Size-dependent dynamic pull-in analysis of beam-type MEMS under mechanical shock based on the modified couple stress theory

Size-dependent stability analysis of a fully clamped micro-electro-mechanical beam under the effect of shock acceleration pulse is the objective of present paper. The size-dependent Euler-Bernoulli beam model based on the modified couple stress theory (MCST) with von Kármán-type geometric non-linearity is utilized in theoretical formulations. The non-linear governing differential equation of motion is derived using Hamilton's principle and solved using a simple and computationally efficient single degree-of-freedom (SDOF) approach. The model's predictions based on the classical theory (CT) are compared with those obtained using the finite element method (FEM) and six modes Galerkin approximations in previous studies and an excellent agreement between them is achieved. It is shown that the present SDOF predictions agree better with the FE results than those obtained using six modes approximations for high shock accelerations. Furthermore, the present model can remove the limitation of previous models in capturing dynamic pull-in instability under enormous shock accelerations. A parametric study is also conducted to show the significant effects of couple stress components on micro-beam motion. It is found that the size effect on both dynamic pull-in voltage and maximum amplitude of micro-beam oscillations is usually negligible, when the ratio of beam thickness to the material length scale parameter is larger than 15.