Rocking bridges

[Ron Nossaman]

>      John Delacour's model, for one,  has plainly shown,  that the bridge 
>could
>not possibly move simultaneously with the strings, due to inertia if nothing 
>else.

I'm afraid not. Find a book that actually deals with forced vibrations with
harmonic excitation (which Seely's Resistance of Materials does not), and
you will find that in the case of a driven frequency higher than the
natural harmonic frequency of the system, displacement will lag behind the
impressed force by a computable phase angle between 0° and 180°. The
amplitude of movement is greatest if driven at the natural harmonic
frequency, and diminishes (but does not disappear) as the frequency rises.
That's specifically from Vibration Theory and Applications, by William T.
Tompkins, but I found something similar in at least a couple more. John may
say the bridge doesn't move, but my textbooks say it does.


>He has shown that the bridge cannot instantaneously repond to the forces 
>exerted on
>it by the vibrating string and in so doing intimated  substantially the 
>difference
>in dynamic and gradual loading.  

And a vibrating string is just that - a gradual loading, smoothly
transitioning from 0 to +, through 0, to -, and back to 0. There is no
impact discontinuity here, it is all gradual loading in a working piano,
the frequency determining the loading rate. Even the initial hammer strike
is transmitted to the bridge by a wave deformation in the string. The
bridge doesn't receive the impact directly even then. That's gradual
loading, very much like my demonstrations only through a shorter time
period. The bridge inertia effects that come in as the loading cycle rate
increases are covered above, and in more than a few technical publications.   


>Your camp, apparently dismisses this as 
>irrelevant
>and in so dismissing this dismisses the critical distinctions of loading, 
>something
>I am not sure you will continue to insist upon.

I just did.


>     In the function of the piano critical distinctions must be made if the
>analysis is to be accurate.  Some of these, in particular, are:  the
mechanical
>stabilization of the vibrations of the string through creation of boundary
>conditions, that is string terminations,  which must  impose conditions that 
>force
>the string to  vibrate at a stable, constant frequency, as nearly as 
>possible; the
>acquisition of the energy by the string, which. also is a problem in dynamic
>loading,  the transduction of the energy of the vibrating string, its 
>dispersion to
>and radiation from the soundboard.  These processes  are best  described by 
>methods
>appropriate to the nauture of loading, which is, as I  say,  a distinction
long
>absent here and in the PTG Journal.

I thought that was exactly what we were doing here. You can help by
contributing sources to support your theory that strings don't move
bridges, like the Theory of Vibration you mention, and explain how it fits
into your theory. I'm particularly interested in how it is the compression
wave "hitting the wall" on the side opposite the applied force
(particularly a gradually applied force from a vibrating string) that moves
the mass, rather than my more simple minded Newtonian view of
action/reaction. I don't want it restated again, I've already read that.
I'd like it specifically explained with some semblance of real world
physics. I still haven't seen supportive evidence to your theory. 

It takes a finite amount of time for a compression wave to pass from the
top to the bottom of the bridge. Physics tells us that an applied force to
a given mass causes an immediate reaction in the mass. The mathematics
don't seem to include a lag time. Momentum accumulates with continual
applied force, but the movement begins immediately. Unless the speed of
sound in a bridge is infinite, the bridge will already be moving by the
time the compression wave gets to the other side. Granted, the quicker the
force is applied, the more local compression there is at the application
point, and the internal compression wave could very well reach the other
side of the mass at the same time that side begins to move, but I still see
no evidence presented indicating that it is that compression wave hitting
the back that moves the mass. The direct reaction to the applied force
moves the mass. Any internal compression waves generated in the bridge are
if anything, stealing string energy from the system in internal friction
converted to heat. It appears to me to be more a detriment than a cause,
and an artifact rather than a driver.


>      Should the distinctions arising from the nature of loading be given
their
>due,  then it will be seen that the acquisition and  termination/
reflection of
>energy in the string is a dynamic problem and the static loading method is
>inadequate for its description, , the transduction of this energy is a dynamic
>problem; the reflection of superposition of this energy in the soundboard is 
>also a
>dynamic problem and finally, the radiation of sound from the board into the 
>air is
>a problem partaking of  both aspects: those that are dynamic problems are best
>analized by the energy load method.
>       Taking note of the flexing of the board when a string is pressed by a
>finger, the flexing of the engine block by hand pressure given by Ron O, the
>requisite "physical, substantial motion," as being necessary to move the 
>board, the
>measured flexion of the plate and rim under static loading of  ten pounds, and
>such,  proceeds, evidently, from a view of the flexion of the system as being
>paramount. As these examples do not address the real question which is   the
>loading of the bridge/soundboard by the strings correctly, then so is their 
>utility
>as a refutation of the something that is in fact the consequence of  this 
>loading
>suspect.

The point, as I said at the time, was that the flex happened, and that any
flex was not no flex at all. I have apparently still failed to make that
point with you.



>  Of  course flexion is important for many reasons.  But it is only
>paramount in the context of what in reality it is - that is the flexural 
>behavior
>of the board operating in a diaphragmatic way to radiate sound. This is not
>necessary, as you seem to believe for the system to acquire energy from the
>strings. 

I didn't say it was necessary, I said it happens, and that's the way it
works. I didn't design the physics, so I don't get to chose. Do you? 



>The undercutting of the bridge, thinning of soundboards, tapering of 
>ribs,
>inner rim angles, etc.  are in fact methods of volume and stress control the
>purpose of which is to equalize the stress distribution in the material and 
>thereby
>optimize its energy absorbtive capacity or control its energy resistance.  

Otherwise known as mechanical impedance, which has been extensively
discussed on the list, and is not the current subject.


>As far
>as I can see this should be a matter dear to the heart of anyone attempting to
>design, remanufacture or otherwise modify a piano soundboard.

It is, and as I said, has been extensively discussed and is not the current
topic. It's all in the archives.
Ron N