Jump to content


Photo

Diy Bandoneon Reed With Zinc Same Youngs Modulus Fiber Plastic


  • Please log in to reply
27 replies to this topic

#19 ttonon

ttonon

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 200 posts
  • Gender:Male
  • Location:New Jersey, USA

Posted 13 February 2018 - 12:37 PM

Hi Umut,

In this thread, we are talking about two kinds of vibrating objects – free reed tongues (also called bars) and gongs (also called plates) - composed of two kinds of materials – metals and concrete. 

I believe your main interest concerns the vibration of concrete gongs, and perhaps your interest in metallic bars is in order to help you get an understanding of concrete gongs. 

I point out these differences because each of these special cases requires different theoretical treatment, and one can error by confusing each of them.

 

 

 

My friends asks me if the modulus density ratio is the same , the fundemental frequency is the same. They asks me what will be the harmonics and their sustain for each different.

 

I read your post on concertina reeds and as fas as I understand , you defend every characteristics would be the same.

 

Is it true ?

 

 

 

Yes, in the case of vibrating bars that are homogeneous (have the same material and cross sectional area throughout their lengths), as described by the Euler-Bernoulli governing equation (which works well for the vibration of tongues of the Free Reed), if the ratios E/Rho and the geometries are the same.

 

As a matter of fact, in these cases, the Euler-Bernoulli ( E-B ) equation allows us to be even more specific; i.e., for two vibrating bars of different materials, if the ratio E*k^2/Rho is the same and if the bar lengths are the same, the vibrational response will also be the same.  Here, k^2 is the “radius of gyration of the cross section,” assumed to be constant over the length of the bar, and for a rectangular cross section, equals (a^2)/12, where a is the (constant) thickness of the bar. 

 

As an aside, this result suggests a very interesting experiment that concertina reed makers might want to try.  Make two different tongues of different materials (say steel and brass), with constant cross sectional area and having the same length and the same parameter E*(a^2)/Rho.  According to these theoretical considerations, both tongues should produce the same acoustic sound: fundamental plus overtones.  My feeling is that, if this conclusion can be experimentally verified, our understanding of the free reed would be significantly increased.

 

 

 

Is total mass of the gong would be the same also ? Or is it not important ?

 

 

 

For gongs, we are having another kind of discussion, for at least two reasons: 1) materials, and 2) governing equation of motion. 

 

For gongs, metals can behave much differently than non metals.  For instance, concrete is supposed to have many micro-cracks throughout its interior, and this will affect the “resonant” or decay-time properties of the gong. 

 

Concerning the governing equation of motion for such gongs, since they are relatively thick, rotational aspects of small sections of the gong can be important.  The Euler-Bernoulli governing equation neglects these rotational aspects, because the thickness of the bar it describes is presumed to be small enough, which is pretty much true.  But for gongs, it’s often best to use a more precise formulation, called the Timoshenko governing equation. 

 

One main criterion deciding which equation to use is to compare the thickness of the gong to the wavelengths of the acoustic frequencies one is interested in.  As usual with acoustic phenomenon, certain “lengths” of the physical system become important, and the major criterion when such lengths become important is a comparison of such lengths to the wavelengths making up the acoustic result of interest.  For a vibrating gong, I’d guess that one would be interested in frequencies up to around 10,000 Hz, which is an upper limit to the overtones average adult hearing responds to.  Corresponding wavelengths here are about 3 cm, which is probably getting down to the thickness of practical gongs.  Thus, one would expect that the Timoshenko governing equation should be used for gongs. 

 

An aside here is to notice the difference between a vibrating bar, or the tongue of the free reed, and a gong.  For the tongue, the frequency response required need not go above a couple thousand Hz, because it responds to only the fundamental of the music tone.  The overtones are produced by the dynamical behavior of air flow.  For a gong, the musical tone in the vibration must be able to respond to all the overtones, which occur at many times the frequency of the fundamental.

 

Thus, for a gong, it’s more appropriate to use the Timoshenko governing equation, which is more complicated than the E-B version.  I was not able to find a clear way to write (display) these equations here, but anyone interested can refer to Wikipedia.  The Timoshenko equation contains not only Young’s Modulus and density, but also the shear modulus, Poisson’s ratio, along with geometry, and all these parameters occur in complex ways. There is thus no simple way to relate gongs of different materials using the more accurate Timoshenko beam theory.

