Thermoelastic dissipation including single-phase-lagging of rectangular-cross-sectional micro/nanoring with point masses

Abstract

Thermoelastic damping (TED) is one of the significant factor to design the high-efficiency sensors or resonators. Up to now, the single-phase-lagging (SPL) has been analyzed for the various TED models without imperfections. Practically, the perfect system cannot be available in a real structure, because imperfections are usually involved as a result of small error in a manufacturing process. And then, the non-uniformity eventually developes the inaccuracy of the precision parts. In this regard, the effect of the point masses is analyzed for the dissipation with time delay of heat flux. The governing equation is established according to the eigenfrequency of the rectangular-cross-sectional ring. And the temperature profile is obtained by the function of the lagging time, vibration mode numbers. Numerical results are compared with experimental and analytical literatures, and the effect due to the imperfection is discussed by the quality factors (Q-factors) for the TED with SPL. Moreover, the temperature distribution is graphically demonstrated through the thickness direction to represent the lagging effect due to the point mass. Significantly, the influence of the imperfection is compared to the models based on classical Fourier’s heat conduction equation in the high-frequency or ultralow temperature.