Mode conversions and intersections of Lamb waves in one-dimensional hexagonal piezoelectric quasicrystal nanoplates based on the integral nonlocal theory

Phonon, phason, and electrical coupling characteristics of Lamb waves in one-dimensional hexagonal piezoelectric quasicrystal nanoplates are studied by accounting for the nonlocal effect. The coupled dynamic models are derived based on the integral form of nonlocal theory and linear elasticity theory of piezoelectric quasicrystal. Subsequently, dispersion curves and displacement distributions are computed employing the Legendre orthogonal polynomial method. All influences of the phonon-phason coupling, piezoelectric and nonlocal effects on the wave characteristics are analyzed. Furthermore, a detailed analysis of the interaction between piezoelectric and nonlocal effects is provided. The results indicate that mode conversions take place when adjacent phonon and phason modes exhibit the same displacement symmetry, while mode intersections occur when the adjacent phonon and phason modes exhibit different displacement symmetries. The coupling of phonon and phason fields induces the mode conversion, and phonon-phason coupling and piezoelectric effect amplifies this phenomenon. The piezoelectric effect enhances the nonlocal effect, whereas the nonlocal effect weakens the piezoelectric effect, with a more pronounced interaction observed in phonon modes. The obtained results establish a theoretical reference for the design and optimization of piezoelectric nanoscale devices.