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Abstract With the development of the micro-electric-mechanical system (MEMS) technology, MEMS devices, such as micro resonators, sensors and actuators, have been applied more and more extensively. Micro-plate is one of the key components of these MEMS devices. The dynamic characteristics of micro-plate have gained more and more attention from a growing number of scholars. At present, the existing theoretical models including surface effects are mainly developed for the single-layer thin plates. However, the micro-plates are usually bilayered or multilayered structures in practical applications. Therefore, considering the structure of resonators in micro biochemical sensors, the governing equations of the bilayered circular plate including surface effects are developed based on the Kirchhoff plate theory and continuum surface elasticity theory in this paper. The displacement field of the bilayered circular micro-plate with a neutral surface unknown beforehand is given. The Galerkin method is employed to obtain the approximate results. The influences of surface effects and surface residual stress on the natural frequency of the bilayered circular plate are discussed. The comparison shows that the natural frequency of the presented model is obviously different form that of the existed circular plate model. For different thicknesses and thickness ratios, the natural frequencies obtained by the existed model are either larger or smaller than the actual value. For the bilayered circular micro-plate including both stiffened and softened surface effects, the critical value of the thickness ratio is 0.6. Considering the surface residual stress, when the normalized tension parameter k is smaller than 4, the natural frequency of the bilayered micro-plate increases slowly. When k is larger than 4, the natural frequency increases rapidly with the increase of surface residual stress. For the study and design of resonators with bilayered structure, the results of the presented model are more accurate than the existing theoretical models.
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Received: 22 June 2020
Published: 14 April 2021
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2021, Vol. 42 
