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Predicting Pressure Field

Predicting Pressure Field

Predicting Pressure Field

(OP)
I am working my way up to more complicated acoustic problems. Currently I am attempting to determine the pressure field in the following system:

An harmonic oscillating piston inside a hollow rigid tube filled with inviscid compressible air and terminated with a acoustic material with a normalized specific acoustic impedance (z).

Now, I have solved the system analytically. I know the anylitical pressure field. I want to use the hemholtz equation and finite elements to predict this standing wave, or pressure field. Inorder to simplify the boundary conditions, I want to use the known (from analytical soln) pressures at the piston and terminated ends of the tube. Should be fairly easy, I thought. But, I am having difficulites.

My formulation yielded the following:

[k] = c^2/L*[1,-1;-1,1]+wL/6*[2,1;1,2]
where c = speed of sound (known)
L = element length (known)
w = excitation frequency (known)

so my system would look as follows
[k]{p}={f}
(c^2/L*[1,-1;-1,1]+wL/6*[2,1;1,2]){p1;p2} = {f1;f2}

I assemble my global stiffness matrix, set the force = 0, impliment my boundary conditions, and solve. This produces more or less a graph of the pressure field which looks like this:
\           /
 \_____/  
obviously it should look more like a sine wave. I am really at a loss here. Using pressure as my field variable is throwing me off I think. I have never done any finite elements where I wasn't just solving for displacements.

Thanks for reading, and your assistance.
Scott.

RE: Predicting Pressure Field

(OP)
As well, if anyone has any suggestions for finite element acoustics texts that deal with things like this and fluid structure interaction please let me know.

Thanks again.
Scott.

RE: Predicting Pressure Field

No specific acoustic or f.e. experience to claim here, but..

It's not obvious to me that the pressure profile should look sinusoidal just because the driver motion is, especially in the presence of standing waves.

What happens to the pressure profile when you start at low frequency and low amplitude, and sweep upward?

Mike Halloran
Pembroke Pines, FL, USA

RE: Predicting Pressure Field

The pressure profile will be a sinusoid, if the driving velocity is a sinusoid, if the system is linear.

Cheers

Greg Locock

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RE: Predicting Pressure Field

(OP)
Thanks for the replies gentlemen. As Greg mentioned, and my analytical solution predicts, the standing wave is a sinusoid.  

I am re-checking my implimentation of the boundary conditions. As easy as the problem seems to be, I must have made a mistake somewhere in that area.

Keep any suggestions coming :)

Thanks
Scott.

RE: Predicting Pressure Field

What's the lowest absolute pressure you predict?

Mike Halloran
Pembroke Pines, FL, USA

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