On the size-dependent behavior of a capacitive circular micro-plate considering the variable length-scale parameter

• In this paper, a micro-plate was modeled based on the modified couple stress theory, considering the variable material length-scale parameter.
• The pull-in voltage was investigated using Modified Couple Stress Theory for the fixed and variable length-scale parameters.
• In the case of gradual application of the voltage, the micro-plate experiences instability through a local saddle node bifurcation.
• In the case of applying a step DC voltage, the micro-plate experiences instability through a global homoclinic bifurcation.

This article deals with the effect of the intrinsic length-scale on the stability and fundamental frequency of a fully clamped circular micro-plate, which can be used as a RF MEMS resonator. A modified couple stress theory is utilized to model the micro-plate, considering the variable length-scale parameter. A variational formulation based on Hamilton's principle is used to obtain the nonlinear governing equation of motion. The static and dynamic pull-in phenomena, limiting the stable regions of capacitive resonators, are determined and compared to those obtained by the classical theory. The numerical results reveal that the intrinsic size dependence of materials leads to an increase in the pull-in voltage and natural frequency depending on the thickness of the micro-plate. Comparing these results with the experimental ones reveals that utilizing the fixed material length-scale leads to unrealistic results in some manner.