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Finite elements for electrically unbounded piezoelectric vibrations.

机译：无限电压电振动的有限元。

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摘要

In the modeling of piezoelectric vibrators, one of the universally used assumptions is that the exterior electroquasistatic field due to the electric flux leakage through the piezoelectric-air interface can be neglected. This approximation, valid for materials with large dielectric constants, can introduce a significant error in the simulation of piezoelectric crystals whose permittivity is comparable with that of free space. Because models that take into account the electric flux leakage are virtually non-existent, the objective of this thesis is to develop a solution of the three-dimensional piezoelectric problem which is referred to, by analogy with electromagnetics, as electrically unbounded.;To begin with, the general piezoelectric boundary-value problem with open electric boundaries is stated in the form of differential, variational, and projective equations. The latter formulation serves to construct the finite element solution of the system of piezoelectric equations. Tetrahedral elements of high order, assembled by means of universal matrices, are used to approximate the coupled mechanical and electric fields in the interior region. The exterior infinitely extending electric field is modeled by a single 'superelement', obtained by the ballooning method, and automatically compatible with the interior finite element discretization. After imposing electrical, static or homogeneous, boundary conditions on the matrix equations, the associated deterministic problem is solved for the full piezoelectric static capacitance using the preconditioned conjugate gradient method, while the eigenvalue problems are solved for the two resonant frequencies by a variant of the Lanczos method. Convergence and computer implementation of both methods, as well as of the associated data structures are described in detail.;The effect of the external electric field on static and motional parameters is studied for various types of rectangular piezoelectric vibrators. Illustrative examples involving different geometries, materials, electrode shapes and modes show that the leakage field increases the static capacitance, reduces the effective piezoelectric coupling and the spacing between the two resonant frequencies, and activates many spurious modes.
机译：在压电振动器的建模中，普遍使用的假设之一是可以忽略由于通过压电-空气界面泄漏的通量引起的外部准静电场。这种近似值适用于介电常数大的材料，会在介电常数与自由空间相当的压电晶体的模拟中引入很大的误差。由于实际上不存在考虑到漏电的模型，因此本论文的目的是开发三维压电问题的解决方案，该问题类似于电磁学，被称为无界的。通常，具有开放电边界的压电边界值问题以微分，变分和投影方程的形式表示。后一种公式用于构造压电方程组的有限元解。通过通用矩阵组装的高阶四面体元素用于近似内部区域中耦合的机械场和电场。外部无限扩展的电场通过气球法获得的单个“超元素”进行建模，并自动与内部有限元离散化兼容。在矩阵方程上施加电，静态或均质边界条件后，使用预处理的共轭梯度方法解决了全压电静电容的相关确定性问题，而两个谐振频率的特征值问题通过以下方法求解： Lanczos方法。详细介绍了这两种方法以及相关数据结构的收敛性和计算机实现。研究了各种矩形压电振动器的外部电场对静态和运动参数的影响。涉及不同几何形状，材料，电极形状和模式的说明性示例表明，泄漏场增加了静电容，减小了有效的压电耦合和两个谐振频率之间的间隔，并激活了许多杂散模式。

著录项

  • 作者

    Antonova, Elena.;

  • 作者单位

    McGill University (Canada).;

  • 授予单位 McGill University (Canada).;
  • 学科 Electrical engineering.
  • 学位 Ph.D.
  • 年度 2000
  • 页码 236 p.
  • 总页数 236
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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