Nonlinear vibration analysis of a partially coated circular microplate under electrostatic actuationpartially coated circular microplate under electrostatic actuation

Abstract

This paper investigates the optimal configuration for a partially two-layered circular capacitive microplate subjected to AC-DC electrostatic actuation. To this end, the static deflection due to DC electrostatic actuation, natural frequency of vibration about static position and primary resonance response due to AC electrostatic actuation are studied. Primarily, the nonlinear equations of motion are derived through classical laminated plate theory (CLPT). Then, the static position and natural frequency of vibration around static position are obtained using Galerkin approach. The linear mode shapes of non-uniform microplate i.e. a microplate coated as partial by a second layer are used as comparison functions. The forced vibration equations around static position are separated using Galerkin method, and solved by the multiple scale perturbation theory. Firstly, the impact of changes in the second layer radius on the variations of static and dynamic response of the system is studied while its thickness remains constant. Then, the effect of changes in the second layer thickness is studied while its radius remains constant. Finally, the impact of simultaneous change in the radius and thickness of the second layer is studied while its volume remains constant.