Dynamic modeling and nonlinear vibrations of a rotating poly-crystalline silicon microplate based on the modified couple stress theory

A novel dynamic modeling method is proposed for a rotating cantilever poly-crystalline silicon microplate which is the core element of the micro-electro-mechanical system in this work. The natural vibration characteristics and complicated nonlinear dynamic responses of the rotating rectangular cantilever microplate are investigated in detail. Considering the nonlinear coupling deformation terms derived from the lateral deformation, the strain energy and kinetic energy of the system are determined by using the modified couple stress theory. The discrete governing equations of the system are derived by employing the Lagrange equations and the Chebyshev polynomials. The accuracy and validity of the present method for the rotating rectangular cantilever microplate are demonstrated by the convergence and comparison studies of the dynamic response and modal characteristics. Finally, the effects of the size-dependency, dimensionless rotational angular velocity and aspect ratio on dynamic properties are investigated through numerical analysis. It is shown that the stiffness of the microplate will change when the size effects are considered, which results in an increase of natural frequency but a decrease of dynamic responses accordingly. Besides, the complex influences of the rotating velocity and the aspect ratio on the dynamic characteristics are discussed in the present work.