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Nonlinear Vibration Analysis of Functionally Graded Nanobeam Using Homotopy Perturbation Method

Nonlinear Vibration Analysis of Functionally Graded Nanobeam Using Homotopy Perturbation Method
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Year:    2017

Author:    Majid Ghadiri, Mohsen Safi

Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 1 : pp. 144–156

Abstract

In this paper, He's homotopy perturbation method is utilized to obtain the analytical solution for the nonlinear natural frequency of functionally graded nanobeam. The functionally graded nanobeam is modeled using the Eringen's nonlocal elasticity theory based on Euler-Bernoulli beam theory with von Karman nonlinearity relation. The boundary conditions of problem are considered with both sides simply supported and simply supported-clamped. The Galerkin's method is utilized to decrease the nonlinear partial differential equation to a nonlinear second-order ordinary differential equation. Based on numerical results, homotopy perturbation method convergence is illustrated. According to obtained results, it is seen that the second term of the homotopy perturbation method gives extremely precise solution.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2015.m899

Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 1 : pp. 144–156

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Homotopy perturbation method Lindstedt-Poincare method analytical solution nonlocal nonlinear free vibration functionally graded nanobeam.

Author Details

Majid Ghadiri

Mohsen Safi

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