Proceedings e report - Firenze University Press

Average r adiated presure field
(dB)
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WOOD SCIENCE FOR CONSERVATION OF CULTURAL HERITAGE
(a) (b)
Fig. 4 Measurement grid
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Fig. 5 Averaged pressure level from 0 to 2000 Hz with modal frequencies retained
It is difficult to compare this spectrum to the one obtained on another harpsichord because each
musical instrument is unique and we do not know another harpsichord made by Couchet kept in the
same state. Moreover, it is impossible to realize another modal analysis on this instrument because it
will imply contact. Nevertheless it is possible to compare this spectrum with theoretical results
obtained from a finite element model (comparison will be analyzed in our afoot article). From this
spectrum, the mathematical process consists in selecting peak one by one to reconstruct the mode
(resonance frequency and modal shape) of the structure. An example is given on the Fig. 6.
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38 Hz
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168 Hz
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73 Hz
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183 Hz
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Frequency (Hz)
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147 Hz
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204 Hz
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243 H 278 H
Fig. 6 First modal shape for the harpsichord Couchet
290 H
The modal decomposition for a structure is the resolution of this equation: [ M ] x
+ [ K]
x = 0 where
[M] and [K] are the mass and stiffness matrices, and x the displacement. For a given structure, any
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