低音樑在小提琴的結構及聲學性質上皆有相當的重要性，它能使面板強度增加且傳遞振動提高自然頻率，並使小提琴低音部分充實優美。本文利用電腦有限元素軟體，從低音樑的必要性、位置以及含水率三個主題來探討低音樑對小提琴振動的影響。由振動模態及驅動點導納圖發現，無低音樑的小提琴導納值較高，會造成泛音的組成改變，甚至可能產生狼音;將低音樑的位置往中線移動6mm會使小提琴的品質下降;而低音樑含水率對高頻的影響大於低頻，但整體來看影響很小。

Bassbar plays an important role in violin structures and acoustic properties. It will enhance strength of the top plate and increases the natural frequencies. Also it could make the bass part full and graceful. In this article, we use finite element analysis to simulate the vibration of violins. The natural modes and input admittances subjected to harmonic excitations are used to evaluate the performance of a violin. The necessity of bassbar in a violin structure is firstly studied. It shows that a violin without bassbar would have higher admittances and change the composition of Harmonics. Then, the position of the bassbar and the moisture content of the bassbar wood are taken into consideration. Shifting bassbar 6mm towards the center line may make the violin quality dropped. And the influence of bassbar moisture on higher frequencies is stronger than on lower frequencies, although as a whole it is not significant.

參考文獻
[1] 鄭德淵，音樂的科學，大陸書店，台北市，2003。
[2] Knott, G. A., “A modal analysis of the violin using
MSC/NASTRAN and PATRAN”, Naval Postgraduate School,
Monterey, CA, March 1987.
[3] Bretos, J., Santamaria, C. and Moral, J. A., “Vibration
pattern and frequency responses of the free plates and
box of a violin obtained by finite element analysis” J.
Acoust. Soc. Am., Vol. 105, No. 3, pp. 1942-1950, 1999.
[4] Saldner, H. O., Molin, N. and Jansson, E.
V., ”Vibration modes of the violin forced via the
bridge and action of the soundpost”, J. Acoust. Soc.
Am., Vol. 100, No. 2, Pt. 1, pp. 1168-1177, 1996.
[5] Rao, S. S., ”Mechanical Vibrations 4e”, Pearson
Education Inc, New Jersey, 2004.
[6] 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，145-146頁，2006。
[7] Fletcher, N. H., and Rossing, T. D., “The physics of
musical instruments”, Springer-Verlag, New York, 1991.
[8] Stowell, R., “The cambridge companion to the violin”, 湯
定九譯，小提琴指南，世界文物出版社，台北市，13-72頁，1996。
[9] 陳元光，提琴的制作與修復，上海教育出版社，上海，2005。
[10] Moral, J. A. and Jansson, E. V., “input admittance,
Eigenmodes, and quality of violins”, STL-QPSR, Vol.
23, No. 2-3, pp. 060-075, 1982.
[11] Jansson, E. V., “Admittance measurements of 25 high
quality violins”, Acustica, Vol. 83, pp. 337-341,
1997.
[12] 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。
[13] Sadd, M. H., “Elasticity 2e”, Elsevier Inc, 2009.
[14] Green, D. W., Winandy, J. E. and Kretschmann, D.
E., “Mechanical properties of wood”, USDA, U.S.A.,
Chapter 4, p. 2, 1999.
[15] Hutchins, C. M., “Research papers in violin acoustics
1975-1993”, Acoust. Soc. of Am., New York, p. 793,
1997.
[16] 王松永、國立編譯館，木材物理學，財團法人徐氏基金會，台北縣，1-
8頁、271-292頁、340-342頁，1993。