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研究生: 陳詩潔
Chen, Shih-Chieh
論文名稱: 壓電複合型懸臂樑熱彈性阻尼分析
Analysis of Thermoelastic Damping in Composite Piezoelectric Cantilever Beam
指導教授: 李旺龍
Li, Wang-Long
學位類別: 碩士
Master
系所名稱: 工學院 - 材料科學及工程學系
Department of Materials Science and Engineering
論文出版年: 2021
畢業學年度: 109
語文別: 中文
論文頁數: 137
中文關鍵詞: 壓電懸臂樑熱彈性阻尼壓電效應驅動模式
外文關鍵詞: piezoelectric cantilever, thermoelastic damping, piezoelectric effect,, driving mode
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  • 隨著醫療科技的發展,人們為了降低侵入式的檢查及治療所帶來的不適感及降低治療可能造成後遺症,並加快復原的速度,醫療用微型機器人成為一個熱門的發展趨勢,而這些微型機器人必須有諧振器作為其運轉及蒐集數據資料的功能,驅動此機器人最重要的便是超音波馬達,而驅動其運作的便是壓電材料所製成的微機電元件,由於其應用於人體當中,人們對微型機器人的操作及追蹤能力尚不足,為此微諧振器穩定性發展尤為重要。為了提高其穩定性需更加深入了解其振盪過程中所造成的能量耗散。
    本研究將建立壓電懸臂樑熱彈性阻尼的模型,分析材料熱特性及壓電應力常數的影響。分為以下幾個部分討論:第一、分析電壓及壓電應力常數在穩態下對不同驅動模式變形影響,第二、分析單層熱彈性材料參數及壓電應力常數的影響,第三、分析尺寸效應對特徵頻率、阻尼因子及品質因子影響,第四、分析複合壓電懸臂樑,帶有質量塊及三層非對稱結構壓電懸臂樑對不同驅動模式的表現。
    從模擬可知,壓電效應使材料變形所造成的熱應力作用明顯,不可忽略,因此將探討材料熱特性及方向性對壓電懸臂樑熱彈性阻尼影響,且對於不同壓電懸臂樑驅動模式有不同程度上的變化,因此深入分析其對熱彈性阻尼的影響。

    The piezoelectric thermoelastic damping model is established, and the influence of different axis’s thermal properties is an important index of thermoelastic damping. In steady-state analysis, the research shows different driving mode of piezoelectric cantilever, and different electromechanical coupling coefficient’s influence. The dynamic analysis, we shows the transversely isotropic thermal properties have the significant influence when the piezoelectric thermoelastic damping. The composites piezoelectric discusses the influence piezoelectric material in different layer and a mass damper in different site’s influences.
    In the research, thermal expansion coefficient has the significant influence in the length. Thermal conductivity coefficient has the significant in the thick. When the piezoelectric beam in high vibration modes has different influence.

    目錄 中文摘要 I Extended Abstract II 誌謝 XIII 目錄 XIV 表目錄 XVIII 圖目錄 XIX 符號總表 XXII 第一章 緒論 1 1.1 前言 1 1.2 文獻回顧 3 1.2.1 壓電效應 4 1.2.2 熱彈性阻尼 6 1.2.3 橫向等向性材料 10 1.3 研究動機與目的 12 1.4 論文架構 13 第二章 研究理論 16 2.1 彈性變形方程式 16 2.1.1 廣義彈性矩陣 16 2.1.2 等向性彈性矩陣(立方晶系) 17 2.1.3 橫向等向彈性矩陣(六方晶系) 18 2.1.4 正交異向性彈性矩陣(正交晶系) 21 2.2 諧振器簡介 25 2.2.1 諧振器簡化模型 25 2.2.2 諧振器阻尼機制 25 2.2.3 諧振器品質因子 28 2.3 壓電理論 29 2.3.1 鋯鈦酸鉛(lead zirconate titanate,PZT) 29 2.3.2 壓電效應 31 2.3.3 壓電方程式 32 2.4 熱彈性能量方程式 34 2.5 懸臂樑特徵頻率方程式 39 2.5.1 樑運動方程式 39 2.5.2 特徵頻率方程式 45 2.5.3 熱彈性阻尼方程式 49 第三章 數值分析 59 3.1 有限元素法 59 3.1.1 數值分析求解流程 60 3.2 模擬分析流程 63 3.3 網格測試 65 第四章 結果與分析 69 4.1 模型驗證 69 4.1.1 等向性懸臂樑模型 69 4.1.2 壓電懸臂樑穩態模型 72 4.1.3 壓電懸臂樑動態模型 73 4.2 壓電懸臂樑不同驅動模式靜態分析 74 4.2.1 不同電壓對不同驅動模式位移量影響 74 4.2.2 不同壓電應力常數對不同驅動模式影響 75 4.3 壓電懸臂樑熱彈性阻尼模型分析 76 4.3.1 考慮力電耦合效應之熱彈性阻尼影響 77 4.3.2 常壓熱容量(C_p)對熱彈性阻尼影響 78 4.3.3 非極化方向熱膨脹係數(α_1)對品質因子影響 80 4.3.4 極化方向熱膨脹係數(α_3)對品質因子影響 82 4.3.5 非極化方向熱傳導係數(k_1)對品質因子影響 83 4.3.6 極化方向熱傳導係數(k_3)對品質因子影響 84 4.3.7 不同壓電應力常數對熱彈性阻尼之影響 85 4.3.8 尺寸效應 86 4.4 複合樑彈性阻尼模型分析 88 4.4.1 帶有質量塊之壓電懸臂樑熱彈性阻尼分析 89 4.4.2 三層非對稱結構壓電懸臂樑在不同振動特徵模態之熱彈性阻尼 90 第五章 結論與展望 130 5.1 結論 130 5.2 未來展望 132 參考文獻 133

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