本文針對壓電系統於柔性結構控制，自由落體感應子及壓電變壓器上的應用提出全新的設計觀點，並引入兩種新型的均佈式感應子來設計柔性結構控制及自由落體感應子的壓電系統，分別為一增益函數與相位可分立設計之振動檢測裝置(APROPOS device)及具對稱特性之增益函數與相位可分立設計之振動檢測裝置(symmetric APROPOS device)。其中增益函數與相位可分立設計之振動檢測裝置於設計過程中引入映象原理及窗函數的觀念，其設計理念將有限域結構投射至無限域中，以求對系統的轉移函數加入具無相位延遲特性的各種低通濾波器；而具對稱特性之增益函數與相位可分立設計之振動檢測裝置利用其對稱的電極來量出結構應變分布的偶函數部分，而可直接於設計理念中，對有限域感應子的轉移函數中加入具沒有相位延遲特性的多種低通濾波器。這兩種新發明之均佈型的振動檢測裝置成功的突破傳統均佈式感應子的限制，可以順利處理結構的邊界條件及消散波的影響，因此本文所發明的這兩種均佈式感應子設計理念可將感應子設置在待測結構上的任意位置，如此一來，點式均佈型感應子的設計理念即可實現，所謂點式均佈型感應子乃是應用增益函數與相位可分立設計之振動檢測裝置來將一柔性結構作為感應子之本體結構，並利用前述創新發明來對此本體結構的轉移函數提供一沒有相位延遲的低通濾波器，而後再將此一以柔性結構為本體感應子結構的感應子當作點式感應子來使用，因此點式均佈型感應子具有高感應度及可用頻寬的特性。本文所發明之自由落體感應子採用了點式均佈型感應子的設計理念，發展成功全球唯一具有量測自由落體運動的小型創新感應子，可提供預警訊號於所附著的系統，用途包含提供各種可攜式裝置的自我保護設計所需之觸發訊號。
不同於前述對柔性結構控制及自由落體感應子的設計觀點，壓電變壓器是一個傳遞能量的元件，需工作在最佳能量傳輸的狀況下，並作用在一個有限結構的共振頻上，所以壓電變壓器是一個力電完全偶合的系統，傳統的壓電變壓器皆以一等效電路來模擬壓電變壓器的機械振動行為，但壓電變壓器本身是一個有限的機械結構，其統禦方程式是一偏微分方程，並非由一個常微分方程所表示的等效電路所可簡化之，再者，壓電變壓器是一個力電完全偶合的結構，其機械共振特性將受到其機械及電性的邊界條件所影響，當用一等效電路模擬壓電變壓器的振動行為時，其力電偶合的現象將被均化，而所有空間的振動特性都無法被此等效電路所描述，本文導出壓電變壓器的完整動態方程式，並考慮其機械及電性的邊界條件，由於壓電變壓器的空間效應被完整考慮，本文提出以空間權重的觀念設計創新壓電變壓器，以達到壓電變壓器的最佳化設計。為了使此一新設計之壓電變壓器可成為一成熟的產品，本文提出其整個壓電變壓器系統的設計觀點，以尋找推動大量生產所需的各種設計參數。一本文所提設計流程，壓電變壓器的架設、導線的設置、熱的導出及尺寸的挑選設計等，可被完整的考慮來設計最佳化的壓電變壓器。易言之，基於所討論的系統設計觀點，本文提出壓電變壓器最佳化的系統設計流程，以達到量產的需求。
總而言之，本文以系統設計的眼光，提出對柔性結構控制，自由落體感應子及壓電變壓器的全新設計觀點，並以理論及實驗證明此全新設計觀點於壓電系統設計的衝擊及其貢獻。

In this dissertation, brand new design viewpoints of piezoelectric systems applicable to the smart structure, free-fall sensor, and piezoelectric transformer were detailed. Two series of innovative devices, which are APROPOS device and symmetric APROPOS device, were introduced pursue smart structure applications. By introducing the concepts of the method of image and the window function, the APROPOS device can introduce additional no-phase delay filters in the infinite domain. On the other hand, symmetric APROPOS device matched the even part of the structure strain to introduce no-phase delay low-pass filters. With the concepts of APROPOS device and symmetric APROPOS device, new design concepts of point and distributed sensors were developed. Both of the APROPOS device and symmetric APROPOS device were distributed sensors that could be placed at any locations on a finite structure and have the abilities to deal with low wavelength range, boundary conditions, and evanescent waves, which broke through the limitations of traditional distributed sensors. A free-fall sensor is a Point-Distributed sensor, which applied the no-phase delay low-pass filter induced by the APROPOS device on its flexible sensor structure, had high sensitivity at low frequency and wide usable bandwidth. By possessing these abilities, the free-fall sensor was found to be the only sensor that could measure the free-fall motion and offer warming signal to the attached object to perform protection.
Different from the design viewpoints of the smart structures and free-fall sensor, the piezoelectric transformer required optimized power transformer. Piezoelectric transformers should be considered not only as a mechanical system but also an electrical fully coupled system, which uses finite structure resonance to perform voltage conversion. Traditional piezoelectric transformers used an equivalent circuit model concept to simulate its mechanical motion. Since the field equation of a piezoelectric transformer is a partial differential equation, an equivalent circuit model developed based on an ordinary differential equation cannot express its performance thoroughly. Since the motion of the piezoelectric transformer is determined by both the mechanical and the electrical boundary conditions, the transfer function and the electrical impedance of a piezoelectric transformer will vary with different electrical and mechanical conditions. However, it has been discovered that once an equivalent circuit was used to simplify the mechanical motion of the piezoelectric transformer, the coupling effects between the mechanical and the electrical properties will be averaged out and all spatial information will be lost. A fully coupled field equation is derived in this article to examine the motion of the piezoelectric transformer by taking into account both the mechanical and electrical boundary conditions. It can be shown that by using this newly developed field equation, a new concept using a weighting function in the spatial domain can be adopted to optimize the electro-mechanical coupling effects. To design a piezoelectric system that could be commercialized, the influences of support structure, heat conduction, wire bounding, and compatibility of mass production were also detailed. In addition, the design flow of a commercialized piezoelectric transformer system was summarized. In summary, all of the design viewpoints of applying the piezoelectric systems onto the smart structure, free-fall sensor, and piezoelectric transformer were all verified theoretically and experimentally.

