Autoparametric vibrations of a nonlinear system with pendulum

J. Warminski and K. Kecik

Mathematical Problems in Engineering, 2006, vol. 2006, 1-19

Abstract:

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.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:080705

DOI: 10.1155/MPE/2006/80705

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