Estimation of pull-in instability voltage of Euler-Bernoulli micro beam by back propagation artificial neural network

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The static pull-in instability of beam-type micro-electromechanical systems is theoretically investigated. Two engineering cases including cantilever and double cantilever micro-beam are considered. 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. By selecting a range of geometric parameters such as beam lengths, width, thickness, gaps and size effect, we identify the static pull-in instability voltage. Back propagation artificial neural network with three functions have been used for modeling the static pull-in instability voltage of micro cantilever beam. The network has 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 network and capabilities of the model in predicting the pull-in instability behavior has been verified. The output obtained from neural network model is compared with numerical results, and the amount of relative error has been calculated. Based on this verification error, it is shown that the back propagation neural network has the average error of 6.36% in predicting pull-in voltage of cantilever micro-beam.