FINITE ELEMENT ANALYSIS OF VIOLIN SHELL MODES
Colin E Gough · 2023
Over the last few years there has been a dramatic increase in the number of acoustic measurements on outstanding Cremonese violins.However, there is still no consensus on the relationship between their acoustical properties and perceived quality.Of particular note have been the modal analysis measurements of George Bissinger 1,2 at the University of East Carolina, which now includes results from the recent 3D laser-scanning project undertaken in collaboration with two leading American violin makers, Joe Curtin and Sam Zygmuntowicz, and Fan Tao of D'Arradio Strings.This project has produced detailed 3-D information of the vibrations and associated acoustic radiation of the 1715 Titian and 1734 Willemotte Stradivari and 1735 Plowden Guarneri del Gesu violins.In addition, there are now a large number of admittance and acoustic radiation measurements on more than a dozen Stradivari and Guarneri violins and other fine Cremonese and modern instruments -and a few "bad" instruments for comparison.All such measurements confirm the acoustic importance of the low frequency "signature" modes: the A0 air resonance at ~ 280Hz, the CBR centre bout rotation mode at ~ 350-450 Hz, and the two strongly radiating B1-and B1+, often referred to as "corpus bending" modes, at typical frequencies in the range 370 -450Hz and 520-580Hz respectively.These modes determine the strength of the first and second partials of all bowed note sounds below the open E-string, and must therefore be important in determining the perceived quality, though the amplitudes of partials at higher frequencies are equally important in assessing quality across the whole playing range.The primary objective of the present proposal is to develop a FEA model of the violin, with fully adjustable parameters -like plate thicknesses, elastic properties and arching, sound post properties and position, rib thicknesses and heights, bridge geometry and resonances, f-hole shape and elastic properties of the central island area, bass bar size, etc -to address violin maker's frequent questions on how such parameters affect the position and strength of the easily measured signature modes and perceived quality of an instrument.A second objective is to achieve a better understanding of the origin and nature of the CBR, B1-and B1+ modes than currently exists.