Hi all,
Im interested in creating a finite element model in Abaqus to estimate the frequency response of pressure waves propagating through flexible tubing. This model would need to be able to predict the frequency response of frequencies less than approximately 300 Hz. Use air as the medium of transport, and take into account the acoustic-structural interaction between the air and flexible tubing. Currently I'm inputting a step function just so it can provide me with a similar output to some experimentation I have done, but in the future I would provide a sinusoidal pressure input.
What I'm struggling with is modelling the viscous damping in the tube which causes propagation loss along the length of the tube. I have created an asymmetric model with acoustic elements and tried to apply an acoustic impedance along the walls according to equation 24 in [1]. Also I have tried to apply a volumetric drag coefficient, which appears to work. However the required volumetric drag coefficient is unknown. The acoustic impedance causes some damping of the signal, however according to my experimentation on rigid tubing the signal should fall to steady state in less than 100 ms. The value of acoustic impedance takes more than 1 s to fall to steady state.
The modelling I have done so far has been assuming a rigid tubing, so I can calibrate the model to achieve the correct level of damping, but I would prefer a more analytical solution to deriving the volumetric drag coefficient and/or acoustic impedance.
So is anyone aware of some resources I can read to correct derive the damping coefficients for a tube or the air within the tube, that would be suitable for use in a model of flexible tubing (polymer, silicone etc).
I have provided a python script that I use to generate my model that uses the volumetric drag approach.
Any help with this problem would be greatly appreciated.
Thanks,
Alistair
[1] Scheidl, R., Manhartsgruber, B., & Ez El Din, M. (2009). Finite Element Analysis of 3D Viscid Periodic Wave Propagation in Hydraulic Systems. International Journal of Fluid Power, 10(1), 47-57.
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