An exact closed-form solution of free vibration of a simply supported and multilayered one-dimensional (1D) quasi-crystal (QC) plate is derived using the pseudo-Stroh formulation and propagator matrix method. Natural frequencies and mode shapes are presented for a homogenous QC plate, a homogenous crystal plate, and two sandwich plates made of crystals and QCs. The natural frequencies and the corresponding mode shapes of the plates show the influence of stacking sequence on multilayered plates and the different roles phonon and phason modes play in dynamic analysis of QCs. This work could be employed to further expand the applications of QCs especially if used as composite materials.

A three-dimensional plate model capturing the size effect is developed for free and forced vibration of a layered two-dimensional quasicrystal nanoplate. The simply supported nanoplate subjected a top surface harmonic excitation is assumed for forced vibration analysis, and the traction free boundary conditions are considered for free vibration analysis. The exact solution for layered two-dimensional quasicrystal nanoplates is obtained by using the pseudo-Stroh formalism, Eringen’s nonlocal theory, and a dual variable and position method. Numerical examples show the effects of nonlocal parameter, stacking sequence and aspect ratio on natural frequency as well as forcing frequency on harmonic response.