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研究生：	劉紀緯 Liu, Chi-Wei
論文名稱：	利用基因演算法於聲子晶體能隙及聲波整流之最佳化設計 The Optimization of Band Gap in Phononic Crystal and Acoustic Rectification Design using Genetic Algorithm
指導教授：	張怡玲 Chang, I-Ling
學位類別：	碩士 Master
系所名稱：	工學院 - 機械工程學系 Department of Mechanical Engineering
論文出版年：	2019
畢業學年度：	107
語文別：	中文
論文頁數：	124
中文關鍵詞：	聲子晶體平板、蘭姆波、頻帶結構、能隙、基因演算法、陶瓷壓電片
外文關鍵詞：	phononic crystal plate, Lamb wave, band structure, band gap, genetic algorithm, PZT transducer
相關次數：	點閱：118 下載：4
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本研究利用基因演算法對平板上的聲子晶體進行最佳化設計，以能隙的頻寬與中心頻率比值作為目標函數，探討不同頻帶間的能隙，設計出具備寬頻且低頻能隙的週期結構，並與圓洞型聲子晶體結構作比較，最後利用圓洞型聲子晶體的部分能隙初步設計聲波二極體結構。

在三維結構中，要找出聲子晶體的完全能隙或甚至部分能隙較一般二維聲子晶體困難。針對圓洞型聲子晶體，藉由不同模態的位移場特徵可將模態分類，剃除掉非蘭姆波的頻帶以降低分析頻帶結構的難度；而在能隙最佳化設計，本文處理手法為將模擬模型簡化成二維模型進行頻帶結構計算，一方面可以過濾掉非蘭姆波模態，同時也減少了大量計算資源有利於基因演算法最佳化。最後透過全波模擬打入特定模態的蘭姆波並計算穿透率，用以佐證頻帶結構中所觀察到的能隙現象。

實驗量測部分，使用陶瓷壓電片式超聲波換能器進行量測，藉由調控壓電片的幾何尺寸使激振的蘭姆波中心頻率在聲子能隙上進行實驗量測，觀察訊號在能隙頻段內的衰減情形，並與全波模擬穿透率的結果進行比對。綜合模擬與實驗結果，本研究提供一套聲子晶體最佳化的流程與分析方法，可作為往後聲子晶體平板元件設計之依據。

In this study, genetic algorithm is adopted to carry out the topology optimization of phononic crystal (PnC) plate with the maximized relative band gap between two prescribed consecutive dispersion branches. This method is to design the periodic structures with broadband and low frequency band gaps, and then comparing the results with round hole-type PnC’s. Finally, we preliminarily designed for the acoustic diode by using the partial band gaps of the round hole-type one.

In three-dimensional model, it is more difficult to find the complete or even the partial band gap than the two-dimensional one, so some strategies are used to analyze the band structure. For round hole-type, we classify the dispersion band by the characteristics of the displacement field of different Lamb wave propagation modes. For band gap optimization, it is useful to filter out the non-Lamb wave modes by simplifying the simulation model into plane stress. At the same time, it also reduces a large amount of computing resource, which is beneficial for the optimization of genetic algorithm.

In experimental measurement, we utilize the PZT transducer to measure the SS304 plate with PnC structures. The decrease of transmittance on band gaps can be found in measurement results, which is consistent with simulation results. Based on this research, we can build a set of procedures and analysis methods for the optimization of PnCs, which can be treat as a basis for the design of PnC plate components in the future.

摘要 I
Abstract II
誌謝 XIV
目錄 XV
表目錄 XIX
圖目錄 XX
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.2.1 聲子晶體平板 2
1.2.2 聲波二極體 3
1.2.3 基因演算法 3
1.2.4 壓電材料 4
1.3 動機與目的 4
1.4 本文架構 5
第二章 基本理論、實驗建置與原理 7
2.1 蘭姆波之理論解及其特性 7
2.2 聲子晶體基本理論 9
2.2.1 倒晶格(Reciprocal lattice) 10
I. 倒晶格定義 10
II. 第一布里淵區(Brillouin zone) 12
2.2.2 布洛赫定理(Bloch’s Theroem) 12
2.2.3 聲子晶體平板的數值計算方法 13
I. 平面波展開法 14
II. 有限元素法 15
2.3 基因演算法基本理論 16
2.3.1 適應函數 16
2.3.2 運算因子 16
I. 選擇複製 17
II. 交配 17
III. 突變 18
2.3.3 終止條件 18
2.4 材料參數量測 19
2.4.1 波速量測 19
2.4.2 材料性質換算 19
2.5 陶瓷壓電片式超聲波換能器 20
2.5.1換能器之構成與製作 20
2.5.2 矩形壓電片之特性 21
I. 壓電片的寬度 21
II. 壓電片的長度 21
III. 壓電片的厚度 21
IV. 壓電片的擺設配置 22
2.6 實驗方法與流程 22
第三章 聲子晶體平板分析與能隙最佳化設計 40
3.1 聲子晶體平板基本分析流程 40
3.1.1 頻帶結構分析 40
3.1.2 模態判斷 41
3.1.3 全波模擬與穿透率之計算 43
3.1.4 幾何尺寸對能隙之影響 45
I. 板厚的影響 45
II. 圓洞直徑的影響 45
3.1.5 聲波二極體結構設計 46
3.2 聲子晶體能隙最佳化設計 48
3.2.1 模擬模型之簡化 48
3.2.2 基因演算法相關設定 50
I. 基因編碼與圖形連續性判斷 50
II. 基因演算之參數設定 51
III. 圖形相似性判斷 51
3.2.3 圖形平滑化處理 52
3.2.4 最佳化流程 53
3.2.5 聲子晶體最佳化問題 54
I. 完全能隙最佳化 54
II. 部分能隙最佳化 56
第四章 聲子晶體平板之實驗量測 93
4.1 量測試片準備 93
4.1.1 陶瓷壓電片之設計 93
I. 壓電片尺寸 93
II. 壓電片厚度 94
III. 壓電片擺設配置 94
4.1.2 聲子晶體結構之設計 95
4.1.3 試件材料參數檢測 96
4.2 試片量測結果 96
4.2.4 圓洞型聲子晶體平板量測結果 97
4.2.5 最佳化聲子晶體結構平板之量測結果 99
第五章 結論與未來展望 113
5.1 結論 113
5.1.1 圓洞型聲子晶體平板之模擬分析 113
5.1.2 能隙最佳化之分析設計 113
5.1.3 實驗量測 114
5.2 未來展望 114
參考文獻 115
附錄 118
A. 不同厚度下，圓洞型聲子晶體平板之頻帶結構 118
B. 二維與三維模型之頻散曲線比較 119
C. 試件材料參數量測 123
                                    

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校內：2024-02-13公開
校外：2024-02-13公開

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