Is an Analytical Solution Possible for Dynamic Loading in Contact Problems?

[Iraphysics]

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

 

[timthereaper]

I'm having a hard time trying to visualize what the problem is. Could you draw it and post a picture?

 

[Iraphysics]

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

 

[wsabol]

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.