Static response and free vibration analysis for cubic quasicrystal laminates with imperfect interfaces

Abstract

Quasicrystals have attracted the tremendous attention of researchers for their unusual properties. In this paper, an analytical treatment is presented for the static response and free vibration of a multilayered three-dimensional, cubic quasicrystal rectangular simply supported plate with bonding imperfections. Based on the basic elasticity equation of three-dimensional quasicrystals, we construct the linear eigenvalue system in terms of the pseudo-Stroh formalism, from which the general solutions of the extended displacements and stresses in any homogeneous layer can be obtained. Furthermore, these solutions along the thickness direction can be utilized to solve any physical variables under given boundary conditions. For multilayered plates, the propagator matrices are employed to connect the field variables at the upper interface to those at the lower interface of each layer. The special spring model, which describes the discontinuity of the physical quantities across the interface, is introduced into the overall propagator relationship of the structure. Compared with the conventional propagator matrix method, a new propagator relation is established to resolve numerical instabilities of the case of large aspect ratio and high-order frequencies for QC laminates with imperfect interface. In addition, the traction-free boundary condition on the top and bottom surfaces of the layered plate is considered to investigate the free vibration characteristics of the laminates. Finally, typical numerical examples are presented to illustrate the influence of imperfect interfaces on static response and free vibration of cubic quasicrystal plates.