Analytical solutions for thermoelastic vibrations of beam resonators with viscous damping in non-Fourier model

• Analytical solution of beam resonator with two dampings in C–V model is presented.
• The spectrum and Q-factor depend greatly on boundary conditions.
• The spectrum and Q-factor depend greatly on the viscous damping.
• The larger the diffusion is, the higher the Q-factor.
• The effect of thermal condition on the spectrum is negligible, but significant on the Q-factor.

Thermoelastic damping is recognized as a significant loss mechanism at room temperature in micro-scale beam resonators in vacuum. In addition, if the resonator operates in air, the viscous damping should be considered. In this study, the forced vibration of beam subjected to a harmonic external force and with the viscous and thermoelatic dampings simultaneously is investigated. Moreover, the heat conduction in the C–V model is considered. The analytical solutions of the system with different boundary conditions are presented. Moreover, the mathematical model of the quality factor (Q-factor) of the system is derived. Finally, the effects of the thermal diffusion, the phase lag for heat flux, the squeezing film damping, the size scale and the boundary conditions on the response ratio and the Q-factor of the system are investigated. It is found that the effects of the thermal diffusion, the squeezing film damping, the size scale and the boundary conditions on the response ratio and the Q-factor are significant.