Induced Damping by a Nearly Continuous Distribution of Nearly Undamped Oscillators: Linear Analysis

摘要

It has been claimed that induced damping can be derived from the coupling of a continuous distribution of undamped oscillators. This claim stems from the fact that the contribution to the damping of a master oscillator by a coupled set of continuously distributed satellite oscillators, is independent of the loss factors of the oscillators in this set. (The distribution is with respect to the frequency of resonance of the satellite oscillators in the set). In the determination of the induced damping, the transition from a discrete-to-a continuous distribution, however, cannot be achieved without the imposition of modal overlap on the distribution and on the inherent damping of the satellite oscillators. It is this imposition that ensures that the contribution to the damping by these satellite oscillators is intuitively real. The imposition forbids equating the loss factors of the satellite oscillators to zero just because their contribution to the surrogate damping -- the induced damping -- of the host master oscillator to which they are coupled, is independent of these loss factors.