楊燿州臺灣大學：機械工程學研究所陳雅媚Chen, Ya-MeiYa-MeiChen2007-11-282018-06-282007-11-282018-06-282004http://ntur.lib.ntu.edu.tw//handle/246246/61494在本文中，我們發展一套三次元有限元素法的壓電計算程式NTUPZE，並進行各種不同壓電變壓器的分析與設計。市售的商用有限元素軟體，如ANSYS和ABAQUS，雖具有分析壓電材料的功能，但卻無法將電路負載的效應加以考慮，所以本研究之壓電計算程式，是根據重新推導後之有限元素的駕馭方程式而發展，可以完整考慮各種不同的電路負載。在NTUPZE中，我們採用8個節點的三次元有限元素(8-node brick element)，並使用頻譜分析的方式(harmonic analysis)，來研究壓電變壓器在不同的頻率之放大率及相位差，並可有效地觀察變壓器中的各種物理場的分佈。本文中所模擬的變壓器的型式包括均佈式(Rosen-type)，模態式(modal-type)及單極化圓碟式(unipoled-disk-type)。關於均佈式壓電變壓器的方析，不同大小的負載為了對負載的效應加以討論，首先我們將採用兩種不同的阻尼模型(damping modal)來對均佈式壓電變壓器進行模擬，發現負載效應的加入將有效的驗證第二模態的增益大於第一模態的現象。從中可以觀察到當負載在 及 之間時，共振頻率會有激烈的變化，而當負載在 及 之間時，增益會有激烈的變化。模態式壓電變壓器之模擬的增益及相位差，也與量測的結果相符合。單極化圓碟式壓電變壓器之模擬的頻率響應結果，也驗證了己發表之實驗量測資料。In this work, we develop a 3-D finite element method (FEM) solver, NTUPZE, for piezoelectric transformer (PT) analyses. Although commercial FEM packages, such as ANSYS and ABAQUS, have the capability of performing piezoelectric analyses, they are not capable of taking electric loading effects into consideration. Therefore, the solver we developed is based on a new finite-element piezoelectric formulation that can account for various types of electric loading conditions. The solver employs the 8-node brick element, and applies the harmonic analysis to study voltage gains and phase difference at different frequencies. Using the NTUPZE, we analyze three different types of piezoelectric transformers: the Rosen-type, the modal-type, and the unipoled-disk-type. In order to discuss the influences of loadings, we adapt two different damping models, the Rayleigh model and the loss tangent model, to simulate a Rosen-type transformer. The simulated results show that the second longitudinal mode has a higher voltage gain than that of the first mode. The resonant frequency changes significantly when the loading is between and ; the voltage gain changes significantly when the loading is between and . Finally, the simulated results of the voltage gains and the phase difference for the modal-type transformers are also verified with the measured results. Also, the simulated frequency responses of the unipoled-disk-type transformers also agree with the measured results published in previous works.Table of Content ACKNOWLEDGEMENT 2 CHINESE ABSTRACT 3 ABSTRACT 4 TABLE OF FIGURES 7 LIST OF TABLES 10 CHAPTER 1 INTRODUCTION 11 1.1 BACKGROUND 11 1.2 PREVIOUS WORKS 15 1.3 MOTIVATIONS 16 CHAPTER 2 INTRODUCTION TO FINITE ELEMENT METHOD 17 2.1 GENERAL STEPS OF THE FINITE ELEMENT METHOD 17 2.2 ADVANTAGES OF THE FINITE ELEMENT METHOD 20 CHAPTER 3 EQUATIONS AND FINITE ELEMENT FORMULATION 21 3.1 THE GOVERNING EQUATION 21 3.2 THE FINITE-ELEMENT FORMULATION 26 3.2.1 Relationship between strain and displacement 28 3.2.2 Relationship between electric field and electric potential 34 3.3 THE GLOBAL MATRIX 38 3.4 DYNAMIC CONSIDERATION AND HARMONIC ANALYSIS 38 3.5 PIEZOELECTRIC TRANSFORMER AND LOADING EFFECT 41 3.6 SOLUTION OF FINITE ELEMENT EQUATION 46 CHAPTER 4 THE STRUCTURE OF THE NTUPZE 47 CHAPTER 5 CASE STUDIES 51 5.1 ROSEN-TYPE PIEZOELECTRIC TRANSFORMERS WITHOUT LOADINGS 51 5.2 THE CHARACTERISTICS OF ROSEN-TYPE PIEZOELECTRIC TRANSFORMERS WITH LOADING EFFECT 55 5.3 MODAL-TYPE PIEZOELECTRIC TRANSFORMER 60 5.4 THE UNIPOLED-DISK-TYPE PIEZOELECTRIC TRANSFORMER 68 CHAPTER 6 CONCLUSIONS 82 APPENDIX A NATURAL COORDINATE AND INTERPOLATION FUNCTION 85 A.1 LINEAR HEXAHEDRAL ELEMENT 85 A.2 QUADRATIC HEXAHEDRAL ELEMENT 87 REFERENCES 901182573 bytesapplication/pdfen-US負載壓電變壓器有限元素法finite element methodFEMpiezoelectric transformerloadingthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/61494/1/ntu-93-R90522734-1.pdf