Thermoelastic vibration of porous functionally graded graphene platelet-reinforced plates under DPL heat conduction: a multimode temperature formulation

Abstract

Abstract

Abstract The thermoelastic vibration of porous graphene platelet-reinforced composite plates depends not only on the amounts of reinforcement and pores, but also on their relative locations through the thickness. To clarify this distribution-dependent behavior under non-Fourier heat conduction, a semi-analytical formulation is developed for porous functionally graded graphene platelet-reinforced composite (FG-GPLRC) plates within the dual-phase-lag (DPL) framework. Kirchhoff plate theory is coupled with a multimode through-thickness temperature expansion, and the resulting thermoelastic eigenvalue problem is solved by Navier’s method. The effective properties are evaluated using the modified Halpin–Tsai model, while porosity degradation is described by a Gaussian random field closed-cell model. The vibration response is governed by the relative positions of GPL-enriched and pore-enriched regions. Surface-enriched GPLs provide the greatest frequency enhancement, whereas surface-enriched pores produce the strongest reduction in bending stiffness and natural frequency. Concentrating pores near the mid-plane weakens this adverse effect, and its combination with surface-enriched GPLs gives the highest frequency among the examined cases. Thermoelastic coupling produces a measurable frequency shift relative to the purely mechanical solution, whereas the additional DPL correction relative to the Fourier model remains very small for the parameters considered. Increasing GPL weight fraction and length-to-thickness ratio further increases the frequency, although the geometry-induced gain gradually approaches a limiting value. Stiffness and mass measures show that the slight non-monotonic response of FG-X + P2 arises from their combined redistribution rather than pore-induced stiffening alone. These results clarify how through-thickness material arrangement governs the thermoelastic vibration response of porous FG-GPLRC plates.