Thermoelastic Damping in Longitudinal Mode Micro- and Nano-Electro-Mechanical Systems

Abstract

Thermoelastic damping is considered the inherent and fundamental mechanism for energy dissipation in micro- and nano-electro-mechanical systems, setting an upper limit on the quality factor. Gaining insight into thermoelastic damping is crucial for designing high-Q resonators. This paper first demonstrates the causes and distinctions of thermoelastic damping in flexural and longitudinal mode resonators. An analytic thermoelastic coupling equation is derived for the longitudinal mode beam resonator. By solving the model, a concise and explicit expression for longitudinal mode thermoelastic damping is proposed, highlighting the crucial role of a new characteristic parameter known as "vibrating thermal efficiency" in thermoelastic damping and revealing that there exists a positive correlation between them. The validity of the formula is confirmed through comparison with experimental data. Additionally, numerical analysis reveals the variation trends of vibrating thermal efficiency and thermoelastic damping in relation to their respective parameters.

Keywords: thermoelastic damping, longitudinal mode, MEMS, NEMS, Q factors, vibrating thermal efficiency