A Euler beam dynamic equation under point load

AI Thread Summary
The discussion centers on deriving the equation of motion for a vibrating beam subjected to a nonlinear point load at x=L. The author is considering two approaches: using a Dirac delta function multiplied by a variable beta, or defining the force differently, both of which are causing numerical issues in their solver. Participants inquire about the nature of the nonlinear point load, its physical interpretation, and whether the focus is on small or large deflection solutions. The conversation highlights the need for clarity on these parameters to determine the correct modeling approach. Overall, the thread seeks guidance on resolving the numerical challenges associated with the dynamic equation of the beam.
Aladdin123
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Hi
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)
upload_2016-12-1_12-36-9.png

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:
upload_2016-12-1_12-36-28.png

Thus
upload_2016-12-1_12-36-47.png


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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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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