A proposed definition for the induced noise control parameter

The response of an externally force‐driven master dynamic system is examined under two conditions. In the first, the master dynamic system is in isolation and the (quadratic) response is stated in terms of its stored energy E⁰₀(ω), where (ω) is the (angular) frequency. In the second, the master dynamic system is passively coupled to an adjunct dynamic system that is not externally driven. The response of the master dynamic system, that is subjected to the same external force drive, is changed due to the couplings. The change is from E⁰₀(ω), in isolation, to E₀(ω), when coupled. The induced noise control parameter ξ(ω) is then defined: ξ(ω)=[E₀(ω)/E⁰₀(ω)]. The smaller ξ(ω) is, the more benefit, by the couplings, is accrued to the noise control of the master dynamic system. When ξ(ω) exceeds unity, by definition, an induced noise control reversal occurs. Illustrations of an induced noise control are provided in terms of a master dynamic system represented by an (harmonic) oscillator and an adjunct dynamic system represented by a set of satellite (harmonic) oscillators. The satellite oscillators are not coupled to each other; they are individually coupled to the master oscillator only. A coupling may include a combination of mass, stiffness, and gyroscopic elements.