Damping of Acoustic Waves in Pipelines due to End Conditions

Acoustic waves in pipelines are of concern because they can cause failure due to structural vibration and fatigue. The maximum wave amplitude that can be generated is limited by damping; a good understanding of damping is therefore vital. The damping considered here is due to the loss of energy from a resonant mode at a reflecting boundary. This type of damping is straightforward to analysis and consequently simple equations for damping are developed. A further aspect of damping is that it considerably modifies the description of acoustic resonance. The use of damped acoustic modes is shown to be problematic because they are complex and do not satisfy orthogonally conditions. A further and more significant observation is that damping prevents modes from being uncoupled and considered as independent. An uncoupled configuration is always found in undamped modes and is useful in forming simplified models however such uncoupling does not, in general, extend to damped modes. A condition for determining if modes can be uncoupled is derived. If a damped mode, which is not uncoupled, is used in an acoustic model it can generate energy as well as absorb energy. This non-physical behaviour greatly complicates the analysis of acoustic systems with damping.