Euler beam dynamic equation under point load

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SUMMARY

The discussion focuses on deriving the equation of motion for a vibrating Euler beam subjected to a nonlinear point load applied at a specific location (x=L). The participants explore two potential approaches: using an impulse Dirac function multiplied by a variable beta, or defining the force in an alternative manner. Concerns are raised regarding numerical errors in solvers when applying these methods, prompting inquiries about the physical interpretation of nonlinear point loads and the type of deflection solution required (small or large).

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  • Understanding of Euler beam theory
  • Familiarity with nonlinear dynamics
  • Knowledge of numerical methods for solving differential equations
  • Experience with impulse functions and their applications in mechanics
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  • Research the application of Dirac delta functions in beam dynamics
  • Study methods for handling nonlinear point loads in structural analysis
  • Explore numerical solvers specifically designed for dynamic systems
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Mechanical engineers, structural analysts, and researchers focused on dynamic systems and beam theory will benefit from this discussion.

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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