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

The static pull-in instability of beam-typemicro-electromechanical systems is theoretically investigated. two engineering cases including cantilever and double cantilevermicro-beamare considered. considering themid-plane stretching as the source of the nonlinearity in the beambehavior, a nonlinear size-dependent euler-bernoulli beammodel is used based on a modified couple stress theory, capable of capturing the size effect. by selecting a range of geometric parameters such as beamlengths, 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 the micro cantilever beam. the network has four inputs of length, width, gap and the ratio of height to scale parameter of the 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 fromthe neural networkmodel 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 the cantilever micro-beam.