Impact of mass ratio and bandwidth on apparent damping of a harmonic oscillator with subordinate oscillator array

Abstract

The response of a lightly damped resonator with a set of substantially less massive attached oscillators has been studied. The collection of attached oscillators is known as a subordinate oscillator array (SOA). An SOA can function as an energy sink, extracting vibration energy from the primary mass and thus adding apparent damping to the system. We have shown that the limit of apparent damping achievable for this class of system is the inverse of non-dimensional bandwidth (ratio of the bandwidth to the fundamental frequency of the primary oscillator). In practice, the utility of this result is limited because a great deal of mass (~25% of primary) is required to approach critical damping. The mass of the subordinate set required to achieve the most rapid energy transfer from the primary is proportional to the non-dimensional bandwidth squared. Low apparent Q is achieved by increasing non-dimensional bandwidth. The presentation will describe numerical optimizations that investigate the impact of the SOA bandwidth, the mass ratio (the ratio of the total mass of the SOA to the mass of the primary structure) and the apparent damping of the system.