How Does a Perpendicular Force Affect a Fixed Elastic Rod?

[pixel8]

I am studying the following phenomenon for my project:
Thin horizontal elastic rod is fixed at both ends and small perpendicular force is applied at middle of the rod perpendicular to its length. I want to study this dynamics and extend it to cylindrical shell. Please suggest books/papers or keywords for this type of phenomenon.
Thanks.

 

[jedishrfu]

Perhaps this will help:

http://blog.cencophysics.com/2009/08/beam-deflection-youngs-modulus/