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Equation of motion coursework

  1. Feb 17, 2009 #1
    1. The problem statement, all variables and given/known data

    I have coursework on rhe convolution integral, however i am struggling to find the equation of motion to start the whole thing off with.

    I will attach a picture of the problem, is is simply a cantilevered bar with a concentrated mass on the end and a damper.

    2. Relevant equations

    I am assuming you find the deflection at the end of the beam as a result of the force P(t), which i think is
    P(t)L^3/3EI

    However i am not sure where to go from here


    3. The attempt at a solution

    Thinking it may possibly be
    m[tex]\ddot{x}[/tex]+c[tex]\dot{x}[/tex]=P(t)L^3/3EI
    however i think i may need to add in stiffness somewhere else..
     

    Attached Files:

  2. jcsd
  3. Feb 23, 2009 #2
    Your simple model for the cantilever, looks OK, and it gives you the stiffness if you look at it properly. You have a deflection relation that is usually written as
    defl = P*L^3/(3*E*I)
    Now re-arrange that to read
    P = (3*E*I)/(L^3) * defl
    and from there you can see that the stiffness of this system is
    K = 3EI/L^3
    Now back to your equation of motion, which will look like
    m*xddot + c*xdot + K*x = F(t)
    where F(t) is whatever applied forcing function acts on the mass.

    See if that will get you going!
     
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