Abstract

This paper presents the analytical solutions for the anti-plane problem in one-dimensional hexagonal piezoelectric quasicrystal plates using the symplectic elasticity approach. The equilibrium equations with body forces are transformed into the Hamiltonian system using the variational principle, and then the corresponding Hamiltonian operator matrix is derived. Furthermore, the completeness of the eigenfunction system of the operator is proved, and the general solutions to the problem are given by utilizing the symplectic orthogonality. As an application, the numerical results are obtained for the rectangular plates under the lateral concentrated load.

中文翻译：

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一维六方压电准晶板反平面问题的辛弹性法

摘要

本文提出了使用辛弹性方法解决一维六方压电准晶板反平面问题的解析解。利用变分原理将具有体力的平衡方程转化为哈密顿系统，并推导出相应的哈密顿算子矩阵。进一步证明了算子本征函数系的完备性，并利用辛正交性给出了问题的一般解。作为应用，获得了矩形板在横向集中荷载作用下的数值结果。