Thermo-elastic Damping Effect Analysis in Rectangular Micro-plate Resonators Using State-Space Approach

Thermo-elastic damping (TED) has been identified as an important loss mechanism in numerous high-Q micro-resonators, so that performances are directly related to the thermo-elastic quality factor, which has to be predicted accurately. For this purpose, in this paper, quality factor, damping ratio and frequency shift due to thermo-elastic coupling in a fully clamped micro-plate resonators at the first mode are analyzed. In order to accurately determine TED effects, the temperature distribution is assumed to be 3-D along the length, width and thickness of the micro-plate. For simultaneous solution of equation of motion and thermal conduction equation, weighted residual Galerkin technique is employed in order to model the general form of the coupled equations and then the solution is obtained using state-space approach in the time domain. The results show that the TED is size dependent and there is a critical thickness at which the quality factor reaches its minimum value and damping ratio reaches its maximum value for a micro-plate. Furthermore, comparison of the results showed that the normal strain in the direction transverse to the plate εzz cannot be neglected because this assumption may lead to inaccurate modeling of micro-plates.

Keywords:

Thermo-elastic damping (TED) , Quality factor , micro-plate.Introduction