Investigation On Thermoelastic Damping Of Laminated Composite Micro-Plate Resonators

Micro-sized beam and plate resonators are important components of Micro Electromechanical Systems(MEMS).However,to obtain a resonator with a high quality factor,it is necessary to minimize the internal energy consumption of thermoelastic damping(TED)through geometric dimensions and material design.Therefore,establishing a mathematical model of the resonator based on the elastic theory of thermo-elastic coupling and accurately analyzing and predicting TED has important theoretical significance for the research and design of high-quality resonators.However,in recent years,in the researches on the TED of composite material laminated micro-plate resonators,almost all of them have adopted the physical neutral surface method to eliminate the tension-bending coupling in the equation of motion,so that the mathematical model of the problem has been simplified.However,the thermal membrane forces are neglected in the physical neutral surface method.Obviously,the material property distribution in the asymmetrically laid laminated micro-plate is asymmetric with respect to the geometric midplane,and the thermal membrane forces therein is not zero.Up to now,there is no research report considering the effect of thermal membrane forces on the TED of laminated micro-plates.In view of the above research status,this thesis selects asymmetrically laid composite rectangular laminated micro-plates as the research object.According to Kirchhoff thin plate theory and the one-way coupled heat conduction theory,the analytical method is used to further study the TED in the micro-plates,quantitatively analyzing the influence of thermal membrane forces on TED and more accurately revealing the energy dissipation mechanism of the TED in composite material laminated micro-plate.The main research contents and innovation points of the thesis are as follows:1.Considering the laminated micro-plate are composited by uniform and isotropic layers with different material properties,based on the Kirchhoff thin plate theory and the one-way coupled heat conduction theory,dynamic governing differential equations of thermal-elastic coupling free vibration of micro-plate are established.By giving up the traditional physical neutral surface assumption,the influence of the thermal membrane forces caused by asymmetric laying on the vibration response is accurately considered.Using the adiabatic boundary conditions of the upper and lower surfaces and the continuity conditions at the interface,the analytical solution of the temperature field in each layer expressed by the deformation is obtained.Then the thermal membrane forces and thermal bending moments are obtained,and by substituting them into the structural vibration differential equation,using the mathematical similarity between the eigenvalue problems of free vibration,the analytical solution of complex frequency of thermo-elastic coupled vibration of composite laminated micro-plate expressed by the natural frequency of the reference uniform material plate without TED is obtained.Finally,using the complex frequency method,the analytical solution of TED is arrived at.It includes the contribution of the thermal membrane forces to the TED.2.As a calculation example,numerical results of TED in a bilayered(Si3N4 and Ni)and trilayered(three materials selected from SiC,Si3N4,Al,and Ni)rectangular micro-plates are given,respectively.Through a large number of curves and numerical tables,the influences of factors such as the geometric size of the micro-plate,the properties and volume fraction of the layered material,the order of the vibration mode and the boundary conditions on the TED are analyzed and discussed.Especially,the level of influence of the thermal membrane forces on the TED are examined in detail.The results show that:(1)The thermal membrane forces make TED increases and the maximum increment of TED can be up to 3.5%comparing with that where the thermal membrane forces are ignored;(2)The peak value of TED is independent of the order of the vibration mode,but the critical thickness decreases as the mode order increases;(3)For a double-layered plate composed of metallic nickel(Ni)and silicon nitride(Si3N4),in a certain thickness range,by optimizing the volume fraction of the component materials of the laminated plate resonator one can obtain a higher quality factor than that of the single component material resonator.3.The main innovation of this paper is to give up the traditional physical neutral surface assumption and to establish a mathematical model of thermal-elastic coupling free vibration of asymmetrically layered laminated micro-plates based on Kirchhoff thin plate theory and one-way coupled quasi-one-dimensional heat conduction theory,in which the stretching-bending coupling effect is considered accurately.The influence degree of thermal membrane forces on TED is analyzed by quantitative calculation.The research results have important theoretical significance and engineering application value for more accurately predicting the TED of multilayer micro-plate resonators.