Lamb Wave Propagate in Two-Dimensional Piezoelectric Quasicrystal Multilayered Plates with Nonlocal Effect

Abstract

In this paper, an exact solution of the propagation of the Lamb wave in orthotropic, multilayered, two-dimensional decagonal piezoelectric quasicrystal plate with the size-dependent effect is presented. According to the elasto-dynamics basic equations of quasicrystal and nonlocal theory, the wave propagating characteristics in the plates are translated into the linear eigenvalue system by employing the pseudo-Stroh formalism. The general solutions along the thickness direction are utilized to obtain the propagator matrix which connects the physical variables on the lower and upper interfaces of each layer. We can obtain the total propagator matrix for the whole laminate, which the interface continuity conditions are employed. Furthermore, if we assume that the upper and surface traction of the laminate is free, the dispersion equation is obtained. Finally, typical numerical examples are presented to illustrate the marked influences of thickness ratios and nonlocal parameters on the dispersion relationship and mode shapes of the two-dimensional decagonal piezoelectric quasicrystal multilayered plates.