Abstract This paper studies the nonlinear free and forced vibrations of fluid-conveying pipes that are made of porous functionally graded materials and supported on nonlinear elastic foundation. A modified power-law function is adopted to model the porous functionally graded materials, with both even and uneven porosity distributions to represent different material imperfections. Equations of motion of the pipe system are then derived through Hamilton’s principle based on Euler–Bernoulli beam theory, with foundation and von Karman nonlinearities and damping effect being considered. The nonlinear free vibration and the primary resonance of the pipe system are investigated analytically, by employing the variational iteration method and the direct method of multiple scales, respectively. Detailed parametric studies for the free and forced vibrations are then carried out numerically, considering different parameters including power-law index, porosity characteristics, fluid velocity, pipe geometries, foundation parameters and so on.

中文翻译：

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非线性弹性基础上输送流体的多孔功能梯度管道的非线性自由振动和受迫振动

摘要 本文研究了由多孔功能梯度材料制成并支撑在非线性弹性基础上的流体输送管道的非线性自由振动和受迫振动。采用修正的幂律函数对多孔功能梯度材料进行建模，具有均匀和不均匀的孔隙率分布以表示不同的材料缺陷。然后通过基于欧拉-伯努利梁理论的哈密顿原理推导出管道系统的运动方程，其中考虑了基础和冯卡曼非线性和阻尼效应。分别采用变分迭代法和多尺度直接法对管道系统的非线性自由振动和一次共振进行了解析研究。