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Im trying to do an analysis in Abaqus of a cantilever pipe, with a tip mass at the free end, that is decelerating to a stop at 10 m/s

^{2}from 10m/s, causing it to vibrate. To validate my results im doing some handcalcs. I have done a static analysis and calculated the maximum deflection of the beam, and my results match. I would also like to estimate the time it takes for the pipe to stop vibrating, could anyone help me out here?

What I know:

Pipe external diameter = 0.1m

Pipe internal diameter = 0.75m

Tip mass = 200kg

Pipe density = 7800 kg/m

^{3}

Young's modulus = 207GPa

Poissons ratio = 0.3

damping ratio = 0.1

Pipe length = 1m

What I have tried so far:

Well to work out the beam deflection I summed the effects of the inertia of the tip mass, as well as the inertia of the pipe mass itself. Shown in the two equations below:

mass deflection = ((mass*acceleration)*length

^{3})/(3*Young's*SecondMoment)

pipe deflection = (((mass*acceleration)/length)*length

^{4})/(8*Young's*SecondMoment)

Then to take into account time and the damping coefficient i just multiplied this answer by (1-0.1)

^{time}

Though this seems to simple and my results to not much to those from my simulation.

Sorry I don't know how to insert my equations as equations!

Any help or tips would be appreciated!