Abstract:The Guzheng string-bridge structure is an important component of Guzheng vocal system, and also, the primary issue of sound mechanism research. The 3-D dynamic model of Guzheng string-bridge has been establish with the Guzheng Bridge be considered as rigid double code feet and the string vibration be considered as bounded string vibration. Then the change rule of normal faces of the two code feet in different plucking angles have been analyzed by using the Matlab numerical calculation. Finally, the calculated results have been verified using the experimental measurement. The results show that the 3-D dynamic model of Guzheng string-bridge is effectively and reliable. When plucking the string in 00, the minimum value of the dynamic force of left code foot is very closed to zero, which is easy to cause bridge hopping; When plucking the string in 900, the phase dynamic forces of two code feet are same, and the resultant force of two code feet is largest; When plucking the string in 450 and 1350, the bridge dynamic forces of two angles are dissymmetry, and the phase dynamic forces of two code feet are opposite in this two angles. The work of this paper optimizes the dynamic model of Guzheng string-bridge structure. And it summarized the change rule of normal faces of the two code feet in different plucking angles, and will provide more or less support and guidance for improvement of future Guzheng.
邓小伟1,余征跃1,姚卫平1,周力2. 古筝弦-码结构的三维动力学分析与实验验证[J]. 振动与冲击, 2022, 41(6): 70-75.
DENG Xiaowei1,YU Zhengyue1,YAO Weiping1,ZHOU Li2. 3D dynamic analysis and test verification of the string-bridge structure of a Guzheng. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(6): 70-75.
[1] 艾莹,冯雷.20世纪中国民族乐器改良发展历程及思考[J].北方音乐,2018(06):1-2(AI Yin, FENG Lei. The improvement and development of Chinese national musical instruments in the 20th century[J]. Northern Music, 2018(06):1-2(in Chinese))
[2] 陈兴华.论中国民族乐器的短板及其演奏组合形式[J].乐器,2020(03):16-19 (CHEN Xing-hua. Research the short board of Chinese national musical instruments and their performance combination forms [J]. Musical Instrument Magazine, 2020(03):16-19(in Chinese))
[3] 苗雨昕.论中国传统古筝的传承与开发[J]. 北方音乐. 2020(01):38-39(MIAO Yu-xin. Research the inheritance and development of traditional Chinese Guzheng[J]. Northern Music, 2020(01):38-39(in Chinese))
[4] 邓小伟.民族乐器古筝的结构振动声学特性分析[D].上海:上海交通大学,2015(DENG Xiao-wei.Analysis of Structure vibration and Acoustic Characteristics of Chinese Musical Instrument Guzheng[D].Shanghai:Shanghai Jiao Tong University,2015(in Chinese))
[5] Roberto Corradi, Stefano Miccoli, Giacomo Squicciarini, Paolo Fazioli. Modal analysis of a grand piano soundboard at successive manufacturing stages[J]. Applied Acoustics, 2017,125:113-127
[6] Schoonderwaldt E. Mechanics and acoustics of violin bowing [D]. Stockholm:School of Computer Science and Communication,2009
[7] Obataya E,Zeniya N,Endo-Ujiie K.Effects of seasoning on the vibrational properties of wood for the soundboards of string instruments [J]. JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA,2020,147(2):998-1005
[8] C. Gough. The violin: Chladni patterns, plates, shells and sounds[J]. The European Physical Journal Special Topics,2007(145):77-101
[9] 韩宝强.乐器声学系统与空间音乐声学[J].演绎设备与科技,2007,02:64-68(HAN Bao-qiang.Acoustics system of musical instruments and musical acoustics of space[J].Entertainment Technology,2007,02:64-68(in Chinese))
[10] 杨健.走进琴弦的世界[J].自然杂志,2004,26(3):177-183(YANG Jian.Into the musical strings of the world[J].Nature Magazine,2004,26(3):177-183(in Chinese))
[11] 李云芳.扬琴弦振动的力学分析[J].青岛理工大学学报,2008,29(3):84-86(LI Yun-fang.Mechanical analysis of dulcimer chord vibration[J].Journal of Qingdao Technological University,2008,29(3):84-86(in Chinese))
[12] Mandal.AK,Wahi.p.Coupled plate-string vibrations in the presence of a finite bridge: Effect on natural frequencies and harmonicity[J].The Journal of the Acoustical Society of America ,2019,146(5):3362–3372.
[13] Tomoyasu Taguti.Dynamics of simple string subject to unilateral constraint:A model analysis of sawari mechanism[J].Acoustical Science and Technology,2008,29(3):203-214.
[14] 邓小伟,余征跃,姚卫平.古筝弦振动及琴码的动力学分析[J].振动与冲击,2015,34:166-170(DENG Xiao-wei, YU Zheng-yue, YAO Wei-ping.The Dynamic Analysis of Guzheng string vibration and Bridge[J].Journal of Vibration and Shock,2015,34:166-170(in Chinese))
[15] 赵旭.现代古筝演奏技法的传承与发展[J].大众标准化,2020,NO(02):74-78(ZHAO Xu. Inheritance and development of modern guzheng playing techniques[J]. Popular Standardization,2020,NO(02):74-78(in Chinese))
[16] 周力,邓小伟,余征跃.从振动与声学的角度研究古筝的制作[J] .乐器,2017(09):20-23(ZHOU Li, DENG Xiao-wei, YU Zheng-yue.Research on the production of Guzheng from the perspective of vibration and acoustics[J]. Musical Instruments,2017(09):20-23(in Chinese))
[17] C.Valette,A.Hirschberg,J.Kergomard,et al."The mechanics of vibrating strings"in Mechanics of Musical Instruments[M].Vienna and New York,Springer Verlag,1995:115-183.
[18] 刘延柱,陈立群,陈文良.振动力学[M].北京:高等教育出版社,2013(LIU Yan-zhu, CHEN Li-chun, CHEN Wen-liang. Vibration mechanics[M].Beijing: Higher Education Press,2013(in Chinese))
[19] 王明新.数学物理方程[M].北京:清华大学出版社,2009(WANG Min-xin. Equations of Mathematical Physics[M]. Beijing: Tsinghua university press ,2009(in Chinese))
[20] M. Aramaki,J.Bensa,L.Daudet,et al.Resynthesis of Coupled Piano String Vibrations Based on Physical Modeling[J].Journal of New Music Research,2001,No.(03):213–226.
[21] Kusumastuti A, Jamhuri M, Hidayati N.A. Analytical solution of the string vibration model on Sasando musical instrument [J].Journal of Physics: Conference Series,2019,1321:022088(9 pp.).
[22] Karel Vergote,Bert Van Genechten,Dirk Vandepitte,Wim Desmet. On the analysis of vibro-acoustic systems in the mid-frequency range using a hybrid deterministic-statistical approach[J]. Computers and Structures,2011(89):868–877.
[23] Robin S. Langley, Julio A. Cordioli, Hybrid deterministic-statistical analysis of vibro-acoustic systems with domain couplings on statistical components[J]. Journal of Sound and Vibration,2009(321):893-912
[24] 邓小伟,余征跃,姚卫平. 传统古筝的振动声学特性仿真分析[J]. 上海交大学报,2016,02:300-305(DENG Xiao-wei, YU Zheng-yue, YAO Wei-ping.Simulation Analysis of Vibro-acoustic Characteristics of Traditional Guzheng [J].Journal of Shanghai Jiaotong University,2016,02:300-305(in Chinese)