Analytical Model for Thermoelastic Dissipation in Oscillations of Toroidal Micro/Nanorings in the Context of Guyer–Krumhansl Heat Equation

Abstract

Thermoelastic dissipation or thermoelastic damping (TED) can restrict the quality factor of micro/nanoring resonators seriously. This paper employs the non-Fourier model of Guyer–Krumhansl (GK model) to render a size-dependent formulation and analytical solution for approximating the amount of TED in micro/nanorings with circular cross-section by inclusion of nonlocal and single-phase-lagging effects. To fulfill this objective, the equation of heat conduction in the ring is first established according to GK model. Then, by placing the temperature distribution obtained from the heat conduction equation in the TED relation defined on the basis of thermal energy approach, an expression in the form of infinite series is given for TED, which includes non-classical parameters of GK model. Finally, after checking the validity of the model through a comparative study, several simulation results are prepared to emphasize on the influence of different factors such as non-classical parameters of GK model, geometry of ring, vibrational mode and ambient temperature on TED value. Numerical examples reveal that the mentioned factors along with the two- or three-dimensional heat transfer (2D or 3D) model have major influences on TED variations.