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中文摘要：
一个方便、通用的残余演算方法被建议学习与随机的噪音刺激和部分顺序移动粘弹性的横梁的一个向轴的方向的随机的反应行为组成的关系在随机的刺激能作为 nonstationary 被分解的地方随机的过程， Mittag-Leffler 内部噪音，和外部静止噪音刺激。基于 Laplace 变换途径，然后，我们通过草地函数技术和残余演算方法导出吝啬的值函数，变化函数和协变性功能，并且获得了理论结果。在部分顺序衍生物的一些特殊大小写中，蒙特卡罗途径和错误功能结果被使用检查分析结果的有效性，并且好同意被发现。最后在一个通用盒子中，我们也经由直接蒙特卡罗模拟证实了分析结论。
英文摘要：
A convenient and universal residue calculus method is proposed to study the stochastic response behaviors of an axially moving viscoelastic beam with random noise excitations and fractional order constitutive relationship, where the random excitation can be decomposed as a nonstationary stochastic process, Mittag-Leffler internal noise, and external stationary noise excitation. Then, based on the Laplace transform approach, we derived the mean value function, variance function and covariance function through the Green＇s function technique and the residue calculus method, and obtained theoretical results. In some special case of fractional order derivative α , the Monte Carlo approach and error function results were applied to check the effectiveness of the analytical results, and good agreement was found. Finally in a general-purpose case, we also confirmed the analytical conclusion via the direct Monte Carlo simulation.
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