Free vibration analysis of bilayered circular micro-plate including surface effects

Abstract

• A new size-dependent Kirchhoff bilayered micro-plate model is developed. • A displacement field is proposed for the bilayered micro-plate. • Natural frequency is larger or smaller than those predicted by existing models. • Larger normalized effective flexural rigidity is predicted. • Transition region is expanded for stiffened surface and reduced for softened surface. Based on the Kirchhoff plate theory and the continuum surface elasticity theory, a novel model of bilayered circular micro-plates including surface effects is developed. Furthermore, the governing equation is derived, and the Galerkin method is employed to obtain approximate results. The influence of surface effects on the natural frequency of bilayered circular micro-plate is investigated. Besides, the effect of residual stresses on the transition behavior of the bilayered circular micro-plate from plate to membrane is predicted. The results are compared with the single-layer model and the modified laminated plate model. It is found that the natural frequency predicted by the present model is obviously different from that of the existing models. For different thickness ratios, the natural frequency obtained by the new model will be larger or smaller than the results of the single-layer model. The transition region from plate to membrane is expanded for stiffened surface and reduced for softened surface. The results of the novel model can provide effective guidance for the design of bilayered circular micro-plate in MEMS devices.