Dynamic loading and contact

In summary, The conversation was about trying to find an analytical solution to a contact problem with dynamic loading involving a cantilever beam resting on a smooth plane. Suggestions for books or papers and the use of a single degree of freedom system versus a multi-degree-of-freedom system were discussed. The idea of using polar coordinates and hybrid system dynamics for simplification and possible solutions was also mentioned.
  • #1
Iraphysics
5
0
Hi All,

I am trying to get an analytical solution to a contact problem with dynamic loading. I am not sure if an analytical solution of such a problem is possible. Here how the problem is:

A cantilever beam, with its free end resting on a smooth plane, is under harmonic loading f(t) tangential to the contact interface. I am looking for a mathematical equation of this problem.

Suggesting any book, any paper, any help would be much appreciated.

Thanks in advance
Ira
 
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  • #2
I'm having a hard time trying to visualize what the problem is. Could you draw it and post a picture?
 
  • #3
Thanks for the reply timthereaper.

I have attached a figure showing my problem. I know if I consider this system as a single degree of freedom system then an analytical solution is possible. For a multi-degree-of-freedom system, I think I'll need to work it out numerically. Using mode superposition method? Or is there any other way?

Thanks for your help.
Ira
 

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  • #4
Which 2 dimensions do you mean? The two horizontal directions? or horizontal and vertical?

If its the 2 horizontal directions, I'd suggest doing the problem in polar coordinates, so it simplifies back to a 1D problem :)
For the vertical component, there is NOT a continuous numerical solution, but their is an analytical solution you can derive. Look up Hybrid system dynamics.
 

1. What is dynamic loading and contact?

Dynamic loading and contact is a phenomenon that occurs when a load is applied to a structure or material at a varying rate or magnitude. This can result in changes in the structure's behavior, such as deformation or stress, and can also cause contact between different components of the structure.

2. What are the main factors that influence dynamic loading and contact?

The main factors that influence dynamic loading and contact include the magnitude and rate of the applied load, the material properties of the structure, and the geometry and boundary conditions of the structure. Other factors, such as temperature and environmental conditions, can also play a role.

3. How is dynamic loading and contact different from static loading?

Dynamic loading and contact differs from static loading in that it involves a varying or changing load, rather than a constant load. This can result in different behaviors and responses from the structure, as well as the potential for contact between different components.

4. What are some common applications of dynamic loading and contact in engineering?

Dynamic loading and contact is commonly encountered in engineering applications such as impact testing, vibration analysis, and structural dynamics. It is also relevant in industries such as automotive, aerospace, and civil engineering, where structures are subjected to varying loads and contact forces.

5. How is dynamic loading and contact simulated or analyzed in engineering?

There are various methods for simulating and analyzing dynamic loading and contact in engineering, including finite element analysis, computational fluid dynamics, and experimental testing. These techniques allow engineers to predict and understand the behavior of structures under dynamic loading and contact conditions, and make informed design decisions.

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