Resonant frequency (Helmholtz resonantor) of a cavity

suktan

I created a cavity 3D model in ViaCad. The model is essentially a larger cube, representing room air, enclosing a smaller cube, representing the actual cavity. STEP file was exported, as attached, for Mecway. Acoustic resonance 3D analysis with 30 modes was employed. The STEP was imported in Mecway. Default setting was used to generate mesh.

I checked all the modes and found Mode 5 (266.7 Hz) resulting highest pressure in the cavity and low room pressure. This should be the resonant frequency of the model. Am I correct?

Both STEP and Mecway files are attached.

Victor

Yes, I'd say so. I also found that changing the size of the room changes the frequencies of the other modes but not the 266.7 Hz one, further indicating that it's independent of the room's geometry, as you'd expect for a cavity mode.

It's also a good idea to refine the mesh and solve again to make sure the mesh is fine enough. In this case it's already pretty good.

tcarson

I agree with victor,

I looked at your model and did hand calc for a Helmholtz resonator.

V=.000512m^3
l=.01m
d= .02 m
c=345m/s
ln=l+1.6*d/2 (this is for the effective length)
A= area of openting

f=c/(2*pi)*sqrt(A/(V*ln))



this gives a resonant frequency for the Helmholtz of
f=266.74Hz

This website appears to take into account the effective length. it gave 265.97Hz

http://www.mh-audio.nl/acalculators.asp#showcalc

suktan

Thanks for your comment. I used an online cavity resonance calculator (http://hyperphysics.phy-astr.gsu.edu/hbase/waves/cavity.html) to verify the result. The cavity volume in the model is 512 cm3. It is equivalent to have a circular port of length 1 cm. Port area is 3.14 cm2. I put these numbers plus 345 m/c for sound speed to the calculator and got 430 Hz, as shown in the graph. Do you see anywhere I did incorrectly?

suktan

Thank you tcarson! I tried the link of mh-audio and got the same result. Now my question is solved.

suktan

Hand calculation and the online calculator are approximation. Correct understanding?

tcarson

Sorry in advance for the long post

It looks like most websites don't take into account the effective length for the port. not always an issue but with the choices you made for the port dimensions it is.

the effective length is equal to the port length plus 1.6x port radius. this is for sudden expansion opening. flared ports would be different. I would not say that hand calcs are approximations, but rather are a model for a very specific case.


you used
r = 1cm
l = 1cm
effective length (ln) =2.6=1+1.6*1 (over 100% increase)

If you pick a better ratio the effect is less important, lets say
r=1cm
l=10cm

effective length (ln) =10+1.6*1=11.6 (16% increase)

If you pick even better ratio

r=.5cm
l=15cm
ln=15+1.6*0.5=15.8 (5%)


When designing the Helmholtz resonator multiple combinations of the parameters will give you the same natural frequency. when designing a "real" part you want it to be as robust as possible so try to pick a ratio that does not change the natural freq much with slight changes in dimensions. that would make it better for manufacturing.

to circle back to the hand calc as an approximation for a minute. many people would say that FE is only an approximation and that physical testing is the only true answer. I would say that physical and simulated tests can agree nicely but it usually depends on how well you know the system and the boundary conditions.

suktan

Thank you for your clear explanation. It is very helpful!