Rocking bridges

[Ron Nossaman]

>These involve calculation of the forces and displacements using 
>vector
>methods as you also indicate below:  a part of this is the application of
these
>methods to calculate the varying downbearing load on the bridge and soundboard
>produced as you and others say, through cyclic behavior of the strings;
>calculations would indicate flexion of the bridge under the strings as being 
>the
>principal motion along with that of  "fore and aft:" and otherwise as Del has
>indicated. The use of  deflection mechanics and various forms of the flexure
>formula are employed enabling one to calculate, approximately,  these 
>deflections
>or to design new soundboards,  rib scalings, string scalings, bridges designs,
>etc. etc.   Inherent in this model is the notion of motion(!) at the bridge, 
>its
>interactive behavior with the strings,(compliance); and the idea that the 
>bridge
>then moves the soundboard hence sound.  This method is presented as the best 
>thing
>since sliced bread, entirely novel and of such import as to completely 
>supersede
>the efforts of all previous periods of piano work.

In the entire bulk of any of the writing that Del, Ron O, or I have
presented on this list or anywhere else that I know of, you will not find
anything remotely resembling a claim that any soundboard motion other than
simple beam deflection of the ribs from static downbearing load is
calculated by any of the three of us to design soundboards. I wrote that I
not only didn't know, but didn't care what contribution to the overall
sound a rocking motion in the bridge produced. I currently have no way to
quantify it, encourage it, or prevent it in soundboard design, so it is
beyond my control. It is not even considered in my design process. It
happens, so be it. Do I want it to happen or not, and to what degree?
Lacking the means to quantify it, I don't know. I've said something to this
effect more than once already.   

And have you actually heard any of these designs you are so quick to
dismiss? Have you designed and built a few soundboards of your own using
the ideas and assembly and crowning methods we have discussed on the list?
If we hadn't found our concepts and methods to produce what we consider
more dependably high performance results than the traditional concepts and
methods we all started out with, you would never have heard of them. The
published information didn't have to be shared. 


>      However, the use  of this method  in  the analysis of the dynamics of 
>energy
>transfer from string to bridge/soundboard and from soundboard to air,  and the
>resultant  vibration of members of the system , is inadequate, except in  
>the most
>vague and diffuse sense, to well describe the processes involved.  It is the
>nature of the load itself in the system, in this case a piano, which
determines
>how best to approach such an analysis.

And as I have said, direct measurement with appropriate equipment is the
only way to prove anything. Even then, there will be another crop of more
minute hairs to split by opinion. 



>      The rate of loading is a critical matter to these issues. Relatively 
>slowly
>applied loads result in  stress/strain relationships that  are susceptible to
>analysis using the methods of statics which the deflection model employs; it 
>then
>works well.  However, in rapid loading such as, I believe,  occurs in 
>connection
>with a vibrating string transfering energy, that is an energy load,  into a
>bridge/soundboard assembly, these stress/strain relationships are not the
same,
>the analysis is incorrect and its conclusions such as bridge rocking, bridge
>motion, however phrased,  are flawed, even if they can be calculated. 

I addressed this with the blanket analogy. 


>requires methods that are somewhat different.   To quote from THE
RESISTANCE OF
>MATERIALS by Seely, second edition, "the dimensions of the resisting
member and
>the properties of the material in the member that give it maximum resistance 
>to an
>energy load are quite different from those that give the member maximum 
>resistance
>to a static load".   This matter has been thoroughly confused, as far as I can
>see, for some years now on this list.

Again, see the blanket analogy. 

By the way, what's the chapter and heading reference on the quote from the
Seely?

Ron N