 

However, there is perhaps an intermediate approach considered by Phillip Morse, in Vibration and Sound, a classic text.  In this approach, Morse considers a circular “plate,” which is the two dimensional analog of the vibrating bar, which as we have seen, can be represented well enough by the E-B governing equation.  This restriction considers only a circular plate (gong) that is fixed at its periphery, although I don’t think this is the usual way to mount a gong.  Regardless, this circumferential boundary condition, produces a governing equation much simpler than the Timoshenko formulation.  With this “plate” equation, a comparison of different materials can be made in a way similar to that done with the E-B equation: as long as the parameter E*t^2/Rho/(1-p^2) and the gong diameter are the same, the response of two different materials should be the same.  Here, p is Poisson’s ratio and t is the thickness of the gong.  All these parameters are considered constant throughout the gong disk. 

 

 

 

What makes bronze does not dissipate energy ?

 

I learned carbon fiber or more exactly epoxy does not waste energy when hit ? Is it true for e glass epoxy laminates ?

 

Thank you,

 

Umut

 

 

 

Although dissipation is a complicated issue, it must have something to do with the internal molecular structure of the material, and it is very dependent on the kind of material.  I think Poisson’s ratio tells us something about dissipation because this parameter is a measure of the relative motion between microscopic elements.  An incompressible material will have a maximum Poisson’s ratio of 0.5, and many metals have around 0.2 – 0.3.  These values suggest that microscopic elements change volume when stressed, and this suggests dissipation.  With metals, different kinds of dissipation are considered, depending how the stress tensor is modeled in relation to it.  There are viscous, Coulomb, and hysteretic models, and one can find much description of these on the web.

For concrete, a common model for dissipation considers the relative motion between the sides of micro cracks in the material, which interestingly doesn’t degrade the material.  This, I believe, is entirely different than the models used for metals, and thus, understanding why bronze is less dissipative than other metals may not give clues as to the dissipation in concrete.  It’s my understanding that Bell bronze (approximately 70% Copper and 30% Tin) has been regarded as a desirable material for gongs and bells for over a thousand years or so, and this is based on empirical evidence.  I don’t know how much scientific understanding is behind this practice, but the link below should provide you with some useful information (“A micro-structural model for dissipation phenomena in concrete”).  I believe additives are introduced into concrete sometimes in order to increase its internal dissipation, as a way to make the material more resistant to earthquakes.

chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/https://hal.archives...194317/document

Best regards,

Tom



#20 Mustafa Umut Sarac

Mustafa Umut Sarac

    Advanced Member

  • Members
  • PipPipPip
  • 31 posts
  • Gender:Male
  • Location:Istanbul - Turkey

Posted 13 February 2018 - 01:21 PM

Tom , thank you very much for your all effort to solve problems and educatng us.

 

You are right , concrete must absorb the energy to protect us.

 

I think glass fiber and polyester or epoxy widely available worldwide and when comparing their price and bronze price plus paying to workforce and to the masters makes fiberglass suggestable even for indonesia.

 

I think with experimenting with different composite databases , it would be even possible to find bronze matching FRP recipe.

 

And they dont absorb the energy  also.

 

May be if the glass rowing or more expensive rowings are bad for instrument - some warns about it - it would be possible to add to liquid plastic some titanium dioxide nano powders or aluminum di oxide nanopowders - extremelly cheap and widely available both - or carbon fiber powder - not expensive like carbon rowing - or some epoxy fiber additive powders could help.

 

Do you think rowing fiber is a must and do rowing makes everything worse ?

 

And do you know powders solve the fiber orientation problem ?

 

Another glass fiber is made with chopping. 

 

Which is makes sense ?

 

Thank you ,

 

 

umut

istanbul



#21 ttonon

ttonon

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 200 posts
  • Gender:Male
  • Location:New Jersey, USA

Posted 14 February 2018 - 12:03 AM

Hi Umut,

 

At this point, I'm not sure what you want to do.  Do you want to make a gong of concrete, or do you want to make a gong with a minimum amount of dissipation, so that it has the longest ring?  

