Size-dependent thermoelastic damping model for vibrating circular cross-sectional micro/nanobeams according to Moore-Gibson-Thompson thermoelasticity theory

Abstract

Motivated by the limitations of classical models in capturing the behavior of materials at the micro/nanoscales, this work proposes an analytical formulation for thermoelastic damping (TED) in circular cross-sectional micro/nanobeams with size-dependent mechanics and heat transfer. This model incorporates small-scale effect through the modified couple stress theory (MCST) for mechanics and the Moore-Gibson-Thompson (MGT) model for heat conduction. To accomplish this objective, the initial step involves introducing the general equations of the MCST and MGT model. Following the establishment of the MGT model, the temperature variations throughout the beam are obtained by solving the heat equation. Additionally, by implementing the principles of the MCST, the model incorporates size-dependent constitutive relations. Finally, the research employs the energy dissipation (ED) approach to render a mathematical expression for TED in tiny beams with circular cross section. This relation, expressed as an infinite series, accounts for size-dependent effects by incorporating the MCST and MGT model. In the section dedicated to numerical results, the initial step involves verifying the accuracy of the proposed model through a validation study. Next, the section showcases various numerical results, focusing on how the MCST and MGT model affect the temperature distribution and TED value. The acquired results underscore that the influence of the MCST and MGT model on the amount of TED in small-sized circular cross-sectional beams cannot be disregarded.