My dedicated audio room build - QuadDiffusor's Big Dig

[sbnx]

Since we are going down the VPR rabbit hole, I thought i would discuss the formulas for the plate bending modes.


Where:
m'' is the mass per unit area of the plate
B' is defined below
pi/2 = 1.570795
Lx is the length of the plate
Ly is the width of the plate
Mx and My are the modes. these are integer values (1,2,3,4 ....) For the first mode you would input Mx =1 and My = 1.


Where:
E is the modulus of elasticity of the material of the plate
t is the thickness of the plate
u is Poisson's ratio for the material of the plate.

E of steel is 30E6 PSI
E of Aluminum is 10E6 PSI
u of steel is about 0.3
u of Aluminum is about 0.33

Notice there is nothing about the foam in this equation. The purpose of the foam is to damp the vibration of the plate. The foam needs to be strong enough to support the plate. The plate needs to be in strong contact with the foam (i.e. glued with elastomeric glue). properties of the foam only come into play if you are wanting to use the "mass-spring" system to target a specific frequency. This is always problematic, and I suggest ignoring it.

To me it was insightful to rearrange the formula a little. Do some algebra of B'/m'' and you will see that the formula reduces to:

SQRT (B'/m'') = t * SQRT [ (E/D)*(1/(1-u^2) ] Where D is the density of the plate material.

Density of Steel = 0.284 lb/in^3
Density of Aluminum = 0.0976 lb/in^3

E/D for Steel = 105.6E6 in
E/D for Aluminum = 102.5E6 in

Sqrt (B'/m'') for steel = 10,772 * t
Sqrt (B'/m'') for Aluminum = 10,725 * t

(Of course, you may want to check my math)

The point is that Aluminum and Steel have basically the same modal frequencies. This is relevant as Aluminum is much lighter than steel, thus making it easier for the foam to support the weight. It also makes it easier to handle during the construction process. The lighter material should also be easier to acoustically excite.

A couple other points to make are that as the thickness of the plate increases the lowest frequency will go up. Keep the plate thin. As the dimension of the plate goes up the frequency goes down. Make the panel large(ish). To spread out the frequencies make the length and width different. Assuming you are going to put more than one of these in your room then you could make different sizes that target different frequencies. Also the thickness of the foam doesn't matter when only using the plates modal frequencies. 1" or 2" foam is sufficient. The closer you get the plate to the wall the better because the pressure is highest right at the wall's surface. If you want a broadband absorber you can glue foam to the front of the plate as well.

Again, these are stupid simple to make. Simply, buy the foam and the plate. Glue the plate to the foam. Hang it on the wall where there is high pressure.

 

[QuadDiffuser]

Wow, sbnx, you're brilliant!
Huge benefits from using aluminum which only has 1/3 the density of steel.
Whoops, but aluminum plates are 2-3 times the cost of galvanized steel plates.

 

[Kingrex]

Aluminum is expensive.

How do you hang it on a wall? Without touching the Aluminum. Glue it to the wall?

If on a ceiling, maybe 4 small holes with aircraft cable through them. A stopper that hangs half and inch or so below the panel. Cable is not touching. Glue it to the ceiling. Cable is not touching the platr. Not unless the adhesive gives out and it drops onto the cable support.

 

[adyc]

A couple other points to make are that as the thickness of the plate increases the lowest frequency will go up. Keep the plate thin. As the dimension of the plate goes up the frequency goes down. Make the panel large(ish). To spread out the frequencies make the length and width different. Assuming you are going to put more than one of these in your room then you could make different sizes that target different frequencies. Also the thickness of the foam doesn't matter when only using the plates modal frequencies. 1" or 2" foam is sufficient. The closer you get the plate to the wall the better because the pressure is highest right at the wall's surface. If you want a broadband absorber you can glue foam to the front of the plate as well.

If the lowest frequency goes up with the thickness of the plate increases, how does it reconcile with Figure 5.11 in post 379? Figure 5.11 seems to show that 2.5mm thickness has a lower frequency absorption than 1mm thickness which seems to contradict the formula.

 

[adyc]

I am also not sure the thickness of the foam is irrelevant. The formula in post 381 is assuming free vibrating plate. I.e there is no constraint of movement in the vertical direction. One can check the derivation in Wiki page if one is interested. If one glues the plate to the foam, this will change the assumption of the derivation.

