Thermoelastic damping in fluid-conveying microresonators

As an inherent energy dissipation mechanism, the thermoelastic damping (TED) imposes an upper limit on the quality factors of microresonators. On the basis of Hamilton principle, the governing equation of solid-liquid-thermal coupling vibration of fluid-conveying microresonator is deduced. For different thermal boundary conditions, the analytical expressions of TED are separately derived by solving the heat diffusion equation of the thermal flow across the fluid-conveying microbeam. The results show that the liquid in the hollow microbeam has significant impact on TED. The natural frequency decreases with the increase of the flow velocity or axial pressure. However, both for the two proposed fluid-conveying models, TED increase with the increase of the flow velocity or axial pressure. The peak value of TED of the proposed models is larger than the hollow beam, but smaller than the solid beam. As a function of channel geometry, beam properties and flow velocity, the second peak is about to occur for the fluid-conveying beam. In addition, different from the results of the hollow beam and the low flow velocity models, the peak value of TED in the high flow velocity model increases monotonously with the increasing ratio of channel width to channel height due to the great area of heat convection between the inner channel and the fluid.