Static response of functionally graded multilayered one-dimensional hexagonal piezoelectric quasicrystal plates using the state vector approach

Abstract

The effect of the non-homogeneity of material properties has been considered the important variation mechanism in the static responses of quasicrystal structures, but the existing theoretical model for it is unable to simulate the material change format beyond the exponential function. In this paper, we create a new model of functionally graded multilayered 1D piezoelectric quasicrystal plates using the state vector approach, in which varying functionally graded electro-elastic properties can be extended from exponential to linear and higher order in the thickness direction. Based on the state equations, an analytical solution for a single plate has been derived, and the result for the corresponding multilayered case is obtained utilizing the propagator matrix method. The present study shows, in particular, that coefficient orders of two varying functions (the power function and the exponential function) of the material gradient provide the ability to tailor the mechanical behaviors in the system’s phonon, phason, and electric fields. Moreover, the insensitive points of phonon stress and electric potential under functionally graded effects in the quasicrystal layer are observed. In addition, the influences of stacking sequences and discontinuity of horizontal stress are explored in the simulation by the new model. The results are very useful for the design and understanding of the characterization of functionally graded piezoelectric quasicrystal materials in their applications to multilayered systems.

摘 要

目 的

功能梯度准晶材料有助于减缓层合板界面处的应力集中现象, 提高层间粘接**度, 从而提升层合板表面的耐磨性。 本文旨在建立功能梯度压电准晶层合板的力学模型, 并研究功能梯度变化和叠放顺序对层合板的影响。

创新点

• 1. 首次将状态向量法推广到功能梯度压电准晶板的分析中;

• 2. 假设功能梯度函数的变化形式为幂函数和指数函数;

• 3. 在准晶层中观察到声子场应力和电势的不敏感点。

方 法

• 1. 通过联立三大基本方程, 推导出准晶板的状态方程, 并求解该微分方程, 得到单层准晶板的解析解;

• 2. 通过引入功能梯度函数, 使解析解中的描述各材料特性的值能够沿厚度方向呈现梯度变化;

• 3. 采用传递矩阵法, 求出多层准晶板的解析解;

• 4. 通过仿真模拟, 将所得结果与已有文献进行对比, 验证所提方法的可行性和有效性。

结 论

• 1. 准晶层合板中的功能梯度效应随着梯度参数的增加而增大, 且材料参数的变化对声子场、 相位子场以及电场的响应均产生影响。

• 2. 在功能梯度效应下, 从准晶层中观察到了声子场应力和电势的不敏感点。

• 3. 与准晶作为中间层相比, 准晶作为表层时机械载荷引起的位移响应更小。 研究结果可以为压电准晶元器件的设计提供理论参考。