Nonlocal dual-phase-lag thermoelastic damping in small-sized circular cross-sectional ring resonators

Abstract

The purpose of current research is to establish a theoretical size-dependent framework for estimating the amount of thermoelastic damping (TED) in miniaturized rings with circular cross section via the nonlocal dual-phase-lag (NDPL) generalized thermoelasticity theory, as one of the most exhaustive non-Fourier heat conduction models. The method used to achieve this goal is based on the definition of TED in the energy dissipation (ED) approach. To do so, after deriving heat equation in the context of NDPL model, the distribution of temperature all over the volume of the ring is specified. Then, the relations of dissipated thermal energy and strain energy in the ring are obtained. Lastly, by employing ED approach, a formula comprising the nonclassical parameters of NDPL model is rendered to determine TED value in small-scaled toroidal rings. By presenting various numerical examples, the dependence of TED on influential parameters including nonclassical thermal constants in NDPL model, ring geometry, vibrational mode number and ring material is surveyed. The Findings enlighten that the inclusion of nonlocal parameter into the model can have conspicuous impacts on TED value, especially in smaller rings or higher vibrational mode numbers. The results also reveal that among the investigated materials (i.e. silicon, copper, silver, and lead), rings made of lead and silicon exhibit the maximum and minimum TED values, respectively.