Guided Wave Propagation in Functionally Graded One-Dimensional Hexagonal Quasi-Crystal Plates

Abstract

Due to the high brittleness, cracks, holes, and other defects that are easily generated in quasi-crystal structures can affect safe applications in serious cases. For guided wave non-destructive testing, the propagation of Lamb and SH waves in functionally graded one-dimensional hexagonal quasi-crystal plates are investigated. Governing equations of wave motion in the context of Bak’s model are deduced and solved by the Legendre orthogonal polynomial method. Dispersion curves, phonon and phason displacement, and stress distributions are illustrated. The convergence of the present method applied to functionally graded quasi-crystal plates is verified. Moreover, the influences of the phonon-phason coupling effect and graded fields on wave characteristics are analyzed. Some new results are obtained: angular frequencies of phason modes always decrease as phonon-phason coupling coefficients, Ri, increase; and phonon and phason displacements of Lamb and SH waves at high frequencies are mainly distributed in the region that contains more quasi-crystal material with a smaller elasticity modulus and less rigidity. The obtained results establish the theoretical foundation of guided wave non-destructive testing for functionally graded quasi-crystal plates.

Dynamic fracture of a partially permeable crack in a functionally graded one-dimensional hexagonal piezoelectric quasicrystal under a time-harmonic elastic SH-wave

“…Recently, more and more attention has been paid to the mechanical research of functional hierarchical quality control structures [36][37][38]. Zhang et al [39,40] studied guided wave characteristics in the functionally graded 1D and 2D hexagonal QCs plate. However, to the best of the authors' knowledge, for the partially permeable electrical boundary conditions, the scattering of cracks by elastic wave in functionally graded PEQCs has not been carried out yet in any open literature.…”

Scattering of SH wave by a crack in a functionally graded one dimensional hexagonal piezoelectric quasicrystals

“…The problem of moving crack in 1D hexagonal PQCs under the action of antiplane shear and plane electric field was analyzed Zhou and Li [31]. Zhang [32] studied guided wave characteristics in the FG 1D hexagonal QCs plate. However, to date, to our knowledge, there is still no article considering scattering of the SH wave by a crack in a FG 1D hexagonal PQCs.…”