Phonon-phason coupling and nonlocal effects on Lamb waves in functionally graded one-dimensional hexagonal quasicrystal nanoplates

Due to the coupled phonon-phason coupling and nonlocal effects, dynamic behaviors of quasicrystal nanostructures are highly complex. Mechanics investigations have mainly focused on the statics, but rarely on dynamics, thus limiting their engineering applications. In the present paper, a fractional order elastodynamics model is proposed to investigate guided waves propagating in functionally graded one-dimensional hexagonal quasicrystal nanoplates in the context of the nonlocal theory. In this model, the fractional order can be flexibly adjusted to describe the role of the phason field accurately. Phase velocity and attenuation curves, as well as stress distributions, are illustrated. The phonon-phason coupling and nonlocal effects on wave characteristics are studied. Some new results are revealed: The fractional order considerably influences phason modes, but weakly affects phonon modes; The phonon-phason coupling and the nonlocal effects promote each other. These results establish a theoretical foundation for designing and optimizing quasicrystal nanostructures.