Thermoelastic damping analysis to CNTs and GPLs reinforced FG microplate based on nonlocal strain gradient theory and nonlocal dual-phase-lag heat conduction model

This study aims to investigate the thermoelastic damping (TED) mechanism of functionally graded (FG) microplates reinforced by graphene platelets (GPLs) and carbon nanotubes (CNTs), addresses the failure of the classical TED model at the microscale, and fills the existing gaps in TED research concerning FG-GPLs/CNTs reinforced microstructures. By integrating the nonlocal strain gradient theory (NSGT) and the nonlocal dual-phase-lag (NDPL) heat conduction model into the Kirchhoff plate theory, a novel comprehensive model that captures spatiotemporal nonlocal effects is derived. The complex frequency method is employed to solve the model, with the effective elastic modulus evaluated by the Halpin–Tsai micromechanical model. The study examines the influence of several key variables on TED across four distribution patterns, i.e., UD type, FG-A type, FG-O type, and FG-X type. The results indicate that the normalized inverse quality factor peaks at the highest value in the FG-X type, reaching 0.96 at 1.96 μm. In contrast, the FG-A type exhibits superior overall damping performance. The elastic nonlocal parameter extends the TED range in the thickness direction, with the peak position shifting approximately 0.2 μm toward the top of the microplate for every 50 nm increase. However, the characteristic length parameter narrows this range. The nonlocal thermal effects diminish energy dissipation. Crucially, GPLs are the primary determinants of TED; an increase in their mass fraction leads to a reduction in peak and an expansion of the dissipation area, while geometric parameters exhibit a negligible influence. Conversely, CNTs solely modify spatial dissipation distribution through mass fraction without affecting the peak values, whereas increased geometric thickness induces strain gradients. Furthermore, TED demonstrates maximum strength under SSSS boundary conditions. The current model and results offer valuable insights for the design of high-performance FG advanced MEMS reinforced by GPLs and CNTs.