Theoretical Upper and Lower Bounds of the Performance of an On-Off Damping Dynamic Vibration Absorber Attached to a Multi-Degree-of-Freedom System

This paper reveals the theoretical (upper and lower) bounds of the performance of an on-off damping vibration absorber attached to an undamped multi-degrees-of-freedom (MDOF) system under harmonic excitation. The solution reduces to the maximization or minimization problem of a simple single-variable function. Among the class of on-off damping controller, which switches the damping level from high to low and back at fixed times every half period, the revealed solutions produce the highest and lowest amplitude–frequency curves. These curves are the good theoretical benchmarks to measure how good or bad an on-off damping controller is. To demonstrate the usefulness of the theoretical bound solutions, two versions of power flow-driven controller are introduced to produce the amplitude–frequency curves tracing the lowest-amplitude curve. A case study of a four-mass system is discussed.