statistics are compared with the solutions obtained by the Monte Carlo and evolutionary spectral methods. The results verified the high accuracy and efficiency of the proposed method.

中文翻译：

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一种精确有效的时域方法，用于线性结构在均匀调制或完全非平稳激励下的随机振动分析

摘要 本文提出了一种用于线性结构非平稳随机振动分析的新时域方法。具体来说，使用众所周知的谱表示方法，首先将随机激励过程分解为一组由一系列正交基随机变量（BRV）调制的三角基函数（TBF）。接下来，每个 TBF 被用作结构模型的确定性激励输入，并使用模态叠加方法解析导出诱导结构响应。在将每个 TBF 引起的确定性响应叠加后，推导出结构随机响应和 BRV 之间的显式闭合表达式，基于该表达式可以轻松评估结构在任何时刻的响应统计数据。此外，解决方案的准确性与所使用的时间步长无关。最后，研究了土木工程中的几个数值例子，包括随机移动载荷下的欧拉梁和受到均匀调制或完全非平稳地震运动的剪切框架结构，以说明所提出方法的性能。将获得的结构响应统计量与通过蒙特卡罗和进化谱方法获得的解进行比较。结果验证了所提出方法的高精度和高效率。研究以说明所提出方法的性能。将获得的结构响应统计量与通过蒙特卡罗和进化谱方法获得的解进行比较。结果验证了所提出方法的高精度和高效率。研究以说明所提出方法的性能。将获得的结构响应统计量与通过蒙特卡罗和进化谱方法获得的解进行比较。结果验证了所提出方法的高精度和高效率。