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Nonlinear Vibration Analysis of Functionally Graded Nanobeam Using Homotopy Perturbation Method

Part of: Elastic materials Dynamical problems Material properties given special treatment Equilibrium (steady-state) problems

Published online by Cambridge University Press:  11 October 2016

Majid Ghadiri  and
Mohsen Safi
Majid Ghadiri*
Affiliation:
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
Mohsen Safi
Affiliation:
Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
*
*Corresponding author. Email:ghadiri@eng.ikiu.ac.ir (M. Ghadiri)
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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.

Keywords

Homotopy perturbation methodLindstedt-Poincare methodanalytical solutionnonlocal nonlinear free vibrationfunctionally graded nanobeam

MSC classification

Secondary: 74G10: Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) 74H45: Vibrations 74E30: Composite and mixture properties 74B99: None of the above, but in this section
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 1 , February 2017 , pp. 144 - 156
Copyright
Copyright © Global-Science Press 2017 

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