Free vibration analysis for micro-structures used in MEMS considering surface effects

Based on state space method, a three-dimensional (3-D) approach is proposed to study the size-dependent dynamical properties of micro-structures considering surface effects. The structure is modeled as a laminate composed of a bulk bounded with upper and bottom surface layers, which are allowed to have different material properties from the bulk layer. On the basis of 3-D fundamental elasticity, the state equations, including the surface properties of the structure, can be established to analyze the size-dependent dynamic responses of the plate-like thin film structures used in MEMS. To show the feasibility of the proposed approach, a simply supported plate-like thin structure, including the surface layers, is considered. An algorithm strategy is proposed for the calculation of the state equations obtained to ensure that the numerical results can reveal the surface effects clearly even for extremely thin surface layers. Comparing with the two-dimensional plate theories based size-dependent models for the thin film structures in literature, the present 3-D approach is exact, which can provide benchmark results to assess the accuracy of various 2-D plate theories and numerical methods. Numerical tests prepared for the prediction of natural frequency are carried out to illustrate the surface effects. Some discussions and conclusions are presented based on the results of the numerical examples. (C) 2008 Elsevier Ltd. All rights reserved.