Wave dispersion analysis with FGM face layers and GPL-reinforced metallic foam core thermally loaded sandwich nanoplate using NSGT

This study investigates the wave propagation characteristics of functionally graded ZrO₂ and Nickel sandwich surface plate with Nickel foam core under various influencing factors, including power-law index, temperature rise, porosity, nonlocal parameter, size parameter, and graphene platelet reinforcement (GPLR) as well as different core distributions. Flexural, longitudinal, and shear wave modes were analyzed using Hamiltonian principle in order to establish small-scale (axial-shear-bending) governing equations utilizing refined shear deformation theory (RSDT) of plate in combination with nonlocal strain gradient theory (NSGT) and validated against published results. The wave responses of the nanoplate, considered with free boundary conditions, are analytically obtained by solving the governing equations. The effects of surface material gradation, thermal expansion, and elastic moduli on phase velocity, wave frequency, and group velocity were systematically explored. Results indicate that a zero-power index surface (ceramic) yields the highest wave properties due to superior stiffness while rising temperature and increasing foam porosity reduce wave velocities and frequencies due to softening effects. Nonlocal parameter increments lower phase and group velocities, whereas size parameter enhancements improve wave properties. Additionally, GPL reinforcement significantly enhances wave propagation behavior, demonstrating its potential for optimizing nanoplate performance. The study offers crucial insights for designing FG nanoplates for advanced thermal and mechanical applications, highlighting the tunability of wave propagation through material and structural modifications.