Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 28430, 11 pages
doi:10.1155/2007/28430
Research Article
Nonlinear Equations with a Retarded Argument in Discrete-Continuous Systems
Faculty of Management and Computer Modelling, Kielce University of Technology, Al. 1000-cia Państwa Polskiego 7, Kielce 25-314, Poland
Received 18 April 2006; Accepted 20 March 2007
Academic Editor: Katica R. (Stevanović) Hedrih
Copyright © 2007 Amalia Pielorz. 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.
Abstract
The paper deals with dynamic problems of discrete-continuous systems
with local nonlinearities, the analysis of which is reduced to solving
nonlinear differential equations with a retarded argument. This concerns
the discrete-continuous systems subject to torsional, longitudinal,
or shear deformations, where the equations of motion for elastic
elements are classical wave equations. It is assumed that the
characteristics of local nonlinearities are of a soft-type and
in the paper they are described by four nonlinear functions.
After a short general description of the approach used, the
detailed considerations and numerical results are presented
for a multimass discrete-continuous system with a local nonlinearity
having the characteristics of a soft-type subject to shear deformations.