Table of Contents
Advances in Artificial Neural Systems
Volume 2013, Article ID 741896, 10 pages
Research Article

Estimation of Static Pull-In Instability Voltage of Geometrically Nonlinear Euler-Bernoulli Microbeam Based on Modified Couple Stress Theory by Artificial Neural Network Model

1Department of Mechanical Engineering, Aligudarz Branch, Islamic Azad University, P.O. Box 159, Aligudarz, Iran
2Faculty of Engineering, University of Shahrekord, P.O. Box 115, Shahrekord, Iran

Received 11 September 2013; Accepted 22 November 2013

Academic Editor: Ping Feng Pai

Copyright © 2013 Mohammad Heidari et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this study, the static pull-in instability of beam-type micro-electromechanical system (MEMS) is theoretically investigated. Considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. Two supervised neural networks, namely, back propagation (BP) and radial basis function (RBF), have been used for modeling the static pull-in instability of microcantilever beam. These networks have four inputs of length, width, gap, and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. Numerical data employed for training the networks and capabilities of the models in predicting the pull-in instability behavior has been verified. Based on verification errors, it is shown that the radial basis function of neural network is superior in this particular case and has the average errors of 4.55% in predicting pull-in voltage of cantilever microbeam. Further analysis of pull-in instability of beam under different input conditions has been investigated and comparison results of modeling with numerical considerations show a good agreement, which also proves the feasibility and effectiveness of the adopted approach.