Truly sorry for picking on you Richard, but that should be "wont". ( English major. Sorry! Sorry! ) Thump --- Richard Brekne <Richard.Brekne@grieg.uib.no> wrote: > Robin > > Wonderful posting ! Dispassionate with regards to > personal preferences > as is your want, and strictly informative. I > particularilly enjoyed > your comments on the nature of structure born sound, > your comments on > the impedance perspective (which provide new thought > for my evening > ponderings) and read with fascination where your > comments and quotes > relative to Seeley seemed to be going. > > These kinds of posts usually take me a few three > four readings to digest > adequately. I would recommend anyone who is > interested in the many > opinions offered about the nature of soundboard > functioning to do the same. > > Thanks muchly > > Cheers > RicB > > > > >> Dale > >> There is just such a relationship and it is > no a mystery, > >> although, as far as I can tell it is neither > comprehended nor taken > >> into account in the flexural view of soundboard > function. This > >> factor is precisely what I suggested be taken > into account in a post > >> put up three years ago during the debate on the > behavior of > >> soundboards, entitled Rocking Bridges, Dec 30, > 2001, in commentary > >> on the Modulus of Resilience, which was ignored, > or misunderstood as > >> an impedance matter which is not the case. In > my opinion, one > >> should view the soundboard, as I have repeatedly > urged, not through > >> the prism of deflection mechanics or cyclic > static pressures but, > >> rather, as an energy absorbtive, concentrating > and transmitting > >> medium, the energy absorbed being the output of > the string, which is > >> a pressure excitation at the terminations. > >> In my opinion, (and, I am going to drop this > phrase through the > >> remainer of this post although it all should be > taken with this > >> qualification) the soundboard should be seen as a > device which has > >> several functions. These functions themselves > are not necessarily > >> complementary and, in fact, are perhaps somewhat > contradictary. How > >> they are adjusted, vis a vis, one another is the > particular solution > >> found by any given design approach. At one and > the same time, the > >> board, bridge and ribs together, must be stiff > enough to ensure > >> loop stability on the strings which motion of the > terminations past > >> certain limits would preclude; at the same time, > it must absorb this > >> energy, which is just sound, another problem in > and of itself;, it > >> must then concentrate the sound in ways that > build up the amplitude > >> and, finally, transfer momentum out of the system > as acoustic > >> radiation. > >> I will not repeat here the many arguments I > have made for the > >> nature of motion at the bridge and the energy > loading that occurs > >> there, they are, likely, well known. > >> What follows will be a synoptic treatment of > this entire > >> question which will be published in substantially > greater detail > >> later this year, elsewhere. > >> There are critical distinctions that arise, > as I said in the > >> post referred to above, from the nature of > loading. These were > >> dismissed as mere impedance issues. Not so. > >> The absorption by the soundboard of this > energy is a function of > >> its energy resistance. Quoting from the post > referred to above, > >> which I will then elaborate upon: > >> "The approach taken by your school of > thought is generally, as > >> far as I can tell, expressed in terms of mass and > stiffness, flexion, > >> and the ratio of stress to strain, that is the > modulus of > >> elasticity.(here I can't render appropriate > notation due to the > >> limitations of the keyboard I am using); These > are the terms of > >> deflection mechanics, among others. When applied > to the transfer > >> relations between string and bridge they are > inadequate. A better > >> measure of the relations is the one used in > energy loading and that > >> is the modulus of resilience which is half the > quotient of the square > >> of the stress to the modulus of elasticity. > Although the modulus of > >> resilience is in fact a measure of how much > energy is absorbed per > >> unit volume of the material when the material is > stressed to the > >> proportional limit, its implications for the > design and manufacture > >> or remanufacture of soundboards are profound as > it can be used as a > >> predictor for the absorbion of energy or energy > resistance of a > >> member and therefore models the transfer > relations between string and > >> bridge, among others. > >> Critical implications of the modulus of > resilience and energy > >> loading arise in comparison to those of static > loading. Static > >> loading, whether flexion or axial depends upon > the maximum stress > >> developed, energy loading is substantially > different, (quoting from > >> Seely) " the resistance... of the bar((bridge, > rh) to an energy > >> load......depends not only the maximum > unit-stress, s, but also, (1) > >> on the distribution of stress through the body, > since the energy > >> absorbed by a given unit volume is ((the modulus > of resilience is > >> quoted, rh)), and hence depends upon the degree > to which that VOLUME > >> (caps mine, rh) is stressed, and (2), > >> and on the number of units of volume of material > in the bar ((bridge, > >> rh)). What this means to those that have not > grasped it is that the > >> transfer relations between string and > bridge/soundboard are a > >> function of the VOLUME and the DISTRIBUTION of > stress in the bridge > >> itself, and not simply the stiffness and mass. > The undercutting of > >> the bridge, thinning of soundboards, tapering of > ribs, inner rib > >> 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 > absorptive capacity or > >> control its energy resistance. 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. > >> To further quote from Seely, "...show that > the material in a > >> beam having a constant cross-section is > inefficient in absorbing > >> energy. For example,........a rectangular beam, > when loaded at > >> mid-span with a concentrated load, can absorb > only one-ninth as much > >> energy as the same beam could absorb if all the > material in the beam > >> were stressed to the same degree." The > requirement for > >> stress-equalization, hence control of energy > resistance, can be > >> expressed as taper of ribbing, undercutting of > bridges, notching of > >> struts, etc. > >> It is absolutely critical to understand that > energy absorption > >> under dynamic loading, as indicated above, is > functionally different > >> from that of static loading, one being dependant > upon the maximum > >> stress developed, the other the nature of the > stress distribution, a > === message truncated === __________________________________ Do you Yahoo!? The all-new My Yahoo! - What will yours do? http://my.yahoo.com
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