impedance for 99

[Ron Nossaman]

> I'm just not comfortable with
>mechanical impedance.  Impedance to me is an electrical quantity.  My
>measured or predicted transfer functions of on excitation and response ARE
>complex (real/imaginary or more to my liking is magnitude/phase).  While I
>have studied simple electrical circuit analysis and understand the basics of
>caps, resistors and electrical impedance, I just can't get comfortable with
>describing a mechanical structure using impedance.  My prejudice I guess.  I
>also work with a BUNCH of mechanical engineers that have never described
>mechanical problems using impedance.......  

* You're among a BUNCH of piano technicians here who, until fairly recently,
didn't either. It's just a one word handle covering the principals and
phenomenae of measured or predicted transfer functions of an excitation and
response, but it's easier to type. 


>
>Next question for you.  Why do you say that pianos are very non-linear?
>
>Just to frame the question, in a FEA model, many material properties are
>cataloged and used.  Most of the time, non-linear analysis is either do to
>exceeding the yield point of a material or a large deflection.
>
>Hammer are for sure!
>
>The rest?  A bunch of steel that is not near yield except maybe strings at
>the termination points and wood.  You may argue that wood is not linear, but
>that gets into long-term load bearing characteristics and how close the
>designer pushed the envelope.  Other that those, what material properties
>fall into the non-linear category?  
>
>doug
>

It's not the material response that's non linear, it's the assembly response
at different points along the bridge. In use, a soundboard assembly is a
driven diaphragm, sort of like a speaker cone, that has to accommodate and
respond to frequencies ranging from roughly 27Hz-4200Hz. That's woofer,
tweeter, and crossover, all in one unit. Let's see the audio engineers do
that in a high performance speaker! It's mounted on a rim that isn't exactly
the ideal shape for naturally conferring the proper frequency responses to
the corresponding area of the board. Designers use cut off bars to minimize
this problem to whatever degree they can. Compounding this (in an over
strung scale), the bass bridge is in roughly the same area of the board as
the low tenor, so this area must respond to a wider range of frequencies
than are required in other areas. The designer has to work with what he's
got to try to achieve the impedance characteristics necessary to the sound
he wants, at every point in the scale. He can re-define the perimeter, to
some degree, with cutoff bars, juggle rib lengths, height, width, crown,
angle, feathering, choice of wood, and crowning method, establish panel
thickness, grain angle, grain density, taper and diaphragming. He can
determine bridge placement on the assembly, construction method, height,
width, stiffness, and mass. He can change the impedance load on the assembly
by designing a different string scale, and/or downbearing schedule. All of
this affects the impedance balance between strings and soundboard, without
any changes whatever in the properties inherent to the materials used. If we
could estimate the impedance response in slices, a note, rib, or section at
a time, configure it as necessary to accommodate the string impedance load
to produce whatever sound quality we're after, and blend them (which is
partly what the bridge and panel stiffness do), we could, hopefully,
eliminate some of the guesswork. I have been considering trying to set up a
crude outline of this process in Pascal to try to establish some rules and
procedures, but the amount of time I anticipate it would take for me to get
to even a Stone Age level tool have, so far, kept me from trying. So, you
see, I'm hoping you can save me from myself by defining some of this stuff
in an existing tool. It's purely selfish.  %-)

 Ron