1/2分数阶线性随机动力系统的非平稳响应解析解

提出随机激励作用下1/2分数阶线性系统非平稳响应解析解的一种新方法.首先，利用特征向量展开得到1/2分数阶阻尼系统的脉冲响应函数解析表达；之后，基于Laplace变换计算得到响应功率谱密度的解析表达式和系统均方响应.通过白噪声、调制白噪声和调制修正金井清谱三种不同随机激励类型的数值算例，利用与蒙特卡洛模拟所得结果对比证明该方法的准确性和适用性.

Analytical solution for non stationary response of 1/2 order fractional linear stochastic dynamical systems

In this paper, a novel method is proposed to obtain an analytical solution for the non-stationary response of 1/2 order systems under stochastic excitation. The method first uses the eigenvector expansion to obtain the analytical expression of the impulse response function. Next, an analytical solution for the response power spectral density is obtained based on the Laplace transform. Through three illustrative numerical examples, including systems subjected to white noise, modulated white noise, and modulated colored noise with modified Kanai-Tajimi spectrum, the responses of the fractional systems are obtained analytically and compared to the pertinent Monte Carlo estimates to demonstrate the accuracy and applicability of the proposed method.