This paper studies the regular and irregular vibrations of two degrees of freedom autoparametrical system, when the excitation is made by an electric motor (with unbalanced mass), which works with limited power supply. The investigated system consists of a pendulum of the length l and mass m, and a body of mass M suspended on the flexible element. It was assumed that the damping force acting on the body of mass M and resistive moment acting on the pedulum are non-linear. In this case, the excitation has to be expressed as an equation describing how the energy source supplies the energy to the system. The non-ideal source of power adds one degree of freedom, and then the system has three degrees of freedom. The system has been researched for known characteristic of the energy source (DC motor). The equations of motion have been solved numerically what permit to enrich the investigations and to examine not only small and steady state oscillations but also large-amplitude oscillations in transient states. The influence of motor’s speed on the phenomenon of energy transfer has been researched. Near the internal and external resonance region, except different kind of periodic vibration, the chaotic vibration has been observed. For characterizing an irregular chaotic response bifurcation diagrams and time histories, power spectral densities, Poincare´ maps and maximal exponents of Lyapunov have been constructed.
Regular and Irregular Vibrations of a Non-Ideal Autoparametric System
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Sado, D, & Kot, M. "Regular and Irregular Vibrations of a Non-Ideal Autoparametric System." Proceedings of the ASME 7th Biennial Conference on Engineering Systems Design and Analysis. Volume 2. Manchester, England. July 19–22, 2004. pp. 221-228. ASME. https://doi.org/10.1115/ESDA2004-58489
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