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The chaotic phenomenons of a system with inertial coupling

Sado D.

Mechanics and Mechanical Engineering

2002

Vol. 6, nr 1

31-42

The nonlinear response of two-degree-of-freedom vibratory beam-pendulum system in the neighbourhood internal and external resonances is investigated. The analysis was realised in the wide aspects of the influence of different kinds of nonlinearities, dampings and excitations. The equations of motion have bean solved numerically. The present paper is a continuation of the author's previous works, where it was shown that in this type system one mode of vibration may excite or damp another one, and that except different kinds of periodic vibration there may also appear chaotic vibration. To prove the character of this vibration and to realise the analysis of transitions from periodic regular motion to quasi-periodic and chaotic, there have been constructed the bifurcation diagrams and time histories, phase plane portraits, power spectral densities, Poincare maps and exponents of Lyapunov. These bifurcation diagrams show many sudden qualitative changes, that is, many bifurcations in the chaotic attractor as well as in the periodic orbits.