Size-dependent dynamic behavior of microcantilevers under suddenly applied DC voltage

This paper investigates the dynamic behavior of microcantilevers under suddenly applied DC voltage based on the modified couple stress theory. The cantilever is modeled based on the Euler-Bernoulli beam theory and equation of motion is derived using Hamilton's principle. Both analytical and numerical methods are utilized to predict the dynamic behavior of the microbeam. Multiple scales method is used for analytical analysis and the numerical approach is based on a hybrid finite element/finite difference method. The results of the modified couple stress theory are compared with those from the literature as well as the results predicted by the classical theory. It is shown that the modified couple stress theory predicts size-dependent normalized dynamic behavior for the microbeam while according to the classical theory the normalized behavior of the microbeam is independent of its size. When the thickness of the beam is in order of its material length scale, the difference between the results given by the modified couple stress theory and those predicted by the classical theory is considerable. As the beam thickness increases, the results of the modified couple stress theory converge to those of the classical theory.