Euler beam dynamic equation under point load

In summary, the conversation discusses the problem of obtaining the equation of motion for a vibrating beam under a nonlinear point force, with one option being to add an impulse Dirac function and the other being to define the force in a different way. The person also asks for clarification on the support and physical interpretation of the load, as well as whether a small or large deflection solution is needed.
  • #1
Aladdin123
16
0
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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  • #2
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 ?
 

Related to Euler beam dynamic equation under point load

1. What is the Euler beam dynamic equation under point load?

The Euler beam dynamic equation under point load is a mathematical equation that describes the motion of a beam that is subjected to a single concentrated load at a specific point along its length. It takes into account the properties of the beam, such as its length, material, and cross-sectional area, as well as the magnitude and location of the load.

2. How is the Euler beam dynamic equation derived?

The Euler beam dynamic equation is derived using the principles of Newtonian mechanics, specifically the equations of motion for a rigid body. By assuming that the beam is a series of connected rigid bodies, the equation can be derived by considering the forces and moments acting on each body and applying Newton's second law of motion.

3. What are the key assumptions made in the Euler beam dynamic equation?

The Euler beam dynamic equation is based on several assumptions, including that the beam is straight, homogeneous, and isotropic (meaning it has the same properties in all directions). It also assumes that the beam is subjected to small displacements and that the load is applied at a single point along the beam's length.

4. How is the Euler beam dynamic equation solved?

The Euler beam dynamic equation can be solved using various techniques, such as analytical, numerical, or computational methods. In most cases, the equation is solved using numerical methods, which involve discretizing the beam into smaller segments and solving the equation for each segment. This allows for a more accurate and efficient solution compared to analytical methods.

5. What are the practical applications of the Euler beam dynamic equation under point load?

The Euler beam dynamic equation is commonly used in engineering and physics to analyze the behavior of beams under different loading conditions. It can be applied to various real-world scenarios, such as designing buildings and bridges, understanding the behavior of aircraft wings, and analyzing the dynamics of moving objects such as cranes and elevators. It is an essential tool for predicting and optimizing the performance of structures and machines that involve beams.

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