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Journal of Applied Mathematics
Volume 2012, Article ID 628503, 12 pages
Research Article

Some Properties of Motion Equations Describing the Nonlinear Dynamical Response of a Multibody System with Flexible Elements

Department of Automotives and Mechanical Engineering, Transilvania University of Brasov, 29 Eroilor Boulevard, 500036 Brasov, Romania

Received 26 August 2012; Accepted 10 November 2012

Academic Editor: Nicolae Herisanu

Copyright © 2012 Maria Luminiţa Scutaru and Sorin Vlase. 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 industrial applications use instruments and machines operating at high speeds, developing high forces, low temperatures, corrosive environments, extreme pressures, and so forth. Under these conditions, the elasticity of elements such a machine is built of cannot be ignored anymore, and models are needed to more accurately “grasp” the mechanical phenomena accompanying the operation. The vibrations and the loss of stability are the main effects occurring under these conditions. For the study on this kind of systems with rigid motion and elastic elements, numerous models have been elaborated, the main idea being the discretization of the elements and the use of finite element method. Finally, second-order differential equations with variable coefficients are obtained; these equations are strong nonlinear ones due to the time-dependent values of angular speed and acceleration, and they can be linearized considering a very short period of time, in which the motion is considered to be “frozen.” The aim of this paper is to present some characteristic properties of these systems.