Hi all,
I need to model the acoustic impedance response of an elastic tube ( Acoustic-solid interaction) in the frequency domain. The acoustic impedance is :Pressure/volume velocity.
Here is the idea:
The geometry is a simple closed-end elastic tube. The acoustic load is generated by a piston on one end, sliding inside the tube. To have the frequency response, a unit step function of the displacement is applied to the piston (i.e., DZ=U(t)) and the pressure of the air inside the tube is measured in a time domain (i.e., P(t)) in front of the piston.
Then I need to calculate the derivative of P(t), (i.e., P'(t)) and do Fourier transformation to find the pressure in the frequency domain.
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Since the tube is elastic, the volume deformation itself is a function of time. Do I need to divide the pressure to the volume deformation? (i.e., Pressure(t)/volume velocity(t)) or I just need to divide pressure to the constant volume velocity, because the initial deformation is caused by the piston?
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How the acoustic pressure is measured? I can measure the stress components on the piston surface, but how I can calculate the acoustic pressure? This pressure is supposed to be the microphone pick-up, so should it be only in the tube direction or I need to calculate the hydrostatic pressure (i.e., 1/3(Sxx+Syy+Szz))?
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Should I do FFT (Fast fourier transform) on both V(t) and P(t) and then divide them to calculate the impedance (i.e., FFT(P)/FFT(V)), or I should do FFT(P(t)/V(t))?
I really appreciate any imput or a reference for a similar problem.
Regards,
bme