Thermoelastic damping in micromechanical resonators operating as mass sensors

This paper presents an analytical study on evaluation of thermoelastic damping (TED) in micromechanical resonators operating as mass sensors by means of the thermal energy approach. Both quasi-one-dimensional model and two-dimensional model are proposed and analytical expressions of TED in infinite series form for micro beam resonator-based mass sensors are derived. We apply the proposed models to examine effects of various factors on TED, such as the position of attached mass particle, boundary conditions, geometry of resonators and mode shape of vibration. Numerical results show that thermoelastic damping of micro-beam resonator-based mass sensors increases obviously with the increase of the mass ratio of the attached mass to mass of the resonator. Compared with results of TED obtained by 2-D model accounting for the two-dimensional thermal conduction in micro-beam resonators, the quasi-1-D model overestimates TED in the high frequency range, and underestimates TED in the low frequency range. Noticeable differences are observed in the results of TED between quasi-1-D model and 2-D model. We also obtain the expressions of mass sensitivity and minimum detectable mass imposed by thermomechanical noise process for resonant mass sensors of bridge and cantilever configurations.