小提琴的品質受到許多因素的影響，無論是其外型結構或是材料的厚度、密度及剛性等等。本文利用有限元素軟體ANSYS模擬小提琴的振動，探討改變幾何及材料參數對小提琴品質的影響。
第一部分先探討面、背板的材料參數對小提琴振動模態與驅動點導納值的影響，結果顯示若適當降低背板之Ex值，或適當提高背板之密度，且其他條件不變的情況下，理論上可提升小提琴之品質。
第二部分探討面板幾何參數之影響，本文將面板修剪的過程分成四個案例討論，結果顯示小提琴面板的外型及厚度在修剪過程中，其第一、第二、第五模態的振動頻率逐漸趨近於1:2:4。

In designing or manufacturing the top and back plates, their geometry, thickness, stiffness and density are the main factors which affect the quality of violins. In this study, the vibration analysis of violin is performed by applying the finite element software package. The variations of natural frequencies, mode shapes, and driving point input admittance with the plate parameters are discussed graphically. All these parameters can be equivalently considered by examining the expression of the natural frequency based on the plate theory.
The results show that the reduction of stiffness or increasing the density of back plate will improve the violin quality. During the assumed four carving steps on the top plate, the first, second, and fifth nature frequencies will approach to the ratio of 1:2:4.

[1] Hutchins, C. M., "The acoustics of violin plates", Sci. Am., pp. 170-186, 1981.
[2] Moral, J. A. and Jansson, E. V., "Eigenmodes, input admittance, and the function of the violin", Acustica, Vol. 50, No. 5, pp. 229-337, 1982.
[3] Moral, J. A. and Jansson, E. V., "Input admittance, eigenmodes, and quality of violins", STL-QPSR, Vol. 23, No. 2-3, pp. 60-75, 1982.
[4] Jansson, E. V., Moral, J. A., and Niewczyk, J., "Experiments with free violin plates", J. Catgut Acoust. Soc. 2d ser., pp. 2-6, 1988.
[5] Jansson, E. V., Niewczyk, B. K. and Fryden, L., "On the body resonance C3 and its relation to the violin construction", STL-QPSR, Vol. 36, No. 4, pp. 1-10, 1995.
[6] Jansson, E. V., Niewczyk, B. K. and Fryden, L., "On the body resonance C3 and its relation to the violin construction", TMH-QPSR, Vol. 37, No. 1, pp. 23-30, 1996.
[7] Bretos, J., Santamaria, C. and Moral, J. A., "Vibrational patterns and frequency responses of the free plate and box of a violin obtained by finite element analysis", J. Acoust. Soc. Am., Vol. 105, No. 3, pp. 1942-1950, March 1999.
[8] Stowell, R., The cambridge companion of the violin, 湯定九譯，小提琴指南，世界文物出版社，台北市，中華民國，13-75頁，1996。
[9] 陳元光，提琴之制作與修復，上海教育出版社，上海，中國，2005。
[10] 鄭德淵，音樂的科學，大陸書局，台北市，中華民國，2003。
[11] Fletcher, N. H. and Rossing, T. D., The physics of musical instruments, Spring-Verlag, New York, USA, 1991.
[12] 唐林、張永德及陶純孝，音樂物理學理論，中國科學技術大學出版社，合肥，1991。
[13] 劉晉奇、褚晴暉，有限元素分析與ANSYS的工程應用，滄海書局，台中市，中華民國，2006。
[14] 劉成群、張超群，汽車振動與噪音（第二版），新文京開發出版股份有限公司，台北縣，中華民國，2006。
[15] 洪國鈞，小提琴琴橋振動分析，國立成功大學機械工程學系碩士論文，2009。
[16] 林冠廷，全尺寸小提琴有限元素模型之建立，國立成功大學機械工程學系碩士論文，2012。
[17] Green, D. W., Winandy, J. E. and Kretschmann, D. E., Mechanical properties of wood, USDA, USA, Chapter 4, pp. 2, 1999.
[18] Knott, G. A., "A modal analysis of the violin using MSC/NASTRAN and PATRAN", Naval Postgraduate School, Monterey, March 1987.
[19] Jansson, E. V., Acoustic for violin and guitar makers, Dept. of Speech, Music and Hearing, KTH, Sweden, 2002.
[20] Jansson, E. V., "Admittance measurements of 25 high quality violins", Acustica, Vol. 83, pp. 337-341, 1997.
[21] Strobel, H. A., Art and method of the violin maker, Aumsville, Oregon, USA, 2006.
[22] Jansson, E. V., "Admittance measurements of 25 high quality violins", Acustica, Vol. 83, pp. 337-341, 1997.
[23] Christensen, O. and Vistisen, B. B., "Simple model for low-frequency guitar function", 1980.
[24] Torres, J. A. and Boullosa, R. R., "Influence of the bridge on the vibrations of the top plate of a classical guitar", Acoustics, 2009.