Guided Wave Propagation in Multilayered Two-dimensional Quasicrystal Plates with Imperfect Interfaces

An analytical solution of the guided wave propagation in a multilayered two-dimensional decagonal quasicrystal plate with imperfect interfaces is derived. According to the elastodynamic equations of quasicrystals (QCs), the wave propagating problem in the plate is converted into a linear control system by employing the state-vector approach, from which the general solutions of the extended displacements and stresses can be obtained. These solutions along the thickness direction are utilized to derive the propagator matrix which connects the physical variables on the lower and upper interfaces of each layer. The special spring model, which describes the discontinuity of the physical quantities across the interface, is introduced into the propagator relationship of the multilayered structure. The total propagator matrix can be used to propagate the solutions in each interface and each layer about the multilayered plate. In addition, the traction-free boundary condition on the top and bottom surfaces of the laminate is considered to obtain the dispersion equation of wave propagation. Finally, typical numerical examples are presented to illustrate the marked influences of stacking sequence and interface coefficients on the dispersion curves and displacement mode shapes of the QC laminates.