Abstract In this paper, a nonlinear Timoshenko beam model is considered to analytically investigate post-buckling and nonlinear vibration of flexible fluid-conveying pipes made of functionally graded materials. Closed-form expressions are presented to study the effects of shear deformation and rotary inertia on the post-buckling behavior and nonlinear vibration of fluid-conveying functionally graded pipes for the first time. It is assumed that the material property of the functionally graded material pipe is changed continuously along the direction of the pipe wall thickness based on a simple power law. Considering the Von-Karman nonlinear strain components and using the Hamilton's principle, the nonlinear governing equations for vibration and buckling of the functionally graded pipe conveying fluid are derived. These nonlinear governing equations are discretized by applying the Galerkin's procedure. The homotopy analysis method is employed to determine the closed-form expressions for the nonlinear frequency and the time history of vibration of the functionally graded pipe. The influences of rotary inertia and shear deformation on the buckling behavior, critical fluid velocity, nonlinear frequency and non-dimensional amplitude of the system are investigated and discussed in detail. The effects of physical parameters of the pipe conveying fluid on the divergence fluid velocity are studied by considering polypropylene random and functionally graded polymer pipes. The numerical results attest to the importance of considering rotary inertia and shear deformation in analyzing of short functionally graded material pipes especially for stiffer materials with higher initial amplitudes.

中文翻译：

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考虑转动惯量和剪切变形效应的功能梯度管道输送流体非线性振动和后屈曲解析解

摘要 在本文中，非线性Timoshenko 梁模型被认为是分析研究由功能梯度材料制成的柔性流体输送管道的后屈曲和非线性振动。首次提出了封闭形式的表达式来研究剪切变形和旋转惯性对流体输送功能梯度管道的后屈曲行为和非线性振动的影响。假设功能梯度材料管材的材料特性沿管壁厚度方向根据简单的幂律不断变化。考虑Von-Karman非线性应变分量，利用哈密顿原理，推导出功能梯度管道输送流体振动和屈曲的非线性控制方程。这些非线性控制方程通过应用伽辽金程序进行离散化。采用同伦分析法确定功能梯度管道非线性频率和振动时程的闭式表达式。详细研究和讨论了转动惯量和剪切变形对系统屈曲行为、临界流体速度、非线性频率和无量纲振幅的影响。考虑聚丙烯无规和功能梯度聚合物管道，研究管道输送流体物理参数对发散流体速度的影响。