Thermoelastic damping in asymmetric vibrations of nonlocal circular plate resonators with Moore-Gibson-Thompson heat conduction

Abstract

Precise estimation of the amount of thermoelastic damping (TED) in small-sized resonators is one of the crucial issues in their optimal design. According to several experimental, numerical and theoretical findings, the behavior of structures with such small dimensions in structural and thermal domains does not follow classical elasticity theory and the Fourier law of heat conduction. The objective of this work is to develop a nonclassical formulation for computing TED in asymmetric vibrations of circular nanoplates according to nonlocal theory (NT) and Moore-Gibson-Thompson (MGT) heat transfer model. To do so, first, the coupled equations of motion and heat are derived in the purview of NT and MGT model. Then, the real and imaginary parts of the system frequency are extracted from the frequency equation affected by thermoelastic coupling. Finally, by means of the existing definition for TED, a mathematical expression including nonlocal parameter of NT and nonclassical constants of MGT model is obtained to make an estimate of TED value. In the numerical examples section, to ensure the credibility of the provided formulation, the results obtained through this model are compared with those reported in the literature in the context of simpler models. Then, by presenting various graphical data, the type and extent of the role of different factors in TED changes are appraised. The obtained results indicate that employing NT and MGT model can substantially impact the amount of TED compared to the estimations of the classical formulation. Furthermore, the comparison of results reveals that the magnitude of TED in asymmetric vibration modes surpasses that in symmetric ones, and consequently incorporating asymmetric vibration modes is crucial for thorough analysis of TED in circular nanoplates. Thus, the formulation presented in this article can aid in achieving an optimal design for such plates, particularly in terms of minimizing energy loss.