impedance for 99

[Doug Richards]

Stephen,

Good sermon!  No argument on the basics.  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.......  

I'll stop now.  (getting off soapbox)

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

HAPPY NEW YEAR!

> -----Original Message-----
> From:	Stephen Birkett [SMTP:birketts@wright.aps.uoguelph.ca]
> Sent:	Thursday, December 31, 1998 11:13 PM
> To:	pianotech@ptg.org
> Subject:	impedance for 99
> 
> First sermon for 99....corrections will follow tomorrow when the wine
> wears off.
> 
> Impedance. Nothing mysterious about it. It's not typical mech eng fare,
> which is why most mechys aren't that familiar with it. Not that they don't
> have the same techniques. Mechys use their frequency response and transfer
> function instead - Doug. 
> 
> Impedance is a complex number, the real part is called resistance and the
> imaginary part is called reactance. Ideal capacitance or inductance are
> purely reactive (imaginary) impedances. Resistances are pure real
> impedances. Actual impedances are something in between. The reactance term
> cause a lead or lag in the response, and affects the energy transfer. 
> Being a complex number, impedance has an amplitude and a phase - the
> amplitude is what is often used for "impedance". 
> 
> Some important stuff:
> 1 impedance has to do with frequency response i.e. response to a 
>   sinusoidal input 
> 2 impedance is frequency dependent
> 3 in resonance situations the reactive part of impedance goes to zero
>   and the response is governed only by the resistance 
> 4 impedance tells you about energy transfer; peak power, average power
> etc.
>   as energy is transferred from sinusoidal input to sinusoidal output
> 5 all this stuff relates to linear systems 
> 
> This terminology has its origin in electrical work, but you can simply
> think voltage = force and current = velocity, and replace capacitors and
> inductors with springs and masses, and resistance with a dashpot (fancy
> term for frictional component). The analogy and all the impedance
> terminology goes over exactly. 
> 
> As for pianos the idea is more useful for explaining and thinking about
> response, than for calculation purposes. Pianos are highly non-linear (5).
> Impedance changes with frequency, so different partials will see different
> impedances (2) and experience different rates of energy transfer (4).
> Resonance (2) is to be avoided. 
> 
> Jim is exactly right with his comments. The art of piano design has a
> large element of choosing and implementing impedance mis-matches between
> vibrating wire and bridge/soundboard, in such a way that a desirable
> frequency response is attained. I proposed a while back that this
> acoustical response is unique enuf to be used as a fingerprint to identify
> pianos of different builders. 
> 
> Back to the wine.
> 
> Stephen
> 
> Stephen Birkett Fortepianos
> Authentic Reproductions of 18th and 19th Century Pianos
> 464 Winchester Drive
> Waterloo, Ontario
> Canada N2T 1K5
> tel: 519-885-2228
> email: birketts@wright.aps.uoguelph.ca