Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 80705, 19 pages
doi:10.1155/MPE/2006/80705
Autoparametric vibrations of a nonlinear system with pendulum
Department of Applied Mechanics, Lublin University of Technology, Nadbystrzycka 36, Lublin 20-618 , Poland
Received 31 December 2004; Revised 18 May 2005; Accepted 11 July 2005
Copyright © 2006 J. Warminski and K. Kecik. 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
Vibrations of a nonlinear oscillator with an attached pendulum,
excited by movement of its point of suspension, have been analysed
in the paper. The derived differential equations of motion show
that the system is strongly nonlinear and the motions of both
subsystems, the pendulum and the oscillator, are strongly coupled
by inertial terms, leading to the so-called autoparametric
vibrations. It has been found that the motion of the oscillator,
forced by an external harmonic force, has been dynamically
eliminated by the pendulum oscillations. Influence of a nonlinear
spring on the vibration absorption near the main
parametric resonance region has been carried out analytically,
whereas the transition from regular to chaotic vibrations has been
presented by using numerical methods. A transmission force on the
foundation for regular and chaotic vibrations is presented as
well.