Thermoelastic Damping in Micro- and Nano-Mechanical Systems

TL;DR

This paper analyzes thermoelastic damping as a key energy loss mechanism in small-scale mechanical resonators, providing a detailed derivation and comparison with classical approximations to inform high-Q MEMS and NEMS design.

Contribution

It offers a precise derivation of thermoelastic damping in thin beams and evaluates the accuracy of Zener's approximation for small flexural vibrations.

Findings

Exact expression for thermoelastic damping derived

Zener's approximation slightly deviates from the exact model

Implications for designing high-Q micro- and nano-mechanical systems

Abstract

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 electro-mechanical systems (MEMS and NEMS). 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.