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.

准晶体因其不寻常的特性引起了研究人员的极大关注。在本文中，提出了一种具有粘合缺陷的多层三维立方准晶矩形简支板的静态响应和自由振动的解析处理。基于三维准晶的基本弹性方程，我们根据伪Stroh形式构造了线性特征值系统，从中可以得到任意均匀层中扩展位移和应力的通解可以获得。此外，这些沿厚度方向的解可用于求解给定边界条件下的任何物理变量。对于多层板，传播矩阵用于将上界面的场变量连接到每层下界面的场变量。描述跨界面物理量不连续性的特殊弹簧模型被引入到结构的整体传播器关系中。与传统的传播子矩阵方法相比，建立了一种新的传播子关系来解决大纵横比和高阶频率情况下具有缺陷界面的QC层压板的数值不稳定性。此外，考虑层状板顶面和底面的无牵引边界条件来研究层压板的自由振动特性。最后，通过典型的数值算例说明了非完美界面对立方准晶板静态响应和自由振动的影响。