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Mathematical Problems in Engineering
Volume 2007, Article ID 28430, 11 pages
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.


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.