 

If the latter, you might find this comprehensive materials survey interesting:

Documentation of damping capacity of metallic, ceramic and metal-matrix composite materials:

https://faculty.engr...9y1993p2395.pdf

 

Best regards,

Tom



#22 Mustafa Umut Sarac

Mustafa Umut Sarac

    Advanced Member

  • Members
  • PipPipPip
  • 31 posts
  • Gender:Male
  • Location:Istanbul - Turkey

Posted 14 February 2018 - 01:26 AM

Glass fibre - -  0.1 Hz  0.l-16 Damping

 

Bronze 0.2 Damping

 

 

Glass fibre have one of the lowest damping factor and your posts indicates it has wonderful ratio close to bronze and nearly same as brass.

 

And Glass fiber and epoxy is widely available worldwide and lightweight and cures in few hours.

 

Tom , of course I want long ringing material. I am sure , your concrete and earthquake example was dang point , concrete wont ring.

 

Now , there is a big problem to solve. Gongs are made of sheet of bronze but they do need to store internal energy like guitar string and gongs are hammered hundreds of times to store internal energy.

 

How one can build a glass reinforced plastic prestressed.

 

Thank you Tom,

 

umut

istanbul



#23 ttonon

ttonon

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 200 posts
  • Gender:Male
  • Location:New Jersey, USA

Posted 14 February 2018 - 09:37 AM

Hi Umut,

 

 

 

How one can build a glass reinforced plastic prestressed.

 

 

 

A few ideas:

 

Solid Glass:

Has anyone tried to make a solid "tempered" glass gong?  You can try  casting a circular molten glass shape, then find a way to cool it rapidly over the entire outside surface, before it can cool throughout the interior.  Then let it cool more slowly in the interior.  This is basically how they make tempered glass, which has the outer surfaces in compressive stress and the inner regions in tensile stress.  

 

Thermoplastic:

Perhaps a thermoplastic (not epoxy) dome can be cooled in a similar way, resulting in its outer surface in compression and its inner regions in tension?

 

Thermoset plastic:

For epoxy, since the cure rate of epoxy increases with temperature, you might first cast the epoxy in a circular shape, then when it becomes firm enough, heat all the outer surfaces uniformly with infra-red (radiative) heaters.  This will cure the outer surfaces first.  Keep heating (maybe with an adjustment on heat flux) until the inner regions become cured. 

 

 

Best regards,

Tom  



#24 Mustafa Umut Sarac

Mustafa Umut Sarac

    Advanced Member

  • Members
  • PipPipPip
  • 31 posts
  • Gender:Male
  • Location:Istanbul - Turkey

Posted 14 February 2018 - 10:20 AM

Hi Tom,

 

These are wonderful ideas. Congrulations.

 

If we will try to temper the glass , no need for that,  there are tempered glass sheets are available at glass factories and they cut the glass with water jet for any desired shape.And they can temper any glass. I learned from your link , glass have even lower , half the damping factor compared to bronze. Do you have an idea , how this plate sounds finally ? I have an idea with this plate below.

 

There is Tiffany glasses at USA from 19th century , they gave the glass exact golden sheen by carboxylic acid:)

 

Thermosets would be used when the glass fibers inside and glass fiber would shadow the infrared lamps to reach in to middle inside of the mass. I dont know when there is no compression physical source on to plate , I dont have idea if there would be a different timed heating curing would gain stress. I think there would be no difference between different timed cured epoxies. They will cure to same now or later.

 

I am giving special attention to above because only material have bronze or brass ratio .

 

Here is the second option below,

 

There is a possible solution ,placing factory tempered glass at the back and hitting surface would be epoxy and glass fiber mixture. This would apply extra compression to glass - after epoxy cured and streched - and correct giass reinforced plastic would sound like brass or bronze. I think extreme low dissipance of glass would amplify the brass bronze modulus density ratio grp at front.

 

I think there is a third option to strech glass fiber epoxy HALF THE GONG THICKNESS plate with mechanical means and streched plate would be coated with grp again to keep the stress , after second coating cured

 

What do you think Tom ?

 

Thank you,

 

Umut

Istanbul


Edited by Mustafa Umut Sarac, 14 February 2018 - 12:55 PM.


#25 Mustafa Umut Sarac

Mustafa Umut Sarac

    Advanced Member

  • Members
  • PipPipPip
  • 31 posts
  • Gender:Male
  • Location:Istanbul - Turkey

Posted 14 February 2018 - 11:55 AM

tiffany-glass-bowl-br091110-0428.jpghere is the interior of louis tiffany glass made with carboxylic acid on glass for tempered glass.



