Free vibration of FG multilayer hybrid nanocomposite microbeam reinforced by GPLs and CNTs under nonlocal dual-phase-lag generalized thermoelastic theory

In recent years, extensive studies on carbon nanotubes-reinforced composites (CNTRC) and graphene platelets-reinforced composites (GPLRC) have been conducted primarily within the framework of the classical elasticity or thermoelasticity. However, there lacks of researches on the thermoelastic behaviors of CNTRC/GPLRC structures based on the generalized thermoelasticity considering non-Fourier heat conduction, especially lacking of studies that address the microstructures of these materials incorporating nonlocal effects. To address this gap, this work applies the generalized thermoelastic theory, which incorporates dual-phase thermal relaxations, thermal nonlocality and elastic nonlocality, to investigating the thermoelastic vibration characteristics of a nanocomposite microbeam reinforced by both GPLs and CNTs. The Halpin–Tsai micromechanical model is used to evaluate the effective elastic modulus of the composite microbeam, which is then analyzed using the Euler–Bernoulli beam model and solved via Navier’s method to determine the natural frequency. In calculation, the unidirectional distribution and three different functionally graded (FG) distributions of CNTs and GPLs, i.e., FG-A, FG-X and FG-O and also the influences of the nonlocal parameters, the volume fraction indices and the mass fractions of GPLs and CNTs on the natural frequencies are examined. The obtained results show that FG-A type significantly influences the natural frequency. The inclusion of GPLs and CNTs in the epoxy resin matrix markedly increases the natural frequency of the microbeam, with hybrid reinforcement being superior to GPLRC and CNTRC. The nonlocal elasticity parameter negatively correlates with the natural frequency, while the mass fraction and volume fraction index of GPLs and CNTs positively correlate with the natural frequency.