Mathematical simulation of generalized thermoelastic dissipation and frequency shift in spinning nonlocal rings with rectangular cross section

• Published in: Journal of engineering mathematics Vol. 152; no. 1
• Main Author: Widatalla, Sabir
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Nature B.V 01.06.2025
• Subjects: Angular velocity; Cross-sections; Dissipation; Equations of motion; Frequency shift; Mathematics; Nonlocal elasticity; Parameters; Phase lag; Temperature distribution; Temperature effects; Thermodynamics; Vibration mode
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-025-10459-2

The functionality and quality factor (Q-factor) of extremely small ring resonators can be severely affected by thermoelastic dissipation (TED). Within the frequency-based methodology, the current study adopts the nonlocal elasticity theory (NET) and the nonlocal single-phase-lag (NSPL) heat equation to introduce a novel scale-dependent model for assessing TED in spinning nanorings with rectangular cross section. As the first step toward this goal, the coupled motion equation, accounting for thermal effects, is formulated within the NET framework. Subsequently, the NSPL model framework is used to derive the coupled heat equation, whose solution determines the temperature distribution in the ring. Applying the frequency-based methodology, a closed-form expression for TED in the spinning nanoring is ultimately extracted. Following model validation, a series of numerical analyses are conducted to evaluate how various factors like specific parameters of the NET and NSPL model, geometrical features, vibrational mode number, surrounding temperature, material composition, and angular velocity influence TED and frequency shift (FS). As per the obtained results, the mechanical nonlocal parameter diminishes TED, whereas the thermal nonlocal parameter can either reduce or elevate TED based on its size.