Journal
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
Volume 9, Issue 1, Pages 144-156Publisher
GLOBAL SCIENCE PRESS
DOI: 10.4208/aamm.2015.m899
Keywords
Homotopy perturbation method; Lindstedt-Poincare method; analytical solution; nonlocal nonlinear free vibration; functionally graded nanobeam
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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 non-local 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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