Nodal line optimization and its application to violin top plate design

• Published in: Journal of sound and vibration 2010-10, Vol.329 (22), p.4785-4796
• Main Authors: Yu, Yonggyun, Jang, In Gwun, Kim, In Kyum, Kwak, Byung Man
• Format: Article
• Language: English
• Subjects: Acoustics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Music and musical intruments; Musical instruments; Optimization; Physics; Plates (structural members); Resonant frequency; Solid mechanics; Sound; Structural and continuum mechanics; Structural vibration; Vibration; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Violins
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2010.05.022

In the literature, most problems of structural vibration have been formulated to adjust a specific natural frequency: for example, to maximize the first natural frequency. In musical instruments like a violin; however, mode shapes are equally important because they are related to sound quality in the way that natural frequencies are related to the octave. The shapes of nodal lines, which represent the natural mode shapes, are generally known to have a unique feature for good violins. Among the few studies on mode shape optimization, one typical study addresses the optimization of nodal point location for reducing vibration in a one-dimensional beam structure. However, nodal line optimization, which is required in violin plate design, has not yet been considered. In this paper, the central idea of controlling the shape of the nodal lines is proposed and then applied to violin top plate design. Finite element model for a violin top plate was constructed using shell elements. Then, optimization was performed to minimize the square sum of the displacement of selected nodes located along the target nodal lines by varying the thicknesses of the top plate. We conducted nodal line optimization for the second and the fifth modes together at the same time, and the results showed that the nodal lines obtained match well with the target nodal lines. The information on plate thickness distribution from nodal line optimization would be valuable for tailored trimming of a violin top plate for the given performances.