The formula may give general guidelines on the design of VPR. For example, the x dimension should not be integer multiple of y direction if one wants to spread the modes. I suspect this is the reason RPG is selling Modex plate as 1x1.5m as a broadband bass trap.

 

[pjwd]

Wow, sbnx, you're brilliant!
Huge benefits from using aluminum which only has 1/3 the density of steel.
Whoops, but aluminum plates are 2-3 times the cost of galvanized steel plates.

I believe you are using these for bass absorbtion not broadband absorbtion so you are using the mass damped spring only .. is that correct.
The figures qouted in the attachment in your post are pretty much exactly what the acoustic engineer specified in my projects .. 100mm foam 1mm steel and largish area ..over 1m in each direction as I recall) .. targeting 125 down to 30 Hz (for some reason in acoustics they always start at 125hz )

 

[sbnx]

There are so many questions that show misunderstanding of how the VPR works. I will try to address some of them. But if you really want to know then buy the book and read it or build a few and test them. I have done both.

First the easiest -- mounting. As I stated in an earlier post, simply glue the foam to a piece of MDF, glue the plate to the foam, and then screw the MDF to the wall. The steel plate should not be touching the floor or any other boundaries. It needs to be free floating on the foam. If you want to make it look nice you could use fabric-track and stretch fabric in front of it. The Modex plates by RPG had a thin stamped steel frame that mounted to the wall. it certainly looked nice but was also very pricey.

The whole point of the VPR or CBA as Fuchs calls it, is that the resonant frequencies of the plate are very evenly spread below 100Hz. In this sense it is a broadband absorber below 100Hz which is almost impossible using any other means. If you don't know what I am talking about then watch this video.

The formula to calculate these fequencies was given by Fuchs in his book. This is the formula. This is what I showed and discussed above.

Below is the formula for the mass-spring resonance. We can see from this formula that the properties of the foam (density and thickness) come into play. We should expect this as the foam is the spring in the mass-spring system. Now look at the relationships. As the thickness of the plate goes up the resonant frequency goes down. As the thickness of the foam goes up the resonant fequency goes down. As the density of the plate goes up the frequency goes down. As the density of the foam goes down the frequency goes down. So, if i want to tune this resonance to a low frequency (say 40Hz) then I need a thick, dense plate on a soft thick foam. Keep in mind that this is a single frequency that we are tuning. The idea being that perhaps we are trying to target one of the lower room modes. The problem with all of these types of panels is it is extremely easy to build it and miss the frequency you are targeting.


Where:
Cd = speed of sound = 343 m/s
2*pi = self explanatory
Pd=density of the foam
Pt= density of the plate
t=thickness of hte plate
d=thickness of the absorber

Again, this device has two modes of operation. 1. as a mass-spring system with a a single resonant frequency. and 2. as a broadband absorber with many, evenly spread resonant frequencies. These two are somewhat at ods with each other. If you want a lower resonant frequency for the mass-spring system them make the plate thicker. If you want a lower range of resonant frequencies using the plate bending modes then make the plate thinner.

I propose that the plate should be thin because then it will be more effcient as it is easier to excite. Use the broadband bass absorption that this device excels at.

 

[adyc]

The formula in Fuch’s book is same as the formula in Wiki’s page of vibration of a plate. The derivation is based on boundary condition of edges do not move and the plate is freely vibrating. I question the usefulness of this formula to predict the bending modes of the plate as the real world construction of these VPR panels do not satisfy these boundary conditions. At best, this formula only show the qualitative behavior.

 

[Kingrex]

I have a friend coming for a few days. I set up a futon in my listening room for guests. Most all the annoying bass boom is gone with the bed set up. It sits between the horn sub in the rear of the room and the speakers in the front. I'm next to the foot of the bed in a chair.

 

[pjwd]

I have a friend coming for a few days. I set up a futon in my listening room for guests. Most all the annoying bass boom is gone with the bed set up. It sits between the horn sub in the rear of the room and the speakers in the front. I'm next to the foot of the bed in a chair.

Put a steel plate on the futon .. that should knock it out of the park ..

 

[Kingrex]

Put a steel plate on the futon .. that should knock it out of the park ..

I honestly though of that. I don't have one.

 

[sbnx]

I honestly though of that. I don't have one.

