Investigating bi-stability of pressurized piezoelectric micro-plates based on the modified couple stress theory

Recently, it has been substantiated that besides initially curved micro-structures, pressurized flat micro-plates can also experience snap-through instability. Given the potential applications of these micro-plates in designing high-sensitive sensors, the present work aims to investigate the bi-stable behavior of such structures when they are integrated with a piezoelectric layer. To this end, the modified couple stress theory together with the geometric nonlinear Kirchhoff plate model are employed. Hiring Galerkin’s method, the reduced governing equilibrium and stability equations are then achieved. The limit points associated with the micro-plate equilibrium path are then determined through the simultaneous solution of these equations. The present findings are compared and validated by available results in the literature. The influence of the piezoelectric actuation on the bi-stable response of the system is then investigated. The results reveal that the shape of the micro-plate equilibrium path and the number and the position of its limit points can seriously be affected by applying the piezoelectric voltage. Despite the previous studies, the present paper shows that applying positive piezoelectric voltage does not decrease the pull-in threshold of the system all the time and can sometimes increase it when the micro-plate undergoes large differential pressures. Furthermore, the results reveal that applying positive piezoelectric voltages expands the snapping zone while negative ones downsize this region. The present results can be very useful for MEMS engineers.