Thermoelastic Damping Effect Analysis in Micro/Nano Flexural Resonators

Understanding the effects of thermoelastic damping on the vibration parameters such as natural frequency and frequency-sensitive is essential for the design of micro-nano-electromechanical systems. In this paper, the effects of thermoelastic damping in micro- and nanomechanical resonators beam with a rectangular cross section will be analyzed. The governing equations in present system are coupled of heat conduction equation and equation of motion where this methodology has been applied to three- dimensional analyses. To solve these governing equations analytically with considering suitable assumption, first the coupled heat conduction equation is solved for the thermoelastic temperature field by considering three-dimensional (3-D) heat conduction along the length, width and thickness of the beam.‫ Next; thermoelastic coupling is modeled into the equation of motion for flexural vibrations through a temperature-dependent moment of temperature distribution. Frequency shifts and quality factor due to thermoelastic damping are analyzed. For special cases, the obtained frequency shift is compared with the result of the frequency shifts computed using 2-D heat conduction; also the obtained quality factor is compared with exact 1-D heat conduction. The results obtained showed that the model presented in this paper were in good agreement with the other models and it predicted the effects of thermoelastic damping on the behavior of micro-nano resonators accurately.