Analytical Model for Thermoelastic Damping in In-Plane Vibrations of Circular Cross-Sectional Micro/Nanorings with Dual-Phase-Lag Heat Conduction

Purpose: The present investigation is devoted to providing two/three-dimensional (2D/3D) models for estimating the amount of thermoelastic damping (TED) in circular cross-sectional micro/nanorings by capturing the effects of size on thermal domain via dual-phase-lag (DPL) heat conduction model. Methods: To achieve the goal of the article, first of all, the equation of heat conduction derived in the framework of DPL model is solved. In this way, for 2D and 3D models of heat propagation, the temperature field in the ring is obtained in the form of infinite series. Next, by exploiting the relation of quality factor in entropy generation (EG) approach, a formulation including the two phase lag parameters of DPL model is extracted to anticipate TED value in small-sized rings with circular cross section. Results: By comparing the results of this investigation with those of studies in the literature that are based on simpler heat conduction models, a validation study is accomplished. An intensive numerical study is also performed to discern the influence of some of the most significant factors such as phase lag parameters of DPL model, vibration mode, the dimensions and ring material on TED. Conclusion: The findings reveal the noticeable effect of phase lag parameters of DPL model on the magnitude of TED in miniaturized circular cross-sectional rings, especially in smaller dimensions and higher vibration modes.