DYNAMIC MODELING AND ANALYSIS OF STRAIN GRADIENT GRAPHENE PLATELET-REINFORCED METAL FOAM MICROPLATES VIA A DEFORMATION-BASED UNIFIED THEORY

This study presents a dynamic model for graphene platelet (GPLs)-reinforced metal foam microplates based on a deformation-based unified theory (DUT) and the modified strain gradient theory (MSGT) for investigating the structural free vibration and wave propagation characteristics. DUT employs a fourth-order displacement field with explicit physical meaning to alleviate thickness-direction constraints, while MSGT incorporates symmetric stretching/dilatation/rotation gradient tensors to characterize material size effects. Equivalent properties of the GPL-aluminum skeleton are determined via a modified Halpin–Tsai model, with foam matrix porosity described by a degradation model. Validation against literature confirms model accuracy. Parametric studies systematically examine porosity distribution patterns, GPL mass fraction, porosity level, geometric parameters (thickness ratio), and material length-scale parameters. Results demonstrate that symmetric non-uniform porosity preserves surface-layer load capacity and bending stiffness, thus elevating natural frequencies while enhancing dispersion frequencies and phase velocities at low-to-mid wavenumbers. Increased GPL mass fraction enhances structural stiffness, thereby increasing natural/angular frequencies and phase velocities, whereas higher porosity reduces stiffness and diminishes these responses. Material length-scale parameters amplify natural frequencies with heightened effects on higher-order modes. Crucially, thickness ratio governs dispersion branch evolution, inducing mode veering between first/second wave branches while the fourth branch exhibits distinct propagation characteristics. A Pearson correlation-based branch-tracking method effectively identifies mode veering, ensuring physical consistency in phase/group velocities. This study provides theoretical foundations for dynamic optimization of GPL-reinforced foam microplates in micro-/nano-devices.