From Wood Mechanical Measurements to Composite Materials for Musical Instruments: New Technology for Instrument Makers
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J
"
"\2lV\fM)
where / is length, b is width, d is thickness, E is Young's modulus, / (= M3/12) is inertial momentum, p is density, n is partial number, and/,, is frequency mode(n).
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But, how do we choose the values of each parameter, since woods are variable materials with a large distribution of values-for samples coming from the same tree? Methodology We had the chance to work closely with a skilled instrument maker (Daniel Friederich) and we tried to understand his criteria for choosing wood. First, the luthier, by knocking on a piece of wood, simultaneously evaluates the pitch and the decay of the sound perceived. At the same time the stiffness and damping of the material can be evaluated. Second, by bending and twisting the plate of wood the luthier completes the evaluation of compliance and density. Moreover, the spectrum of the "taptone" reveals the capability of the wood in high frequency. Thus, predictions can be made about the
brightness, sustaining properties, and power of the instrument's sound. For 20 years, the guitar maker with whom we have worked has recorded the results of his experience. He is able to specify that with one particular wood the sound is very sharp but has poor sustaining power. With another kind the sound is sweet, powerful, and sustained. By chance he preserved about 20 samples of the best woods with which he has succeeded in making a variety of highquality instruments. Next, our goal was to make mechanical parameter measurements for each sample. The unique aspect of Dominique Douau's work3 was not to make averages about an ideal abstracted wood, but, on the contrary, to separate each cloud of parameters derived from each sample of wood. In this way, by factorial analysis of the data she was able to associate a supercloud first with a typology of sound and then with wood qualities. Measurements By measuring density and Young's modulus along the grain and across the grain we assessed the modal frequencies. The damping measurements reveal the temporal behavior. These measurements need comparative rather than absolute values. We prepared several series of test samples as cantilever bars (250 mm long X 10 mm wide X 3 mm thick). The longitudinal and radial Young's moduli were extracted by measuring the frequency of the free-oscillating clamped bar. Density was measured as the average of the dry weight and the wet weight divided by the dry volume. To measure damping versus frequency requires more caution because results are very sensitive to initial conditions. Thus, damping includes both internal losses and the losses concerning the coupling between the fluid and the vibrating structure.4 We used two methods: (1) We measured the band width of the cantilever force's response excitated up to the sixth mode, and (2) we measured the logarithmic decay decrement of the freeoscillating modes. It is very important to eliminate the losses on account of the air breaking so the amplitude movement of the vibration must be less than lmm. Last, a factorial analysis of the data permitted class
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