@Article{AAMM-9-1,
author = {Majid, Ghadiri and Safi, Mohsen},
title = {Nonlinear Vibration Analysis of Functionally Graded Nanobeam Using Homotopy Perturbation Method},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2017},
volume = {9},
number = {1},
pages = {144--156},
abstract = {<p style="text-align: justify;">In this paper, He&#39;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&#39;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&#39;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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2015.m899},
url = {https://global-sci.com/article/73243/nonlinear-vibration-analysis-of-functionally-graded-nanobeam-using-homotopy-perturbation-method}
}