Thermoelastic Damping In Micro-And Nanomechanical Resonatrors

This paper studies thermoelastic damping in microelectromechanical systems(MEMS) and nanoelectromechanical systems(NEMS) in the following three parts:The first part studies thermoelastic damping in the longitudinal vibration mode. Expression of thermoelastic damping is obtained by using the thermal-energy method and then validated by comparing with the exact solutions deduced from the coupled thermoelasticity equations. It is demonstrated that Landau-Lifshitz’s model overestimates thermoelastic energy loss by employing the adiabatic assumption. Results of the present study indicate that the peak value of thermoelastic damping for isothermal boundary condition is lower than that for adiabatic boundary condition in the longitudinal vibration mode. Furthermore, a comparison was made between the longitudinal vibration mode and flexural vibration mode to distinguish their different characteristics. It manifests that the thermoelastic damping of rods or beams reaches peak values at the length scale of 10-8 m for longitudinal vibration in contrast to the order of 10-5 m or above for flexural vibration in the numerical examples of the present study.The second part is concerned with the effect of geometrical shape of cross-section on thermoelastic damping of micro and nano beams under adiabatic thermal condition. Following the similar assumptions and procedures of Lifshizt and Roukes, the expressions of thermoelastic damping of micro/nano beams of elliptical and triangular cross-section are derived. To validate the two expressions, COMSOL is employed and the numerical results based on finite element method are then obtained. The comparison between expressions and the numerical results indicates that the difference between them for triangular cross-section is much larger than that of elliptical cross-section, thus the least square method is adopted to get the fitting function. Moreover, the relative difference of the latter is around 10 percent or even near zero at some special ranges of the ratio, which shows that the expression of the thermoelastic damping for elliptical cross-section beams can be used instead of numerical results obtained by finite element method.The third part investigates the thermoelastic dissipation of micro resonators by using the relation between the elastic stress and the elastic strain of G-L generalized thermoelasticity theory and dual-phase-lagging model. The dual-phase-lagging model is derived based on the Boltzmann transport equation, and the relation of thermoelastic strain and stress from G-L generalized thermoelasticity theory is obtained by using the theory of thermodynamics and solid state physics. The generalized expression of the thermoelastic damping are deduced, and the distinct characteristics between the generalized expression and the Lifshizt-Roukes’ exact solution are studied.