International Journal of Aerospace and Lightweight Structures, Volume (2), No (3), Year (2012-12) , Pages (317-334)

Title : ( Analytical Approximations to Nonlinear Vibration of a Clamped Nanobeam in Presence of the Casimir Force )

Authors: Amir Reza Askari , Masoud Tahani ,

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Abstract

In this paper, combination of the Galerkin decomposition procedure and homotopy analysis method (HAM) is used to derive analytical approximate solutions for oscillatory behavior of a nanobeam under the effect of the Casimir force. The model accounts for the inherent nonlinearity of the Casimir force, and the geometric nonlinearity of mid-plane stretching. It is found that stable equilibrium does not exist if the Casimir force parameter defined in this paper exceeds its critical value and Casimir dynamic pull-in instability has been accrued. Using numerical integration, the critical value of the Casimir force parameter is also presented. Furthermore a parametric study investigated the effects of design parameters such as applied axial loads and the aspect ratio of the nanobeam. It is found that there is a linear relationship between critical value of the Casimir force parameter and applied axial loading in constant aspect ratio of nanobeam and the value of dynamic Casimir pull-in parameter is around 87% of the static counterpart. Additionally, the HAM is optimized to accelerate the convergence of approximate solutions. The presented results are found to agree well with those obtained by the fourth-order Runge-Kutta method as well as the available results in the literature for static pull-in case.

Keywords

, Galerkin decomposition method, Homotopy analysis method, Casimir force, Static and Dynamic pull-in instability
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@article{paperid:1033810,
author = {Askari, Amir Reza and Tahani, Masoud},
title = {Analytical Approximations to Nonlinear Vibration of a Clamped Nanobeam in Presence of the Casimir Force},
journal = {International Journal of Aerospace and Lightweight Structures},
year = {2012},
volume = {2},
number = {3},
month = {December},
issn = {2010-4286},
pages = {317--334},
numpages = {17},
keywords = {Galerkin decomposition method; Homotopy analysis method; Casimir force; Static and Dynamic pull-in instability},
}

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%0 Journal Article
%T Analytical Approximations to Nonlinear Vibration of a Clamped Nanobeam in Presence of the Casimir Force
%A Askari, Amir Reza
%A Tahani, Masoud
%J International Journal of Aerospace and Lightweight Structures
%@ 2010-4286
%D 2012

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