Two-Dimensional Simulation of Generalized Thermoelastic Damping in Vibrations of Strain Gradient Beam Resonators

The operation of micro/nanobeam resonators is greatly impacted by the thermoelastic damping (TED) phenomenon, highlighting the need for precise determination of its value. Given the confirmed size effects in both mechanical and thermal fields, along with the importance of utilizing the two-dimensional (2D) heat transfer model over the 1D model for more accurate simulation of the thermomechanical behavior of small-scale beams, this paper aims, for the first time, to present a 2D model for TED using the modified strain gradient theory (MSGT) and the nonlocal dual-phase-lag (NDPL) heat equation. To accomplish this, the 2D NDPL-based temperature distribution is calculated using the Galerkin method, while the MSGT is applied to determine the size-dependent constitutive equations. The obtained relations are then used in the energy dissipation (ED) method to derive a TED formula in the form of infinite series. To validate the model’s accuracy, a simplified version is employed for comparison. A detailed convergence study is also performed to determine the optimal number of terms needed for precise results. Finally, a thorough parametric analysis is undertaken to explore how key factors like 2D heat transfer and non-classical constants in the MSGT and NDPL model impact TED. The findings highlight the importance of using the MSGT and NDPL model in micro- and sub-micro dimensions, and the need for the 2D model in beams with low aspect ratios.