Thermoelastic Dissipation in Vibrations of Couple Stress-Based Circular Cross-sectional Beams with Nonlocal Single-Phase-Lag Heat Conduction

Given the need for utilizing size-dependent elasticity theories and non-Fourier heat transfer models in extremely small dimensions, the present research intends to provide a novel theoretical framework for thermoelastic dissipation (TED) in circular cross-sectional micro/nanobeams on the basis of the modified couple stress theory (MCST) and nonlocal single-phase-lag (NSPL) heat conduction model.

In the first step, the coupled heat equation of Euler–Bernoulli beams in polar coordinate system is derived by capturing the nonlocal and phase-lagging effects. By solving this equation, the function of temperature change is attained. Substitution of the couple stress-based constitutive relations and obtained temperature field in the definition of TED from the point of view of energy yields a TED relation in the form of infinite series encompassing mechanical length scale, thermal nonlocal and phase lag parameters.

Numerical results are provided in three sections. In the first section, the correctness of the extracted formulation is explored via conducting a comparative study. In the second section, a convergence analysis is performed to ascertain the sufficient number of terms of the obtained infinite series for achieving well-founded outcomes. In the final section, a parametric analysis is made to illuminate the dependence of TED on some factors like mechanical length scale parameter, thermal nonlocal parameter, beam geometry, ambient temperature and beam material.

According to the obtained results, utilization of MCST lowers the amount of TED. Moreover, the incorporation of thermal nonlocal parameter in the governing equations can have substantial impacts on both the amount and the trend of TED, especially at high vibration frequencies.