#26 Mustafa Umut Sarac

Mustafa Umut Sarac

    Advanced Member

  • Members
  • PipPipPip
  • 31 posts
  • Gender:Male
  • Location:Istanbul - Turkey

Posted 14 February 2018 - 12:53 PM

Hello again Tom,

 

By the way , if we want to add another stress to tempered round cut sheet glass with glass fiber epoxy composite, what would it be needed for thickness selection. There are variety of glasses everywhere , even bronze colored glass for architecture use and later tempered at moderate size glass shop within oven.

 

Is it true , low damping factor of tempered glass would amplify the top bronze or brass ratio grp coating ? Or is this the fully wrong way ?

 

Thank you,

Umut



#27 ttonon

ttonon

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 200 posts
  • Gender:Male
  • Location:New Jersey, USA

Posted 14 February 2018 - 01:06 PM

Hi Umut,

 

I think I have a much better idea on what you're asking, and let me offer the following.  

 

In general, metals have the lowest Damping Capacity of all materials, and of these, from the information I sent you, Aluminum appears to have the lowest.  Thus, I would recommend you try making a gong out of Aluminum.  Do you know of other people trying Aluminum gongs?  Perhaps a serious problem with Aluminum might be its relatively low endurance limit.  In order to evaluate this, you need to estimate the maximum internal stresses that the metal would experience as a gong, and at what frequencies those stresses occur.  For this, you can consult the circular plate vibration solution that Morse has in his book (as I explained above).  With that information, you should be able to estimate the life time of the gong.  Important also is the fact that there are many different kinds of Aluminum alloy, each with its own Damping Capacity and endurance limit.  Hopefully, you'd get lucky and find a good enough alloy that's affordable.  Traditional gongs and bells aren't made out of Aluminum because this metal wasn't widely available until this last century.  When it was discovered about 200 years ago, it cost more than gold, and it wasn't cheaply produced until only the last century.   Copper and bronze however have been utilitarian for a few thousand years now.       

 

It's not correct to conclude that the low tabulated Damping Capacity for glass fiber ( 0.1) means that you can use it in a composite and it will increase the Damping Capacity of the composite.  This value must be valid for a single fiber stretched longitudinally, and not for broken fibers immersed in a matrix. 

 

Putting any additive (fibers, nanotubes, powders, etc.) into a material will most likely increase  the Damping Capacity over that of the material alone.  This is because there will always be some relative motion between the additive and the matrix, and this rubbing produces dissipation of energy, heating the material.  

 

Making a gong out of separate components should be avoided, because again, there will be relative motion between these components, causing vibrational energy losses.  The gong should be made out of one homogeneous material (e.g., Aluminum, or an alloy of Aluminum).

 

I haven't seen much data, but my guess is that thermoplastics, thermosets, and other polymers have more Damping Capacity than metals, because they have long molecular chains that easily distort, using up vibrational energy.  If you do find any will lower levels, please let me know.

 

Glass bells and gongs are fairly common in small sizes.  Wind chimes, wine glasses, the glass harmonica (the one invented by Benjamin Franklin), etc. all prove that solid glass can be a resonant material.  But again, I think that a solid glass gong would perform best, and in order to make one, I'd first talk to a glass worker. 

 

Best regards,

Tom 

 

 



#28 Mustafa Umut Sarac

Mustafa Umut Sarac

    Advanced Member

  • Members
  • PipPipPip
  • 31 posts
  • Gender:Male
  • Location:Istanbul - Turkey

Posted 14 February 2018 - 02:02 PM

Tom,

 

tempered glass is excellent and the aluminum. There is a school at gamelan making called american gamelan , all uses aluminum , other school uses steel.

You can make % 65 of gamelan orchestra from cut flat panel metal. Steel is cheapest.

 

This is solved long before us.

 

But the problem is making the large resonating pots which is size of a large cooking pot and fully closed. My main concern was not gong but the pots.

Thats why I wanted concrete or  grp. I am sorry , I missed to tell.

 

I need to find a material which will able to do the job. .






1 user(s) are reading this topic

0 members, 1 guests, 0 anonymous users