Nonstationary random vibration problems of nonlinear fractional systems are challenging and drawing increasing attention. This study presents an efficient numerical method for the random vibration analysis of large-scale nonlinear fractional systems subjected to fully nonstationary excitations. Firstly, the fast Fourier transform (FFT)-based frequency domain method originally proposed for the nonstationary random vibration analysis of linear integer-order systems is extended to linear fractional systems, in which the explicit expression of dynamic responses of fractional systems is derived based on the load superposition principle and Newmark method. Secondly, an equivalent linearization analysis framework is constructed to solve the nonstationary responses of hysteretic systems with fractional derivatives, in which the nonstationary response analyses of equivalent linear systems are accomplished by the FFT-based frequency domain method. The presented method can account for nonstationary excitations with arbitrary forms of evolutionary power spectrum, even of the non-separable one. Two numerical examples are used to confirm its superior performance in terms of accuracy and computational efficiency.

中文翻译：

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基于 FFT 频域法的分数阶导数滞回系统非平稳随机振动分析


非线性分数系统的非平稳随机振动问题具有挑战性并引起越来越多的关注。本研究提出了一种有效的数值方法，用于对完全非平稳激励下的大规模非线性分数系统进行随机振动分析。首先，将最初提出的用于线性整数阶系统非平稳随机振动分析的基于快速傅里叶变换（FFT）的频域方法扩展到线性分数阶系统，其中基于荷载叠加原理和纽马克法。其次，构建了求解分数阶导数滞环系统非平稳响应的等效线性化分析框架，其中基于FFT的频域方法完成了等效线性系统的非平稳响应分析。所提出的方法可以解释具有任意形式的演化功率谱的非平稳激励，甚至是不可分离的。通过两个数值例子证实了其在准确性和计算效率方面的优越性能。