壓電層板之靜態與動態分析

Abstract

近幾年來，壓電複合材料已經被廣泛的運用在各個領域，大多數是作為致動器或感測器當中的原件，因為具有不可或缺的重要性，所以研究其結構的振動分析便有著長遠的興趣，特別是研究多層的壓電複合材料，然而大部分研究報告顯示，所研究的壓電複材結構通常是在厚度方向有對稱性，很少有人對於不對稱的壓電複材作探討。 本文主要研究是對於兩層壓電複合材料之靜態與動態的分析，其幾何結構可表示為兩種材料的結合，上層是壓電圓板，下層是玻璃圓板，在力學方面的主要理論是根據Kirchhoff plate model，而對於電位能方面的假設，主要是要讓電位移可滿足divergence-free的要求，本篇理論模式的正確性可藉由比對理論所求出的位移，跟模擬所求出的位移相互比較，對於這樣的理論可用來當設計壓電致動器的工具或應用在生醫方面，例如微幫浦(micro-pump)。

As piezoelectric materials are widely used either as actuators or sensors, there has been a long-standing interest in the analysis of piezoelectric structures, especially for multi-layered structure. However, in most research the geometric configurations considered are symmetric in the thickness direction. There have been relatively few discussions on the vibration analysis of an asymmetric piezoelectric composite plate. In this thesis a circular glass plate with one of its surfaces bonded by a piezoelectric layer is studied. The classical Kirchhoff plate model is adopted for mechanical deformations, and the electric potential field in the piezoelectric layer is assumed such that the divergence-free requirement of the electrical displacements is satisfied. The accuracy of the analytic model is assessed by comparing the displacements in the direction obtained by the analytic model with those obtained by the finite element method. The model developed can be used as a tool for designing piezoelectric actuators such as micro-pumps.