Analysis to thermoelastic wave propagation in CNTs- and GPLs-reinforced FG microplate with surface effects under NSGT and TPL model

Carbon nanotubes (CNTs) or graphene platelets (GPLs) are perfect fillers to generate advanced functionally graded (FG) nanocomposites due to their remarkable thermal and mechanical properties. At present, the thermoelastic response analysis to FG-CNTs/GPLs-reinforced microstructures considering size-dependent effects and thermal lagging behavior is rare. To address this gap, this research first integrates Kirchhoff plate theory with surface effects, the three-phase-lag (TPL) heat conduction model, and the nonlocal strain gradient theory (NSGT) to investigate the thermoelastic wave propagation characteristics of the FG microplate simultaneously reinforced by CNTs and GPLs. The effective elastic modulus is evaluated employing the Halpin–Tsai micromechanical model. Then, the governing equations are derived, and the dispersion relation and phase velocity are obtained by applying the wave-type solution method. In calculation, in addition to the unidirectional distribution (UD) pattern of CNTs and GPLs, three distinct FG distribution patterns, i.e., FG-X type, FG-A type and FG-O type, and the effects of several key parameters on frequency and phase velocity are investigated. From the results, it can be concluded that the FG-X type is most affected by the surface effect, leading to the greatest influence on the frequency and phase velocity. The characteristic length parameter, the surface residual stress, the surface modulus of elasticity, and the volume fraction of GPLs and CNTs positively correlate with phase velocity and frequency, while the nonlocal elasticity parameter negatively correlates. Additionally, the influence of surface residual stresses on phase velocity and frequency is smaller than that of the surface modulus of elasticity, and the surface effect amplifies the influence of the characteristic length parameter and nonlocal parameters on phase velocity and frequency. The results of this model provide some references for the design of high-performance micro-resonators and acoustic sensors based on FG-CNTs/GPLs.