Static, free and forced vibration analysis of a delaminated microbeam-based MEMS subjected to the electrostatic force

In this paper, the delamination effect on the static and natural frequency response of a microbeam subjected to the nonlinear electrostatic force is studied using a semi-analytical approach for the first time. The Euler–Bernoulli beam assumption along with the non-classical modified couple stress theory is used to obtain the governing differential equation of motion and then a reduced-order model based on Galerkin’s decomposition method is obtained. At first the microbeam with very small delamination like an intact microbeam is solved and then the solution is compared with those reported in the literature and the solution obtained using 3D-coupled electromechanical software. After validation, the effects of delamination length and its locations in thickness and length directions on the microbeam behavior are investigated in details. It is shown that the delamination has remarkable effects on the characteristics of the microbeam, especially near the pull-in voltage. Also, the delaminated microbeam with various thicknesses is studied using both the classical and the non-classical theories. It is found that the difference between the two models is significant for the thin microbeam with a thickness near of below than its material length scale parameter. This investigation is helpful for the nondestructive detection of the delamination in the beams.