Nonlinear vibrations of functionally graded porous micropipes conveying fluid flow

Authors

Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

In this paper, using homotopy analysis method, an analytical solution for the nonlinear free vibrations of the functionally graded porous micropipes conveying fluid flow is presented. The equations of motion are obtained based on Euler-Bernoulli beam theory and modified couple stress theory with consideration of geometric nonlinearity. It is assumed that the micropipe is porous and the porosity distribution is in three forms; uniform, non-uniform symmetric, and non-uniform asymmetric distributions. The Hamilton principle is used to obtain the governing equations of motion. Also, the Galerkin method is used to convert partial differential equations to ordinary differential equations. Finally, by considering immoveable simply-supported boundary conditions and using the homotopy analysis method, the analytical solution for the governing equations is performed. The results obtained from this method has been verified by the Runge-Kutta numerical method which shows that the homotopy analysis method has good accuracy by considering two terms of the Taylor series. The results showed that between the proposed porosity distribution schemes in the micropipe, the non-uniform asymmetric distribution pattern is the most suitable, because the microtube becomes unstable at a higher fluid velocity.

Keywords

Main Subjects

References

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Journal of Solid and Fluid Mechanics
Volume 13, Issue 2
May and June 2023
Pages 89-101

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