What is it about?
This paper describes the freely supported modes of freely supported violin plates and, using a finite element computational approach, their dependence on shape, arching, and anisotropy. For typical violin plates, it demonstrates that the arching height and spatial profile is just as important as their thickness and thickness graduations. In addition, it shows that both the acoustically important #2 and #5 modes are largely dependent on the geometric mean of the along- and cross-grain elastic constants, rather than the cross- and along grain properties respectively that is often assumed. The ratio of their frequencies then varies only weakly with anisotropy.
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Why is it important?
The paper is important because measurements of free plate frequencies and mode shapes are often made by makers as a way of optimising the plates before assembly on the ribs to form the body shell. Understanding the factors which determine the low frequency freely supported modes is therefore important, particularly because it is just such modes that eventually transform into the modes of the assembled body shell, as described in the subsequent paper on the body shell modes illustrating the transition from the freely supported plate modes.
Perspectives
This paper describes the dependence of freely supported plat modes on a larger number of important parameters (shape, symmetry, arching and anisotropy) than earlier models, which is important for the maker. The model and qualitative predictions are applicable to the free plates of all instruments of the violin family including the viola, cello and double bass.
Colin Gough
Read the Original
This page is a summary of: Violin plate modes, The Journal of the Acoustical Society of America, January 2015, Acoustical Society of America (ASA),
DOI: 10.1121/1.4904544.
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