Hi there! 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/s2 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/m3 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)*length3)/(3*Young's*SecondMoment) pipe deflection = (((mass*acceleration)/length)*length4)/(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!