Analytical investigation of vibration behavior of damaged micro sensor based on modified couple stress theory

Due to the extensive development and increasing use of microsystems, it is important to predict the behavior of these structures, especially their vibration behavior. In this study, a micro sensor that has been damaged by a crack is investigated. The damaged micro sensor is modeled as a micro beam with a crack. In this modeling, the crack is modeled as a torsion spring. In the modeling, flexoelectric effect, piezoelectric effect, and electric field caused by the applied voltage have been considered. After mathematical modeling, the governing equations have been extracted using Hamilton's principle based on the modified couple stress theory(MCST). The results of the analytical solution of the equations show that increasing the voltage applied to the micro sensor causes the natural frequency to increase and increasing the piezoelectric constant causes the effective stiffness of the micro structure to increase and as a result the natural frequency increases. Also, the results show that changing the flexoelectric constant in the micro sensor does not significantly change the natural frequency of the system.