In this paper, the stochastic properties of a uniform Timoshenko cantilever beam are investigated systematically. Based on the external viscous damping and Kelvin–Voigt viscoelastic damping, the partial differential equations of the Timoshenko beam subjected to random excitation are derived. The applied load is the concentrated force, and the excitation related to includes the ideal white noise, the band-limited white noise, and the exponential noise. Expressions are obtained for the space–time correlation functions and the space–frequency power spectral density functions of the transverse displacement response. The evident improvement is that the infinite integral and the definite integration in the mean square responses are worked out by means of the residue integral method and the integration by partial fraction, and the exact solutions of the mean square response are obtained in the form of an infinite series finally. This improvement provides a basis for both the mode truncation and the modal cross-spectral densities whether which can be ignored. Providing the numerical example, the numerical results obtained show the effectiveness of the theoretical analysis.

中文翻译：

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不同随机过程下粘弹性Timoshenko悬臂梁的稳态随机振动

本文系统地研究了均匀铁木辛哥悬臂梁的随机特性。基于外部粘性阻尼和 Kelvin-Voigt 粘弹性阻尼，推导出了随机激励下 Timoshenko 梁的偏微分方程。施加的载荷为集中力，与此相关的激励包括理想白噪声、带限白噪声和指数噪声。获得了横向位移响应的时空相关函数和空频功率谱密度函数的表达式。明显的改进是，均方响应中的无限积分和定积分是通过残差积分法和偏分数积分法计算出来的，最终以无穷级数的形式得到均方响应的精确解。这种改进为模式截断和模态交叉谱密度提供了基础，是否可以忽略。给出数值例子，得到的数值结果表明了理论分析的有效性。