Abstract
This paper demonstrates effects of harmonically varying damping on a structure with an isolation layer. We applied the method of 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 a natural frequency of the system, a 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 multi-degree-of-freedom systems have been conducted. This paper presents the effect of harmonically varying damping on the multi-degree-of-freedom systems, especially; the influence on a structure with an isolation layer is discussed. The new proposed semi-active control laws require the phase information of the structural vibrations. However, obtaining the phases of the vibrations would be difficult if the vibrations were complex. Therefore, in this study, the Stuart-Landau Oscillator filter is used for estimation of the phase information from the response of structure. The filter is taken advantage of the synchronization properties of a 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.
