Thermoelastic Damping In Hollow Multilayer Microbeam Resonator With Circular Cross-section

Micro-resonator is one of the MEMS devices,which is widely used in biomedical,aerospace,communication and other fields.Quality factor(Q)is the key parameter to evaluate the performance of micro-resonator.The micro-resonator with high quality factor has higher sensitivity,better stability and lower energy loss.Thermoelastic damping(TED),which determines the upper limit of the quality factor of the micro-resonator,is a kind of internal inherent damping and cannot be completely eliminated by improving the manufacturing method.Therefore,the study of thermoelastic damping is a hot spot in this field,which has important academic and application value.Based on Fourier heat conduction theory,Green’s function method is used to approximate the temperature field distribution function of the hollow bilayered and trilayered microbeam resonators with circular cross-section.The main research contents and innovations are as follows:(1)Thermoelastic damping in hollow bilayered microbeam with circular cross-sectionAn analytical model of thermoelastic damping of the hollow bilayered Euler-Bernoulli microbeam resonator with circular cross-section is established.Compared with Zener’s model and TR’s model,it is found that the analytical model can be reduced to Zener’s model and TR’s model.In addition,the convergence of the analytical model is tested,and the effectiveness of the analytical model is verified by comparing with the FEM model.The effects of metal coating,geometrical dimension,restraint mode and external exciting force on the thermoelastic damping of bilayered microbeam are discussed.The results show that the metal coating can increase the thermoelastic damping of bilayered microbeam resonator,and the Zener modulus of the plated metal is not positively related to the peak value of the thermoelastic damping;for the microbeam composed by Si C and Si,the peak value of the TED is constant when the volume ratio is constant,but the peak frequency will decrease with the increase of the volume of the microbeam;for Si/Si3N4 microbeams,when the total thickness remains unchanged,the peak of TED decreases with the increase of the thickness ratio of the inner and outer layers,but the critical damping frequency increases with the increase of the thickness ratio of the inner and outer layers;for the slender microbeam,the thermoelastic damping is not related to the length of the microbeam,the restraint mode and the magnitude of the external excitation force.(2)Thermoelastic damping in hollow trilayered microbeam with circular cross-sectionAn analytical model of thermoelastic damping of the hollow trilayered Euler-Bernoulli microbeam resonator with circular cross-section is established.Compared with bilayered microbeam’s model and FL’s model,it is found that the analytical model can be reduced to bilayered microbeam’s model and FL’s model.In addition,the convergence and validity of the analytical model are verified by comparing with FEM model.The influence of the geometrical size of trilayered microbeam and the metal coating on the thermoelastic damping is discussed.The results show that:for Ni/Si/Ni microbeams,only increasing the thickness of the third layer,the thermalelastic damping peak value of the microbeam increases,but the critical damping frequency decreases;for the Al/Si C based microbeam,under the same coating thickness,the thermalelastic damping peak and critical damping frequency of Cu coated microbeam are higher than that of Ni plated and Ti plated microbeam;the thermoelastic damping of Ti plated microbeam is smaller than that of Cu and Ni plated microbeams in the whole frequency range.