Analysis Of Thermoelastic Damping Of Microbeam Resonator Based On Non-Fourier Heat Conduction Model

Under the background of the development and application of modern integrated circuit technology,the technology research of high performance micro(nano)electromechanical system has been widely concerned.Resonator is the main working device in micro(nano)motor system.It is found that thermoelastic damping is one of the main forms of energy loss of resonator.At present,there is a certain research foundation for the thermoelastic damping of beam,plate,ring and other common structural elements of uniform single material.Because functionally graded material devices have the characteristics of continuous change of components in a certain direction,it can realize the differential performance requirements of the used materials,and can achieve different use conditions through the design of material component distribution,which has a very broad application prospect.Therefore,in recent years,scholars have paid more and more attention to the thermoelastic damping of functionally graded material resonators.In addition,when the scale of the structure reaches micron level,the temperature changes rapidly when the free vibration is caused by the high natural frequency,and the traditional Fourier heat conduction model is used to describe the heat transfer process.Therefore,it is necessary to use the generalized heat conduction model to conduct in-depth study on the thermoelastic damping of the structure.Based on the generalized heat conduction theory,this paper studies the factors affecting the thermoelastic damping of uniform materials and functionally graded materials respectively,which provides theoretical guidance for the manufacture and engineering application of resonators.The research mainly includes:1.Based on the generalized heat conduction theory of two-phase hysteresis,the control equation of thermo-elastic coupling of Levinson microbeam with uniform material and the analytical approximate solution method of thermo-elastic damping are given.In the solution process,only the heat flow caused by the temperature gradient along the thickness direction of the beam is considered,and the axial heat flow of the beam is ignored.Subsequently,based on the generalized thermoelastic theory,the natural frequency of the uniform solid beam is calculated by the finite element method,and the thermoelastic damping of the beam is obtained.The approximate analytical solutions of thermoelastic damping of the obtained uniform material(Ni)microbeam and silicon nitride(Si3N4)microbeam are compared with the finite element calculation results,and it is found that the results are in good agreement.It is also found that the heat flow caused by ignoring the axial temperature gradient will bring some error when the beam size is small.2.Based on the research and analysis of non-Fourier thermoelastic damping of homogeneous material microbeam,the generalized thermoelastic coupling vibration control equation of functionally graded material solid microbeam is given.For the functionally graded material microbeams with component materials of silicon nitride(Si3N4)-nickel(Ni)and silicon carbide(SiC)-aluminum(A1),the numerical simulation and analysis of the thermal elastic damping of silicon nitride(Si3N4)-nickel(Ni)and silicon carbide(SiC)-aluminum(A1)microbeams under the first three modes under the simple support constraint at both ends are carried out,and the results are compared with those in the existing literature to verify the reliability of the calculation method.Subsequently,the influences of the thickness,gradient index,frequency order,boundary conditions and material properties of the micro-beam on the thermoelastic damping results of the micro-beam are calculated and analyzed.The main conclusions are as follows:when the microbeam vibrates at different frequency orders,the maximum thermoelastic damping and critical thickness decrease with the increase of frequency orders.The critical thickness corresponding to the maximum thermoelastic damping of microbeam under different boundary conditions decreases with the increase of constraint stiffness.The main innovation of this paper is that based on the generalized thermoelastic theory,the analytical approximate solution method of thermoelastic damping of Levinson microbeam with uniform material is given.Based on the three-dimensional non-Fourier heat conduction model,the thermo-elastic coupled vibration equation and heat conduction equation of homogeneous material and functionally graded material structure are established,and the finite element analysis is carried out.Based on the existing commercial software,the generalized thermoelastic theory is adopted to realize the finite element solution of thermoelastic damping of micro-beam structure.