Thermoelastic dissipation of circular-cross-sectional ring including nonlocal and dual-phase-lagging effects

In the high-frequency region, thermoelastic damping (TED) is essential to ensure the accuracy of micro- or nanoprecision sensors or actuators. The size-effect of molecules should be considered in the design and analysis since the atomic volume is not negligible in the nanoscale model. Moreover, a toroidal ring is easy to manufacture, so there is a high possibility that it will be developed in the near future. And thus, the 3-dimensional (3D) TED model of a circular cross-sectional ring is investigated by adopting dual-phase-lagging (DPL) and modified couple stress (MCS) theories based on nonlocal elasticity. Additionally, the size-dependent influences are specified by length-scale parameters in the elastic and thermal fields. Then the TED results are predicted as a quality factor (Q) with the peaks of the spectra and are compared separately by the causes of physical quantity. Moreover, the phenomenon is analyzed in terms of how the properties and length-scale parameters correlate with each other. Finally, it is confirmed that nonlocal elasticity should be considered when the size of the resonator decreases to the scale of the energy-carrying mean-free path. In this regard, this work provides an idea for the analysis of DPL TED of the toroidal ring, including nanoscale effects based on nonlocal elasticity and MCS theories.