Electroelastic high-order computational continuum strategy for critical voltage and frequency of piezoelectric NEMS via modified multi-physical couple stress theory

piezoelectric structures can be used in many systems, such as nano-electromechanical systems (NEMS) and micro-electro-mechanical systems (MEMS) devices. This research aims to study a 2Dnumerical nth-order solution strategy for investigating the stability and frequency characteristics of the nano-sized rectangular plate made of electrically materials. For modeling size-dependent factors of the piezoelectric NEMS, modified nonlocal couple stress theory (MNCST) with one length scale parameter and one nonlocal factor is presented. This theory adds symmetric rotation gradient tensor to the strain components. Also, the nonlocal theory is coupled with the time domains. First-order shear deformation plate theory (FSDT) is utilized for modeling the electrically nanoplate structure. Hamilton's principle is used for obtaining the governing equations of the current nanostructure. Consequently, an attempt is carried out to investigate the impacts of the geometry of nanoplate, applied voltage, length scale, and nonlocal parameters on the frequency performance of the three-dimensional nano-sized electrically plate. The results show that, When the foundation is considered, the effect of the length of the nanoplate on the critical voltage of a piezoelectric nanoplate reduces. As another important outcome, there is a direct relation between l/h factor and dynamic stability of the piezoelectric nanoplate, but at the greater value of l/h factor, there is not any change in the frequency of the nanosystem due to increasing this factor.