Nonlocal dual-phase-lag thermoelastic damping in in-plane vibrations of rotating rectangular cross-sectional nanorings according to nonlocal elasticity theory

Since thermoelastic damping (TED) plays a pivotal role in miniature structural elements, accurate simulation of this thermomechanical behavior can significantly ameliorate their functionality. A key aspect of precisely modeling the thermoelastic performance of small-scale structures is incorporating the impact of size in both mechanical and thermal analyses. In this work, the nonlocal theory (NT) and the nonlocal dual-phase-lag (NDPL) heat transfer model are utilized to develop a new size-sensitive formulation for TED in ultra-small rotating rectangular cross-sectional rings. To accomplish this, the governing equations for motion and heat transfer are derived in the first place according to the NT and NDPL model. Following this, the complex frequency (CF) approach is applied to define damping, leading to a single-term formula for TED. The numerical analysis includes multiple cases to appraise the effects of key parameters, particularly the scale factors in the NT and NDPL model, on TED. Results suggest that the NT and NDPL model have a crucial role in determining TED, particularly when the ring’s size approaches the structural or thermal characteristic lengths, making this influence undeniable.