Effect of cross-sectional shape on thermoelastic dissipation of micro/nano elastic beams

In spite of practical relevance, little effort has been made to analyze the effect of geometrical shape of cross-section on thermoelastic dissipation of micro/nano beams under different surface thermal condition. The present paper aims to study thermoelastic dissipation of micro/nano beams of elliptical, triangular or arbitrary rectangular cross-section with accurate satisfaction of the surface thermal condition. Detailed formulas are derived for quality (Q-) factor of beams of the above-mentioned cross-sections. Our results show that for all cross-section discussed, thermoelastic dissipation is a non-monotonic function of the absolute size of the cross-section provided the beam length is fixed, and the maximum dissipation appears at a specific size which is of the order of a few hundreds of nanometers for examples discussed. These results suggest that thermoelastic dissipation could increase with decreasing cross-sectional size within the micron scale, while it could decrease with decreasing cross-sectional size within the nano scale. In general, for all beams of the above-mentioned cross-sections, the Q-factor for isothermal surface is always higher than the Q-factor for adiabatic surface under otherwise identical conditions at micro/nano scales. The present analysis also indicates that, to achieve a high quality factor, beam resonators with elliptical or triangular cross-sections are best to operate at higher frequencies while beams of rectangular cross-sections are best to operate at lower frequencies.