Ninth MSU-UAB Conference on Differential Equations and Computational Simulations.
Electron. J. Diff. Eqns., Conference 20 (2013), pp. 133-149.

Title: Computational study of a dynamic contact problem

Authors: Jigarkumar Patel (Univ. of Texas at Dallas, Richardson, TX, USA)
         Janos Turi       (Univ. of Texas at Dallas, Richardson, TX, USA)
	  
Abstract: 
 In this article, we describe a computational framework to study the
 influence of a normal crack on the dynamics of a cantilever beam;
 i.e., changes in its natural frequency, amplitude and period of vibration, etc.

 Due to the opening and closing of the crack during beam vibrations,
 unilateral contact boundary conditions are assumed at the crack location.
 In the numerical implementation the contact conditions lead to the
 consideration of a linear complementarity problem. An effective solution
 strategy for this problem using a modification of the simplex method is
 presented. Numerical experiments are included.

Published October 31, 2013.
Math Subject Classifications: 34N05, 65P99, 49M99, 90-08,  90C05, 37M05, 35L87, 93C20, 93C55.
Key Words:  Vibrations of cracked beams; elastic structures with defects;
            linear complementarity problem with FEM.