more on ribs and beam stuff

[Ron Nossaman]

At 11:12 AM 12/8/98 -0500, you wrote:
>Ron wrote:
>> Not really, because the end restraints (case) aren't maintaining the crown
>> in a real soundboard, and the installed soundboard assembly stiffens as it's
>> deflected. 
>>
>What you are really saying is the boundary conditions on a soundboard + 
>ribs are something in between clamped and hinged...another aspect of the 
>compexity of a real soundboard.

* No, what I'm "really" saying is the model doesn't fit the reality.


> 
>I do agree with both you and Del that soundboard behaviour is not going to
>be explained by *any* of these types of models, either 1-D or 2-D, beams
>or whatever. Remember the purpose of all this discussion was originally to
>try to theorize why Del observed a non-linear deflection in response to
>compression of a glued-in soundboard. 

* I posted what I thought was a fairly rational and plausible possible
explanation, citing the panel stiffness as a likely cause. What's wrong with
that one?



>That #4 experiment I described, the arched beam with clamped ends is not
>relevant to the soundboard because buckling behaviour only occurs for a
>comparatively flexible beam - soundboard + ribs being much too stiff - the
>radius of curvature required for buckling is much less than that of a
>soundboard, and the displacements and forces involved for buckling are
>much greater than those experienced in a soundboard loading. Looking at
>this is useful, though, since it shows that even as simple a system as a
>clamped arched beam can behave in a wildly non-linear fashion, including
>the possibility for chaotic vibrations if driven in the right way. 
 
* It wasn't relevant because it didn't exhibit the property of stiffness
increasing with deflection, and it was a buttress maintained arch. Not at
all like a soundboard, like I said. The buckling behavior you described,
however, is quite common in old (and sometimes not so old) compression
crowned soundboards, in spite of their being "much too stiff" for this to
happen, and results in what is somewhat misleadingly called a "rolled"
bridge. It doesn't seem to much matter at what "radius" the board was
originally crowned, if we had any way of knowing that for sure anyway. As
for this model being a useful example of non-linear deflections, it's still
backward of what is observable in a soundboard, and you seem able to
generate plenty of chaos whenever the mood strikes without the help of any
inside out thought model.   



>I would be interested in your observations Ron if you take some.
>
>Stephen

* I've included a few above. I'll surely make some more, even if it's by
accident.

 Ron