| The microresonator plays an important role in the Micro-Electro-Mechanical System(MEMS)、and it acts as a sensor of which the main function is to convert mechanical energy to other forms of energy,so as to realize energy transfer.Quality factor and resonant frequency are two key parameters of a MEMS resonator,and they are signi ficant indicators to measure the vibration characteristics of the microresonator at work.Therefore,it is necessary to predict the resonant frequency and quality factor accurately in the relevant design of MEMS.Energy loss has been limiting the promotion of overall performance of microresonators,which has an important impact on the quality factor of microresonators.In fact,there are many kinds of energy loss in microresonators,and the thermoelastic damping mechanism is one of the most important loss mechanisms.Thermoelastic damping is caused by the irreversible internal friction of thermoelastic structural materials,and it is inevitable in all microresonators at work.Therefore,the study of thermoelastic damping has always been a hot topic in the field of MEMS.At present,most of studies about thermoelastic damping are carried out in those microresonators with the simple beam,plate or ring structure,but with the increasing demand for microresonators,the application range is wider and wider,and microresonators with the complex structur have also produced a certain application significance.The main structure material of microresonators is the semiconductor material Si,but the practical application range of the microresonator with the homogeneous single-layer silicon structure is limited.If the surface of microresonator is fixed with another material by electroplating process,the surface correlation characteristics of microresonators can be changed,and the overall conductivity or the reflectivity can be improved.Therefore,there are more and more studies on multi-layer composite microresonators with the silicon micro-plate structure.Actually,an analytical model of one-dimensional thermoelastic damping in a bilayered rectangular microplate resonator has been established,but in this model,the energy loss along the thickness direction of the plate is merely considered.Therefore,in order to obtain more accurate thermoelastic damping characteristics in the bilayered rectangular micro-plate,the paper aims to establish the theoretical model of three-dimensional thermoelastic damping in the bilayered rectangular microplate resonators,and the heat conduction along the thickness,length and width of the plate is comprehensively considered.The cantilever,fixed-fixed,and fully clamped rectangular microplate resonator are taken as the study objects,and the main work of this paper is as follows:(1)The analytical modeling of thermoelastic damp in the rectangular plate microresonator under fully clamped,fixed-fixed and cantilever boundary conditions is carried out,respectively.Firstly,the maximum elastic potential energy stored in the bilayered micrplate is solved according to the relevant mechanics theory of the elastic plate,and then the distribution function of the temperature field along length,width and thickness direction is solved by the generalized orthogonal function method,respectively.Subsequently,the total energy dissipated in the bilayered microplate at work is calculated.Finally,thermoelastic damping is solved based on Bishop and Kinra theory.(2)The equivalent comparison between three-dimensional thermoelastic damping models of the present bilayered rectangular microplate resonator and the previous single-layer homogeneous rectangular microplate resonator under fully clamped,fixed-fixed and cantilever boundary conditions is carried out,respectively.Assuming that materials in the bilayered plate are identical,the three-dimensional thermoelastic damping model is rederived,so a new analytical expression of three-dimensional thermoelastic damping is obtained.Then According to Zener’s theory,the first term in this expression is retained,which is compared with the first term in the analytical expression of thermoelastic damping in the previous single-layer homogeneous microplate resonator.Additionally,from another point of view,the analytical results of thermoelastic damping in the two models above are analyzed and compared by the numerical analysis software,and this can verify the accuracy of the model to a certain extent.(3)The analysis on the characteristics of the present models of three-dimensional thermoelastic damping in the bilayered rectangular microplate resonator under fully clamped,fixed-fixed and cantilever boundary conditions is carried out.Based on different material combinations,the characteristics of thermoelastic damping spectrum of the three models,i.e.convergence,are analyzed,and effects of different materials on thermoelastic damping values of the three models are analyzed.Then effects of different boundary geometric sizes(length and thickness)on thermoelastic damping values of the three models are analyzed.Moreover,effects of the number of fixed edges on thermoelastic damping values of the three models are demonstrated.(4)The accuracy and feasibility of the present analytical models of three-dimensional thermoelastic damping in the bilayered rectangular microplate resonators under fully clamped,fixed-fixed and cantilever boundary conditions are verified.The numerical models of thermoelastic damp under adiabatic and isothermal boundary conditions are established by finite element software,respectively,and different boundary clamping conditions and material parameters are set up,which corresponds to the analytical models of thermoelastic damping under three boundary conditions established in this paper.Then the FEM models under adiabatic and isothermal boundary conditions and the present three-dimensional models are compared with the previous theoretical models of one-dimensional thermoelastic damping in the bilayered microplate resonators,so as to verify the accuracy and feasibility of the three models established in this paper. |
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