Dynamic Analysis of Nonlocal Magneto-Electro-Elastic Kirchhoff Sandwich Plate with Irregular Boundaries

We develop a unified dynamic formulation for nonlocal functionally graded magneto-electro-elastic (MEE) sandwich plates of irregular boundary based on the Yan-Dowell sandwich theory extended within Eringen’s differential nonlocal elasticity framework. The derived sixth-order governing equation consistently incorporates thickness-wise material gradation, size-dependent stiffness effects, and linear magneto–electro–mechanical coupling in a multi-field continuum setting. A generalized dimensionless transformation is introduced to obtain closed-form dispersion relations, stability admissibility conditions, and explicit expressions for phase and group velocities. The formulation captures the transition from classical bending-dominated behavior to microstructure-sensitive nonlocal regimes and predicts finite high-frequency saturation limits absent in local models. Parametric analysis quantifies the coupled influence of wave number, nonlocal parameter, gradient index, effective MEE stiffness, together with external electric and magnetic potentials on dispersion characteristics. The results demonstrate broadband stiffness amplification under MEE activation, curvature-enhanced wave modulation at short wavelengths, and well-defined electromagnetic stability boundaries. The proposed model establishes a predictive mechanics framework for tunable wave propagation and regime-classified design of smart graded sandwich nanostructures.