John and Stephen,
Here is an interesting site as regards the effects of non-linearity in
vibrating structures. It is:
http://www.fam.dtu.dk/html/FVP/Jon/Theory1.html.
There are many other interesting sites on this subject. In pointing out
the importance of nonlinear mechanics I don't argue, at least for the
moment, that this is the last word on the subject, but merely wish to point
out that the pressurists view runs into this very substantial problem as
regards the periodicity and amplitude of such motion should their view be
taken to be sufficient to account for the harmonic behavior of the
soundboard. This is the question of loading.
It may well be, and I think it likely, that, in fact, the forces
produced at the bridge are insufficient to create such motion as is
claimed which would render moot the question of its linearity. But, it
seems unavoidable to me that the implications of non-linearity or loading
must be considered and dealt with for the pressurists view to stand
scrutiny, since they believe such motion does exist. As the effects of
nonlinearity, or loading, must be to alter the frequencies and amplitudes
produced in ways that make them no longer identical, in the case of
frequencies, or similar in the case of amplitudes, to those of the
vibrating string, while, in fact, the frequencies and amplitudes emanating
from the soundboard have an essential identity or similarity, as the case
may be, to those of the strings then, it would seem, a fundamental
contradiction exists which renders unsupportable the pressurists view.
This is, once again, just one of the numerous "troublesome questions"
inherent in this view some of which have been voiced in the last few
months.
Regards, Robin Hufford
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