Chapter 1. Introduction 1
1.1 Piezoelectricity 4
1.1.1 The constitutive equations of piezoelectric materials 7
1.1.2 The governing equations of piezoelectric solids 12
1.1.3 The boundary conditions and continuity conditions of a piezoelectric solid 13
1.2 Overview 16
Part I. Electro-mechanically decoupled piezoelectric system
A. Smart Structures
Chapter 2 Smart Structures and the Flexible Structure Control 22
Chapter 3 Theory of Piezoelectric Laminates 29
3.1 The Sensor Equation for a Fourth Order Structure System 35
3.2 The Sensor Equation for the Second Order Structure System 38
3.3 The Concept of Distributed Sensor and Actuator 41
Chapter 4 The Concepts of the APROPOS Device 44
4.1 Wave Modes in One-Dimensional Plate 44
4.2 The Method of Image 49
4.3 Design Concepts of APROPOS Device 51
4.3.1 The base of the APROPOS device 59
4.3.2 The superposition characteristic of the APROPOS device 63
4.3.3 Implement the APROPOS device by the method of image 70
4.3.4 Implement the APROPOS device by the window function 84
4.3.5 The APROPOS device for various boundary conditions 95
4-4 The APROPOS Device for Second Order Structure System 98
4.4.1 Wave modes in second order structure system 98
4.4.2 The sensor equation of a second order APROPOS Devices 100
4.4.3 Implementation of a second order APROPOS devices 101
4.4.4 Developing testing methodology: A new shaker 103
4.4.5 Experimental set-up 105
Chapter 5 The Frequency Selectivity of the APROPOS Device in Spatial Domain 109
Chapter 6 Concepts of the Symmetric APROPOS Device 117
6.1 Sensor Equation of the Symmetric APROPOS Device 118
6.2 Sensor Equation of a Symmetric APROPOS Device on a cantilever Plate 121
6.2.1 Symmetric APROPOS device as a point sensor 129
6.2.2 Experimental set-up
6.3 Point-Distributed Strain Gage Designed by the Symmetric APROPOS Device 137
6.3.1 Point-Distributed strain gage 142
6.3.2 Experimental set-up 144
Chapter 7 The Active APROPOS Device 144
7.1 Active APROPOS Device by Feedback Control Theory 145
7.2 Experimental Setup 152
B. Free-Fall Sensor
Chapter 8 Introduction to the Miniature Free-Fall Sensor 156
8.1 The Possibility and Practicability of the Free-Fall Sensors 157
8.2 Free-fall Sensors and Flexible Structures Sensing 158
Chapter 9 The Concept of the Miniature Free-Fall sensor 164
9.1 The Concept of Point-Distributed Sensor 162
9.2 The Measurement of Free-Fall Motion: Filtered by Electrical circiuts 170
9.3 Implementation of a Miniature Free-Fall Sensor by the APROPOS Device 177
9.4 Other Applicable Physical Effects 179
Chapter 10 General View of the APROPOS Device and the Symmetric APROPOS Device on Point and Distributed Sensors 186
Part II. Electro-mechanical fully coupled piezoelectric system
C. Piezoelectric Transformer
Chapter 11 Introduction to the Piezoelectric Transformer 193
Chapter 12 Theory of Piezoelectric Plate 203
12.1 Two Dimensional Constitutive Equation of Piezoelectric Plates 204
12.2 Governing Equations of one-Dimensional Piezoelectric Plate 209
12.2.1 Governing equations of the surface-to-surface piezoelectric transformer 209
12.2.2 Governing equations of the Rosen-type piezoelectric transformer 212
Chapter 13 The Field Equation of the Piezoelectric Transformer 219
13.1 General Solutions for Surface-to-Surface Piezoelectric Transformer 219
13.1.1 Optimization of the surface-to-surface piezoelectric transformer 224
13.1.1-1 Maximum power transfer by impedance match 225
13.1.1-2 Optimizing sensors and actuators by matching modal strain 228
13.1.2 Experimental set-up of the surface-to-surface piezoelectric transformer 230
13.2 General Solutions for the Rosen-type Piezoelectric Transformer 238
13.2.1 Optimization of the Rosen-type piezoelectric transformer 242
13.2.1-1 Maximum power transfer by impedance match 242
13.2.1-2 Optimizing sensors and actuators by matching modal strain 244
13.2.2 Experimental setup of the Rosen-type piezoelectric transformer 246
Chapter 14 Systematic Design of the Piezoelectric Transformer 254
14.1 The Design of the Feedback Node 259
14.1.1 Pole-zero alternating phenomenon between sensor and actuator on a finite structure 261
14.1.2 Transfer functions of the feedback node on piezoelectric plates 263
14.1.3 Experimental set-up 272
14.1.4 Feedback node design for piezoelectric transformers 281
14.2 The Support Structures of the Piezoelectric Transformer 285
14.3 The Shape Effect of the Piezoelectric Transformer 291
14.4 Manufacturing Process Design 295
14.5 Design Flow of the Piezoelectric Transformer 300
Chapter 15 Conclusions 302

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