Linear free vibration of micro-/nano-plates with cut-out in thermal environment via modified couple stress theory and Ritz method

Abstract

This article aims to study the natural frequency of defective micro-/nano-plates because not only the existence of cut-outs in plates may be essential on the basis of their desired functionality but also the resonant frequency can be changed by cut-outs. In this study, the modified couple stress theory is combined with Kirchhoff thin plate hypothesis to incorporate size effect to classical plate theory. The Rayleigh-Ritz method is employed to derive discrete equations of motion which yields eigenvalue problem. In the ‘numerical results’ section, the effects of different boundary conditions, location of the cut-out, side-length to thickness ratio and a rise in the temperature on dimensionless fundamental frequency of polysilicon micro-plates are studied. Results demonstrate that the natural frequency of micro-plate, the cut out of which is far from the plate center is more than that of micro-plate with a square hole close to the plate center.