Natural Frequency of a Foam Block?

[Invertalon]

Hello everyone,

Looking for some help on how to go about finding the natural frequency of a block of foam. The foam has a density of 0.37 lbs./ft^3 and is 48"x48"x8" (LxWxD) in size. Weight is approximately 5.4 lbs.

I have been digging around the internet for quite some time with no such luck in finding a similar problem or method of solution.

Any guidance on how to go about this?

 

[Mister T]

Frequency is a property of a wave, or of a vibration. For example, I would need to know what kind of a wave is propagating through this foam. Presumably a sound wave. Do you know the speed of sound in the foam? These would be longitudinal vibrations.

On the other hand, if it's a transverse vibration, like it's clamped at one end and given thwack to set it vibrating that's a much more complicated calculation.

Another approach would be entirely empirical. Set it vibrating in one of its resonant modes and measure the frequency of vibration.

 

[Invertalon]

I do not have the speed of sound data for the foam at this time. A majority of the sound would be coming from combustion sources, primarily. There is vibration as well occurring. These foam panels will be secured to a wall that will encounter both vibration and sound waves.

I suppose though for right now, the transverse vibration (fix at one end and strike with hammer type deal and measure frequency) may be what I am trying to come up with right now, though, as a theoretical estimate for the natural frequencies of the block itself (and not the complete system... the adhesives, panel the foam is secured to, etc...).

We do plan to do testing in the future on the foam, but in the meantime looking for a method to calculate the natural frequencies if possible before hand.

Sorry I can not be more clear... Vibrations/physics is not my strong suit (mechanical...) so trying to wrap my head around how to go about doing this. I appreciate your guidance!

 

[Mister T]

I do not have the speed of sound data for the foam at this time. As far as the type of wave, the foam use is acoustic (so sound waves primarily). But it would be a mix of frequencies on the foam, low and high. A majority of the sound would be coming from combustion sources, primarily.

So, is this being used to dampen the sound? Is the foam open cell or closed, that is, can you blow air through it?

The folks who work with acoustic damping materials that I know about are speaker builders. They are very dedicated to details, for example the dimensions of the speaker cabinet, the characteristics of the drivers, and especially the design of the crossover. but when it comes to damping material they will tell you to use just about any open cell foam or the like, and they are not too fussy about how much or where it's placed, unless the speaker cabinet is ported and then care must be taken to not block it.

 

[Invertalon]

Open cell foam. Melamine foam, to be exact.

 

[Khashishi]

Foam has a low q factor (https://en.wikipedia.org/wiki/Q_factor) since it dampens the input a lot. So, there is a large spread in the resonant frequency. Also, there are multiple different modes with different frequencies that can exist.

From https://en.wikipedia.org/wiki/Speed_of_sound, the speed of sound propagating in the longitudinal direction is
##\sqrt{\frac{K+\frac{4}{3}G}{\rho}}##
where K is the bulk modulus and G is the shear modulus
and for transverse sound is ##\sqrt{\frac{G}{\rho}}##
I don't know the modulus of your foam.

The uncorrected resonance frequency is just approximately some integer times the speed of sound divided by the length or width or height. Damping shifts the resonance frequency down, perhaps a lot, because foam is very dissipative.

If you look here: https://en.wikipedia.org/wiki/Resonance
you see that when you have high damping, the peak amplitude is around 0 frequency (DC) rather than around the natural resonance. The concept of resonance really isn't very useful in this situation.