Estimation of Static Pull-In Instability Voltage of Geometrically Nonlinear Euler-Bernoulli Microbeam Based on Modified Couple Stress Theory by Artificial Neural Network Model
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. 1. Introduction Micro-electromechanical systems (MEMS) are widely being used in today’s technology. So investigating the problems referring to MEMS owns a great importance. One of the significant fields of study is the stability analysis of the parametrically excited systems. Parametrically excited micro-electromechanical devices are ever being increasingly used in radio, computer, and laser engineering [1]. Parametric excitation occurs in a wide range of mechanics, due to time-dependent excitations, especially periodic ones; some examples are columns made of nonlinear elastic material, beams with a harmonically variable length, parametrically excited pendulums, and so forth. Investigating stability analysis on parametrically excited MEM systems is of great importance. In 1995 Gasparini et al. [2] examined the transition between the stability and instability of a cantilevered beam exposed to a partially follower load. Applying voltage difference between an electrode and ground causes the electrode to deflect towards the ground. At a critical voltage, which is known as pull-in voltage, the electrode becomes unstable and pulls in onto the substrate [3]. The static pull-in behavior of MEMS actuators has been
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