Effect of surfaces on thermoelastic damping of nano-resonators

The objective of this study is to investigate the role of surfaces on thermoelastic damping of flexural vibrations in nanobeams. In the past, the role of surfaces on thermoelastic damping of a vibrating nanobeam has been discussed by considering only mechanical interaction between surfaces and the rest of bulk without accounting for thermal interaction between them. In this paper we account for heat flow due to conduction between the surface and bulk and a coupled thermo-mechanical heat equation for a thermoelastic surface has been derived. Quality factor of vibrating rectangular nanobeam has been computed using modified thermal boundary conditions for the bulk under adiabatic surface conditions. An expression for surface heat capacity used in modified boundary conditions has been derived using the modified Debye model. A simplified expression for quality factor of thin rectangular nanobeam has been obtained. We note that the quality factor and the frequency at which the maximum dissipation occurs is a function of both mechanical and thermal properties of surface. It has also been noticed that the relative change in thermoelastic dissipation due to surface effect is a function of operating frequency. The present analysis shows that effect of surfaces on quality factor and peak damping frequency increases with decrease in beam thickness. Coupled heat equation for a surface derived in the present work can be used for any general thermoelastic surface.