Lamb waves in multilayered quasicrystal nanoplates with imperfect interfaces and size effects

The propagation characteristics of Lamb waves in multilayered quasicrystal nanoplates are investigated within the framework of surface elasticity theory, nonlocal theory, and the spring model. To tackle the challenges posed by the complex nonclassical boundary conditions and the inherent phonon–phason coupling field in quasicrystals, we develop an improved Legendre orthogonal polynomial method and a corresponding finite element method, whose calculation results are mutually validated to ensure accuracy. We systematically analyze the individual and combined influences of the surface effect, nonlocal effect, and imperfect interface effect. The key results can be summarized as follows: the size effect increases the wave velocity in the low-frequency regime, while inducing a significant velocity reduction in the high-frequency regime. The imperfect interface effect causes a marked decrease in wave velocity, with its influence exhibiting a strong mode dependence and frequency dependence. The cutoff frequency shows a nonlinear decreasing trend with a saturation value as the surface effect and imperfect interface effect are enhanced. The surface effect and nonlocal effect exhibit significant mutual enhancement, while the size effect and imperfect interface effect exhibit pronounced mutual inhibition. This work provides theoretical guidance for the optimal design of quasicrystal nanostructures and is expected to promote their engineering applications in nano-electromechanical systems.