Open AccessAutoparametric vibrations of a nonlinear system with pendulum
Author(s) -
Jerzy Warmiński,
Krzysztof Kęcik
Publication year - 2006
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/mpe/2006/80705
Subject(s) - pendulum , parametric oscillator , vibration , kapitza's pendulum , nonlinear system , physics , simple harmonic motion , double pendulum , classical mechanics , parametric statistics , harmonic oscillator , chaotic , equations of motion , control theory (sociology) , inverted pendulum , mathematics , acoustics , quantum mechanics , computer science , statistics , control (management) , artificial intelligence
Vibrations of a nonlinear oscillator with an attached pendulum,excited by movement of its point of suspension, have been analysedin the paper. The derived differential equations of motion showthat the system is strongly nonlinear and the motions of bothsubsystems, the pendulum and the oscillator, are strongly coupledby inertial terms, leading to the so-called autoparametricvibrations. It has been found that the motion of the oscillator,forced by an external harmonic force, has been dynamicallyeliminated by the pendulum oscillations. Influence of a nonlinearspring on the vibration absorption near the mainparametric resonance region has been carried out analytically,whereas the transition from regular to chaotic vibrations has beenpresented by using numerical methods. A transmission force on thefoundation for regular and chaotic vibrations is presented aswell
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