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Autoparametric vibrations of a nonlinear system with pendulum. (English) Zbl 1100.70012
Summary: Vibrations of a nonlinear oscillator with an attached pendulum, excited by the motion of its point of suspension, have been analysed. 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 pendulum oscillations. The influence of a nonlinear spring on the vibration absorption near the main parametric resonance has been examined analytically, whereas the transition from regular to chaotic vibrations has been examined by numerical methods. A transmission force on the foundation for regular and chaotic vibrations is presented as well.

##### MSC:
 70K28 Parametric resonances for nonlinear problems in mechanics 70K40 Forced motions for nonlinear problems in mechanics 70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
Dynamics
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##### References:
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