小提琴之振動與聲場耦合分析與實驗驗證

Vibration and Acoustic Coupling Analysis and Experimental Verification for Violin

馬凱齡(Ma Kai-Ling)

指導教授 ： 王栢村

國立屏東科技大學/工學院/機械工程系所/碩士(2020年)

https://doi.org/10.6346/NPUST202000187

摘要

小提琴的發聲機制，係由拉弓激發琴弦振動、透過音箱路徑傳遞、到聲音輻射進而發出聲音，若想探討小提琴發聲過程，除了發展實驗量測方法外，建立模擬仿真分析技術，可以藉由虛擬測試來探討不同零組件之振動與聲音輻射效應，本論文旨在建立有經由實驗驗證過之有無琴弦張力效應之小提琴模型，在小提琴結構建立，其零組件木材機械性值及幾何形狀等，都對小提琴模型產生影響。因此本文針對小提琴面板素材，利用實驗模態分析(Experimental modal analysis,EMA)結果，測定面板素材機械性值，應用測定結果於小提琴模型建立。小提琴模型先以無琴弦結構進行研究，透過EMA求得之實驗模態參數，與理論分析得到理論模態參數，對無琴弦小提琴進行模型驗證(Model verification,MV)，確認無琴弦小提琴模型等效於實際結構。完成MV後加入琴弦預應力與琴弦、琴橋、拉弦板結構模擬有琴弦張力效應之小提琴，透過琴弦預應力的修正使理論模態參數與實驗模態參數相近，即完成MV。後續藉由改變不同面板幾何與材料參數，探討對小提琴琴身模態參數影響，以及應用組件模態合成法(Component mode synthsis,CMS)於小提琴面板，由分析結果驗證與完整模型一致，最後進行小提琴結構與空氣偶合之聲振耦合分析，模擬小提琴的聲音輻射效應。結果顯示，小提琴琴弦張力，對小提琴面板頻率影響微小，面板幾何變化比材料參數變化對小提琴自然頻率影響更大，小提琴不同聲場模態會貢獻不同聲音波輻射，本文建立的小提琴有限元素模型，可進一步應用於研究小提琴的模型修改，以探討不同幾何形狀或材料的變化而產生的聲音和振動影響。

關鍵字

小提琴 ； 小提琴面板素材 ； 振動 ； 聲音 ； 聲振耦合分析

並列摘要

Violin’s sound generation mechanism is from the bow motion, string vibration, and sound box vibration to sound radiation. Other than experimental measurement on sound and vibration, the simulation approach is of interest to explore the violin’s vibration as well its sound characteristics. This work is to build up the violin numerical model in considering with and without string tension effect. Since material properties may affect the simulation, this work determines mechanical properties of different wooden plates by experimental modal analysis (EMA). The obtained material properties are then applied to construct the finite element (FE) model of violin. The violin structure model without string is first studied to obtain theoretical modal parameters that are compared to those obtained from EMA. Model verification (MV) process is carried out to justify the FE model being equivalent to real structure. The string tension effect on violin is then examined, including strings, bridge and neck components in FE model. By adjusting the string pre-stressed strain, the violin model can be tuned properly for MV. Different top plate’s geometery and material constants are also examined to compare the differences in modal parameters. The component mode synthsis (CMS) model is used to simply the top plate only model and shown nearly equivalent to the full violin model. Finally, violin structure for vibro-acoustic coupling analysis is performed to study the sound radiation effect from violin. Results show the string tension has slight effects on top plate natural frequencies. The top plate geometry variation may have more effect on violin natural frequencies than materials. Different violin acoustic modes may contribute different level of sound radiation. The constructed FE model can be further applied to study model modification on the violin and explore the sound and vibration effects due to the change of geometery or materials.

並列關鍵字

violin ； top plate material ； vibration ； sound ； vibro-acoustic coupling analysis

參考文獻

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