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.