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Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 82691, 20 pages

Nonlinear oscillations of a coupled autoparametrical system with ideal and nonideal sources of power

Institute of Machine Design Fundamentals, Warsaw University of Technology, 84 Narbutta Street, Warsaw 02-524, Poland

Received 16 October 2005; Revised 5 June 2006; Accepted 16 July 2006

Copyright © 2006 Sado Danuta and Kot Maciej. 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.


An ideal and nonideal autoparametrical system excited by DC motor with unbalanced mass is presented in this work. The system consists of the body of mass M which is hung on a nonlinear spring with a nonlinear damper, and a pendulum of the length l and mass m mounted to the body of mass M. It is assumed that the motion of the pendulum is damped by nonlinear resistive forces. Vibrations of both models (ideal and nonideal) are researched. Solutions for the system response are presented for specific values of the parameters of system and the energy transfer between modes of vibrations is studied. Next excited vibrations for both models have been examined analytically and numerically. Except different kinds of periodic vibrations, there may also appear chaotic vibrations.