This paper deals with the vibration quenching problem of the one-degree-of-freedom system with a limited power supply. This system is forced by centrifugal force of rotating unbalance, and the system is quenched using a Hula-Hoop and a motor to assist the rotation of Hula-Hoop. The entrainment region, the amount of vibration quenching, and the energy consumptions of the system are studied from the approximate analysis using the averaging method, the numerical integration analysis, and the experiment. Following was made clear: (1) When the unbalance is large, the entrainment region of the voltage of the assistant motor is large. On the other hand, when the unbalance is small, the entrainment region becomes narrow. (2) When the unbalance is large, by setting the voltage of the assist motor to a value smaller than the optimum value for vibration control, within the range that satisfies the allowable vibration amplitude level, the increase amount of the energy consumption becomes low. (3) The approximate solutions obtained by the averaging method are in good agreement with those obtained by the numerical integration method, and the characteristics of these results coincide with those of the results obtained by experiment.

This paper deals with the vibration quenching problem of the single-degree-of-freedom system with a limited power supply using a Hula-Hoop and displacement magnification mechanism. This system is forced by the centrifugal force of rotating unbalance. If the unbalance is small, the amplitude of vibration of the main system becomes small and Hula-Hoop does not rotate. Therefore, the vibration of main system is not quenched. To solve this problem, the two types of displacement magnification mechanisms are adopted, namely, the one is the mechanism using beams with fixed ends that move and the other is that using cantilever. The quenching effects and the quenching frequency regions are studied. Following was made clear by the numerical integration of the equation of motion and the experiment: (1) The main system is quenched well by enlarging the displacement at the rotational center of Hula-Hoop using each type of displacement magnification mechanism. (2) The optimal vibration quenching condition of the Hula-Hoop and the displacement magnification mechanism for the first mode is obtained. (3) The frequency regions suitable for vibration quenching are the regions those are higher than the natural frequencies. (4) The vibration mode and the phase relation between unbalance and Hula-Hoop are made clear in each vibration mode. (5) The characteristics of the solutions obtained by the numerical integration method coincide qualitatively with those of the results obtained by the experiment.

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