# 臺灣博碩士論文加值系統

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 本文建立一全尺寸小提琴有限元素模型，藉由彈性力學與振動力學進行模態分析，求出其自然頻率與振動模態，同時利用頻率響應分析求出驅動點導納。首先比較琴體與全尺寸小提琴有無架設弦之間的頻率響應。結果顯示全尺寸小提琴架設弦與琴體之自然頻率是十分接近的，接近的現象同樣發生在驅動點導納值的比較。因此，預先施加張力之弦在全尺寸小提琴模型中是不可被忽略的。其次討探弦張力對於振動行為所帶來之影響；分配給各弦三組不同的張力，其可能對整體小提琴帶來動態響應之差異。結果指出T1、C3 和C4 模態之自然頻率與驅動點導納幾乎是相同的。考量弦之使用壽命，建議給予較小之弦張力即可。最後討論小提琴琴橋之高度在固定四條弦的自然頻率下所扮演之角色。琴橋高度分別為34mm、33mm 和32mm。依據小提琴製琴師王聖哲老師所提出之建議：小提琴四條弦，G、D、A 與E 弦，四條弦應等長，長度容許差異值為±0.1mm；而本模型之弦長度最大差異為0.9mm，故小提琴琴橋高度所帶來影響之結果，其驅動點導納之結論僅為參考依據。依據本主題數值結果顯示，琴橋高度34mm 與33mm 會呈現較佳之驅動點導納值。
 A finite element model of a full size violin is established in this research. The natural frequencies and modes are computed by performing the modal analysis according based on the theories of elasticity and mechanical vibration. Also, the input admittances are obtained by using the harmonic response analysis. Firstly, the difference of the vibration response between the models of the simple violin body and the full size violin with or without the strings attached is studied. It shows that the natural frequency of the full model with attached strings is approximately the same as that of the violin body model. Similar results can be observed from the variations of the input admittances. Therefore, the strings with pretension cannot be ignored when the full model of violin is considered. Secondly, the influence of the string tensions on the vibration responses will be investigated. Three tension forces, that may affect the whole structure dynamic response, are assigned to the strings. The results indicate that the natural frequencies and the input admittances of modes T1, C3, and C4 in three cases are almost the same. In order to extend the string life, smaller tension forces assigned to the strings are suggested. Lastly, the role of the bridge height will be studied under the condition that the natural frequencies of the four strings are kept to be the same. Three bridge heights chosen in this study are 34mm, 33mm and 32mm, respectively. According to the opinion of a violin repairer-restorer, Baroque Wang, the lengths of four strings G, D, A and E for a good violin should be kept within the tolerance ±0.1mm. In our model, the largest difference between the strings is 0.9mm. Therefore, the conclusion of the bridge height effects on input admittance can be used only as a reference. In our case, the heights with 34mm and 33mm give better input admittance.
 摘要 ............................................. IAbstract.......................................... II誌謝 ............................................. IV目錄 ............................................. V表目錄............................................ VIII圖目錄............................................ IX符號表............................................ XIV第一章 緒論....................................... 11.1 前言.......................................... 11.2 文獻回顧...................................... 11.3 研究動機...................................... 71.4 論文架構...................................... 7第二章 小提琴簡介與理論基礎....................... 92.1 小提琴簡介.................................... 92.1.1 小提琴的構造................................ 92.1.2 琴體的振動.................................. 152.2 彈性振動力學.................................. 182.2.1 非等向性材料................................ 182.2.2 正交性材料.................................. 192.2.3 圓柱正交性材料.............................. 212.2.4 等向性材料.................................. 232.2.5 弦的振動.................................... 242.2.6 模態分析.................................... 252.2.7 簡諧響應分析................................ 262.2.8 驅動點導納.................................. 27第三章 有限元素模型建立與問題分析................. 293.1 三維模型建立.................................. 293.1.1 琴體........................................ 293.1.2 琴頭、弦軸、琴頸、弦枕與指板等.............. 363.1.3 尾板、尾枕與尾端腸弦環...................... 413.1.4 組合........................................ 433.1.5 弦之架設.................................... 443.2 有限元素模型建立.............................. 443.2.1 單位系統.................................... 443.2.2 有限元素之選擇.............................. 453.2.3 MPC（Multi-Point Constraint） .............. 483.2.4 有限元素模型................................ 493.2.5 材料性質參數................................ 503.3 問題分析...................................... 543.3.1 邊界設定.................................... 543.3.2 討論主題.................................... 563.3.3 模擬流程.................................... 57第四章 結果與討論................................. 594.1 琴體與全尺寸小提琴之差異...................... 594.2 弦張力大小的影響.............................. 684.3 琴橋高度的影響................................ 82第五章 結論....................................... 95參考文獻.......................................... 97
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 1 小提琴琴橋振動分析 2 音柱對小提琴振動之影響分析(Ⅱ) 3 低音樑對小提琴振動之影響 4 音柱對小提琴振動之影響分析 5 微震監測自動化系統程式之建立 6 複合材料積層板之振動模態分析 7 旋轉三維Timoshenko梁之振動分析 8 複合圓環板之軸對稱有限元素法與實驗振動研究 9 基於聲音特性之鐵琴片設計分析 10 附帶多個質量與彈簧多跨距樑的自然頻率及模態之研究 11 爆炸銲接雙金屬樑之動態性能分析 12 利用力偶應力理論與大變形理論對微形樑自然頻率之探討 13 具有多個不同截面形狀段樑及剛體之混合樑的自由振動分析 14 附帶多個剛體之複合樑的動態分析 15 加工中心機組立對切削性能之影響

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