If you laid out the futon cushion on the floor and placed a 3'X1.5' X 0.75mm metal plate on it then it will likely help with the vertical room mode. Some calculation would help to ensure that the frequency of the room mode lined up with one of the dimensions of the plate.

 

[Kingrex]

You know where these plates might really help. Mitigating.noise from Mini split compressors.

What are the thougjts on these plates of metal glued to foam vs and ASC tube?

 

[Kingrex]

Whats your guys thougbts on making these plate on foam vs ASC tube traps.

Van Zly who made my subs said to use Audio Tools app and run a frequency generator to make the bass mode. Then walk the room to find the worst spots. Then place the traps there.

 

[pjwd]

Whats your guys thougbts on making these plate on foam vs ASC tube traps.

Van Zly who made my subs said to use Audio Tools app and run a frequency generator to make the bass mode. Then walk the room to find the worst spots. Then place the traps there.

I would just do corner traps that perform from 125 to 30 hz .. all the bass energy accumulates in the corners and this will clean up the reverberation .. then speaker and chair position .. then target the remaining problems ..

 

[microstrip]

Whats your guys thougbts on making these plate on foam vs ASC tube traps.

Van Zly who made my subs said to use Audio Tools app and run a frequency generator to make the bass mode. Then walk the room to find the worst spots. Then place the traps there.

IMO simple frequency generators and ears are a poor tool, unless you are very experienced. You need some noise or sweep generator and RTA to understand your room. One of the best tools to see the effect of bass traps are waterfall type measurements.

 

[MPW]

IMO simple frequency generators and ears are a poor tool, unless you are very experienced. You need some noise or sweep generator and RTA to understand your room. One of the best tools to see the effect of bass traps are waterfall type measurements.

Agreed. REW with a calibrated microphone is inexpensive and easy to use. IMO a must if one is serious about solving setup and room treatment challenges quickly and effectively.

 

[QuadDiffuser]

After further examinations and deliberations, these two prototype 1.5mm and 3.0mm steel plates will be modified in the following manner:

1) steel on the horizontal sections (both top and bottom) - keeping only what's essential for the resilient mounting brackets (about 20%), and removing the rest (about 80%) for freer vibrational movement
2) mounting bracket - to be shortened, eliminating the air gap
3) abundant application of 3M spray glue, to bond Basotech foam directly to the underside of the steel plates
4) direct contact between the Basotech foam and the gypsum wall
5) for vertically mounted units, potentially use only one mounting bracket on top (instead of two) to maximize vibrational freedom

Thanks everyone, your contributions have been very helpful in guiding me to understand how best to modify the steel-plate bass absorbers for optimal performance!

1) remove all 90-degree angled bending, leaving just one flat rectangular piece to maximize resonance modes
2) minimize mechanical contact between the mounting bracket and the metal plate
3) full contact between the steel plate and the foam
4) full contact between the foam and the substrate (gypsum board)

Referencing the two photos of my prototype 3mm VPR panel:

1) the entire top (and bottom) angled portion will be removed (cut along the red line), leaving just the flat rectangular metal plate
2) the (blue) "C" portion of the mounting bracket will be bent down 90 degrees to create a tab, modifying the "L" shape into an "S" shape
3) the air gap between the foam and the gypsum board will be reduced to zero, allowing the tab to "hook" over at a 90-degree angle
4) the tab's surface will be parallel to the metal plate; two screws will be used to secure the two together
5) four mounting brackets will hold the metal plates minimally but securely using just four tabs, effective in all directions/orientations including both vertical walls and the horizontal ceiling

 

[QuadDiffuser]

The following steel plates will be used, totaling over 57 pcs:

Ceiling:
12 pcs. 1.5mm thick, 1.0m x 1.5m

 

[QuadDiffuser]

Front wall:
4 pcs. 3.0mm thick, 1.2m x 1.8m
2 pcs. 3.0mm thick, 0.8m x 1.8m
2 pcs. 3.0mm thick, 1.0m x 1.5m
1 pc. 3.0mm thick, 1.2m x 1.5m

Front L corner:
2 pcs. 1.5mm thick, 1.2m x 1.5m (mounted diagonally)

Front R corner:
2 pcs. 1.5mm thick, 1.2m x 1.5m (mounted diagonally)