impedance (was negative crown_

[Ron Nossaman]

At 07:38 AM 12/30/98 -0800, you wrote:
>Frank,
>Exactly my point!  Here I thought I was going to show how much I didn't
>know.  In mechanical optimization of disk drives, we like to talk about
>things we can measure and then change.  If you can't measure it, all the
>beautiful words describing the concept are just that.  Why not switch gears
>and talk of things you can measure and then optimize?  I'm a finite element
>modeler so I do lots of computer simulations to show trends, but I always
>have to talk in terms that  the lab guy can go out and test the structure
>and corroborate my predictions.  He measures mechanical properties like
>displacement, velocity and acceleration and can display them in terms of
>real/imaginary or magnitude/phase as a transfer function.  These are the
>tools we use to measure and describe vibrating mode shapes, resonant
>frequencies, internal damping, transient shock response and so on.
>

Doug,

I've put more than a few engineer types on the spot about this. Those that
have even heard of mechanical impedance can't seem to come up with a way to
compute it. "That's another flavor of engineer, I'm a -(insert specialty)-",
is the universal disclaimer. There may be someone out there in engineering
land who knows, but I haven't found him, or he's not admitting it.
Meanwhile, an observed  general cause and effect relationship between
measurable and predictable stiffness, mass, frequencies, tempered against an
accumulated body of empirical evidence, and a healthy distrust of unverified
"truths" is the best I'm able to do at present. I assume from tuning and
servicing the current standard state of the piano manufacturers' art out
there, that  the rest of the industry is in, at best, a similar position.
Just like with disk drives, pianos are a complex cause and effect
organization. It is only very recently that the mathematics of string
scaling have been reasonably understood, much less how soundboards work. The
informational components for understanding how soundboards work are, to a
large degree, obtainable and predictable on a simplistic level. The concept
of mechanical impedance is an attempt to put some of this data into a
manageable format to get an idea of how it all fits together. Some day,
someone will waltz in with a set of formulae that quantifies these
interactions. Then we can all set around and wonder why in the world any
given soundboard assembly was designed that way when any fool can see, right
there on the spreadsheet chart, that it was done wrong. Someone has to build
the tools to manipulate the concepts, and the tools themselves start as
concepts, often crudely defined. Perhaps some enterprising finite modeler
will come up something that does the job, and saves us all a lot of
unnecessary work. He could make a few of us very happy. 

 Ron