Nonlocal strain gradient model for thermoelastic damping in small-scale rectangular plate resonators with nonlocal dual-phase-lag heat conduction

Abstract

Given the critical role of thermoelastic damping (TED) in micro/nanoscale structures, precise modeling of this phenomenon can greatly enhance their operational efficiency. One of the main factors influencing the accurate modeling of thermomechanical behavior in tiny structures is accounting for the size effect in the constitutive and heat transfer equations. Based on the frequency approach, the present study seeks to offer an exhaustive formulation for determining TED value in tiny rectangular plates by integrating two robust scale-dependent models: nonlocal strain gradient theory (NSGT) and nonlocal dual-phase-lag (NDPL) heat equation. To achieve this, the motion and heat transfer equations are derived using NSGT and NDPL model. Subsequently, a one-term expression for TED is obtained by applying the definition of damping within the frequency approach framework. The numerical results section presents multiple examples to investigate how different factors, such as scale parameters in NSGT and NDPL model, geometry, boundary conditions, and material, affect TED. The outcomes reveal that the sensitivity of TED to the implementation of NSGT and NDPL model in dimensions comparable to the characteristic lengths of the material in the structural or thermal domains is meaningful and cannot be overlooked.