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Advances in Acoustics and Vibration
Volume 2012, Article ID 268595, 9 pages
Research Article

Nonsmooth Modeling of Vibro-Impacting Euler-Bernoulli Beam

1Department of Mechanical Engineering, Indian Institute of Technology Hyderabad, Ordnance Factory Estate, Yeddumailaram 502205, India
2MSC Software, 101 North Brand Boulevard, Suite 900 Glendale, Santa Ana, CA 91203, USA
3Systems Design Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1

Received 3 April 2012; Accepted 17 June 2012

Academic Editor: Abul Azad

Copyright © 2012 C. P. Vyasarayani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new technique to simulate nonsmooth motions occurring in vibro-impacting continuous systems is proposed. Sticking motions that are encountered during vibro-impact simulation are imposed exactly using a Lagrange multiplier, which represents the normal reaction force between the continuous system and the obstacle. The expression for the Lagrange multiplier is developed in closed form. The developed theory is demonstrated by numerically simulating the forced response of a pinned-pinned beam impacting a point-like rigid obstacle.