Nodal line optimization and its application to violin top plate design

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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. (C) 2010 Elsevier Ltd. All rights reserved.
Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
Issue Date
2010-10
Language
English
Article Type
Article
Keywords

STRUCTURAL TOPOLOGY OPTIMIZATION; SENSITIVITY-ANALYSIS; HOMOGENIZATION METHOD; MODE SHAPES

Citation

JOURNAL OF SOUND AND VIBRATION, v.329, no.22, pp.4785 - 4796

ISSN
0022-460X
DOI
10.1016/j.jsv.2010.05.022
URI
http://hdl.handle.net/10203/99306
Appears in Collection
GT-Journal Papers(저널논문)ME-Journal Papers(저널논문)
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