Generalized thermoelastic damping model for small-scale beams with circular cross section in the framework of nonlocal dual-phase-lag heat equation

In light of the certainty of size effect on heat conduction process in extremely small dimensions, the present article seeks to introduce a new theoretical framework for thermoelastic damping (TED) in micro-/nanobeam resonators with circular cross section by utilizing the non-Fourier model of nonlocal dual-phase-lag (NDPL). The first stage involves using NDPL model in order to develop the non-Fourier heat equation of circular cross-sectional beams in polar coordinates. This differential equation can be solved to arrive at temperature distribution in any arbitrary point of the beam. When the constitutive equations of the beam together with the extracted temperature distribution are substituted in the energy-based formulation of TED, an infinite series is produced as the TED relation in the context of NDPL model. Through a comparison study, the reliability of the acquired formula is analyzed. To shed light on how some key factors like nonclassical parameters of NDPL model, beam dimensions and material affect TED, several numerical data are prepared. As per the acquired outcomes, notably at high frequencies of oscillation, the use of NDPL model may profoundly impact the quantity and pattern of TED.