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2-DOF problem with unknown stiffness and velocity

  1. Apr 21, 2016 #1
    1. The problem statement, all variables and given/known data

    I have a 2-DOF system, whereby I have one body that is grounded by a spring (body A), and a second body (body B) attached to the first by a spring and a viscous damper. For body A, I know the velocity and amplitude (before body B is added). I think I also have the stiffness value for body A (I'm looking at some old notes and I think this was given as part of the original problem). For body B, I know the mass and the damping coefficient.

    I would like to solve the velocity or stiffness of body B (by knowing one I can solve the other). With the information I have, is this possible, or must one of these values be known to begin with?

    2. Relevant equations
    equation of motion for body A:
    MAx"A+KAxA+KB(xA-xB)+c(x'A-x'B)=P0sinωt

    body B:
    MB+x"B+KB(xB-xA)+c(x'B-x'A)=0

    3. The attempt at a solution
    I've attempted to rearrange the equation above, but ultimately I think I have 2 unknowns here, the velocity and stiffness of B, and I'm uncertain if it is possible to calculate these values without firstly knowing the other. I have Den Hartog's Mechanical Vibrations book which has an example of such a system, but it assumes that these values are already known.

    I have all the above information in my notes, so I have been able to check my attempts against the real values, but I am certain that in this problem I did not have stiffness/velocity for B to begin with.

    Any assistance would be greatly appreciated, I am quite new to this area of study so please don't hold back if I have made any glaring errors or I'm missing anything obvious!

    Thanks,

    Nigel
     
  2. jcsd
  3. Apr 26, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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