Edgar,
Are you sure that this is "slug flow"? To me it seems more like an abrupt process condition with intermittent flow conditions (I mean a pulsating type of flow)!!Though I can't be 100% sure about it as you've not mentioned whether your line is horizontal or vertical at the points of vibration. Can you elaborate your problem a bit more like the layout,supporting,process parameters & line size.
In the meanwhile, get information from the site such as the displacements (amplitude) of vibration, nature of vibration (like incessant or occuring at longer intervals) etc!!
As you've correctly said , the forces in negative & positive directions won't be equal in magnitude.
But in order to get to the crux of the problem, elaborate your problem.
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Keep Smiling
SJ