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A Euler beam dynamic equation under point load

  1. Dec 1, 2016 #1
    So the problem I have is I want to get the equation of motion of a vibrating beam under a nonlinear "Point" force.
    The equation would be like this for a distributed load (Which is not the case)
    But I want the load to be at a point at x=L
    So I have to options. Add an impulse dirac function multiplied by the beta (Causes numerical errors for my solver), or define the force as follows:

    Which one is correct or if both wrong what do I do.
    Also even if one of them is correct, any better options? (The above cases messes up my numerical solver)

    Note: Obviously, z is a function of (x,t) and also beta is a function of (t)

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    Last edited: Dec 1, 2016
  2. jcsd
  3. Dec 1, 2016 #2


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    How is the beam supported ?

    What do you mean by non linear point load ? Has it got any physical interpretation or any defining equation ?

    Are you looking for a small deflection or large deflection solution ?
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