Nonlinear free and forced vibrations of porous functionally graded pipes conveying fluid and resting on nonlinear elastic foundation

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 Kármán 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.