Presenting a size-dependent electro-mechanical model for rectangular plates-based resonant micro-sensors based on modified couple stress theory

Rrectangular plates-based resonant micro-sensors utilize the resonance frequency of electrically pre-deformed clamped micro-plates for sensing. Free vibration analysis of such systems in order to find their resonance frequency is the objective of present paper. For this aim، the modified couple stress theory (MCST) together with the Kirchhoff plate model is considered and the size-dependent equation of motion which accounts for the effect of axial residual stresses as well as the non-linear and distributed electrostatic force is derived using the Hamilton''s principle. The lowest frequency of the system as the resonance frequency of these micro-plates is extracted using a single mode Galerkin based reduced order model (ROM). It is found that the fundamental frequency of the system is decreased with an increase of applied voltage and becomes zero when the input voltage reaches the pull-in voltage of the system. The findings of present paper are compared and validated by available results in the literature and an excellent agreement between them is observed. Also it is found that using the MCST in pull-in analysis of clamped rectangular micro-plates can remove the existing gap between the results of classical theory (CT) and available empirical observations. Furthermore، it is observed that accounting for the size-effect on free vibration analysis of electrostatically pre-deformed micro-plates is more essential than flat ones.