Thermoelastic Damping in Vibrations of Small-Scaled Rings with Rectangular Cross-Section by Considering Size Effect on Both Structural and Thermal Domains

Abstract

In this paper, thermoelastic dissipation or thermoelastic damping (TED) in micro/nanorings with rectangular cross-section is examined by accounting for small-scale effect on both structural and thermal areas. The modified couple stress theory (MCST) and nonlocal dual-phase-lag (NDPL) heat conduction model are exploited for incorporating size effect within constitutive relations and heat conduction equation. By employing simple harmonic form for asymmetric vibrations of the miniaturized ring and solving the heat conduction equation, for one-dimensional (1D) and two-dimensional (2D) cases of heat transfer, the solution of temperature distribution in the ring is extracted in the form of infinite series. By employing the definition of TED on the basis of entropy generation approach, an analytical relation in the series form containing structural and thermal scale parameters is established to estimate TED value. To appraise the precision and validity of the developed solution, a comparison study is performed by utilizing the outcomes of researches published in the literature. An exhaustive parametric study is then conducted to ascertain the role of structural and thermal scale parameters in the magnitude of TED. The influence of some key parameters such as vibration mode, geometrical properties, directions of heat conduction (1D and 2D model) and material on TED is also addressed.