An analytical framework is developed to explore the dispersion behavior of Rayleigh waves in a functionally graded piezoelectric (FGP) plate interfaced with a dry sandy foundation, accounting for nonlocal elasticity effects and interfacial imperfections. The governing equations are formulated using nonlocal elasticity theory and solved analytically via harmonic wave analysis approach. Interface effects are modeled using normal and tangential stiffness parameters, allowing for partial bonding at the interface. Numerical simulations are performed considering both electrically open and electrically short surface conditions. The influence of key parameters including material gradation, nonlocal scale effects, interfacial stiffness, and substrate properties on the phase velocity of Rayleigh waves is examined in detail. Parametric analysis reveals that variations in the plate thickness and nonlocal parameter considerably affect the phase velocity and dispersion behavior of Rayleigh waves. The 2D and 3D plots of the displacement and electric potential fields are generated using Mathematica, illustrating the spatial variation and confinement of wave energy within the FGP layer. The results not only validate classical trends under limiting conditions but also reveal important coupled effects that are absent in traditional local models. These findings contribute to a deeper understanding of wave mechanics in smart-layered structures and offer valuable guidance for the design and optimization of advanced piezoelectric sensors, actuators, and SAW devices.
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