Abstract
This paper demonstrates effects of harmonically varying damping on a parallel-coupled structure and the filtering using the Stuart-Landau equation. We applied the method of the harmonically varying damping to vibration mitigation of a single-degree-of-freedom structure with sinusoidal base excitation having two frequencies. In the study, an ideal variable damper was used in conjunction with the secondary sinusoidal base excitation to reduce the response due to the primary base excitation. When the primary sinusoidal base excitation contains the natural frequency of the system, the resonance is induced. However, another resonance can be generated by the modulated component caused by the variable damping device and the secondary base excitation. The additional resonance was adjusted to be out of phase with the primary response, and the response of the structure was effectively reduced as a result of the damping. However, no such study considering the multi-degree-of-freedom system has been conducted. This paper presents the effect of the harmonically varying damping on the multi-degree-of-freedom system, especially; the influence on two structures in parallel with a variable damper between them is discussed. In addition, the new filter is also demonstrated in this study. The new proposed semi-active control laws require the phases of the structure's vibrations. However, obtaining the phases of the vibrations would be difficult if the vibrations were complex. Therefore, the new filter using a nonlinear oscillator, Stuart-Landau equation, is proposed. The filter is taken advantage of the synchronization properties of the nonlinear oscillator, and the output of the oscillator has the characteristic frequency designated by the oscillator. The validity of the proposed system is shown by numerical simulation.
