Theoretical 3D model of thermoelastic damping in laminated rectangular plate resonators

Thermoelastic damping (TED) can lead to energy loss in microscale resonators, which is an intrinsic mechanism. To minimize the energy loss, it is required to determine the TED of resonators. Laminated plate resonators are commonly used in practice. However, existing researches on TED of the laminated resonators use mainly the one-dimensional (1D) heat conduction model, as the 3D governing equation is complicated, which cannot show the influences of boundary conditions along the supporting edges. In this paper, the governing equation of thermoelastic problems with 3D heat conduction was established for the out-of-plane vibration of the laminated rectangular plate. The analytical expression of the TED was derived using its physical meaning, namely, the ratio of the energy dissipated to the total elastic strain energy stored per cycle of vibration. It was found that the size and shape of the plate affect crucially the TED. The values of TED for higher-order vibration modes were also evaluated. Most importantly, the influences of supporting conditions and heat conduction conditions along the four edges were studied, which is the first report for laminated plates. The present approach can provide guidance for the design of high-quality bilayered resonators.