In this work, the thermoelastic dissipation (TED) for circular-cross-sectional micro/nanoring model is studied including the single-phase-lag (SPL) time based on the non-Fourier heat conduction model. The toroidal solid ring is simple to manufacture and thus the potential is high for future development. Also, the present model is more precise than the 1D or 2D beam or rectangular-cross-sectional ring because the governing equation is established by 3D coordinate system. Moreover, the SPL shows the delay time of heat-flux and is especially important in cryogenic or ultrafast-vibration environments. In this regard, characteristics of the TED is mainly analyzed according to the lagging time, geometrical shape, mode number and temperature, etc. Using the experimental data in literatures, the effectiveness of this work is verified to represent the investigations. The spectra of the TED with the phenomenon of multiple peaks are presented, and then the results can be grouped and compared with previous works. Moreover, the temperature distribution is graphically described to explain the SPL mechanism.

在这项工作中，研究了圆形横截面微/纳米模型的热弹性耗散（TED），包括基于非傅立叶热传导模型的单相滞后（SPL）时间。环形实心环制造简单，因此具有很高的未来发展潜力。此外，本模型比一维或二维梁或矩形截面环更精确，因为控制方程是由 3D 坐标系建立的。此外，SPL 显示了热通量的延迟时间，在低温或超快振动环境中尤为重要。对此，主要从滞后时间、几何形状、模态数和温度等方面分析TED的特性。 利用文献中的实验数据，验证这项工作的有效性以代表调查。呈现了具有多峰现象的TED光谱，然后可以将结果分组并与以前的工作进行比较。此外，还以图形方式描述了温度分布以解释 SPL 机制。