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Oscillations of an Autoparametrical Systems with the Spherical Pendulum

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Dynamic properties of the three degrees of freedom autoparametric system with spherical pendulum in the neighbourhood internal and external resonance are investigated. It was assumed that the spherical pendulum is suspended in the main body which is suspended by the element characterized by elasticity and damping and is excited harmonically in the vertical direction. The spherical pendulum is similar to the simple pendulum, but moves in 3-dimensional space, so the model with spherical pendulum is more similar to the real systems than the model with simply pendulum. In this paper the position of the main body is described by coordinate z and position of the pendulum is describe by the coordinate z and two angles: θ and φ in the vertical planes. This system has three degrees of freedom. Dynamic properties of the system described by three differential equations containing strongly nonlinear terms are investigated numerically. In autoparametric system one mode of vibration may excite or damp another one, and for except periodic or quasi-periodic vibrations there may also appear chaotic vibration. For characterizing an irregular chaotic response, time histories, bifurcation diagrams, power spectral densities, Poincaré maps and maximal exponents of Lyapunov have been developed.
Opis fizyczny
Bibliogr. 10 poz., wykr.
  • Warsaw University of Technology, Institute of Machine Design Fundamentals
  • International School of Gdansk
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