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 ===
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