The importance of thermoelastic damping as a fundamental dissipation mechanism for small-scale mechanical resonators is evaluated in light of recent efforts to design high-$Q$ micrometer- and nanometer-scale electromechanical systems. The equations of linear thermoelasticity are used to give a simple derivation for thermoelastic damping of small flexural vibrations in thin beams. It is shown that Zener’s well-known approximation by a Lorentzian with a single thermal relaxation time slightly deviates from the exact expression.

• Received 20 September 1999

DOI:https://doi.org/10.1103/PhysRevB.61.5600