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.
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.
