Coupled dynamic systems and Le Chatelier’s principle in noise control

Abstract

Investigation of coupling an externally driven dynamic system—a master dynamic system—to a passive one—an adjunct dynamic system—reveals that the response of the adjunct dynamic system affects the precoupled response of the master dynamic system. The responses, in the two dynamic systems when coupled, are estimated by the stored energies (Es) and (E0), respectively. Since the adjunct dynamic system, prior to coupling, was with zero (0) stored energy, E0s=0, the precoupled stored energy (E00) in the master dynamic system is expected to be reduced to (E0) when coupling is instituted; i.e., one expects E0<E00. In this case a beneficial noise control of the master dynamic system would result from the coupling. It is argued that the change in the disposition of the stored energies as just described may not be the only change. The coupling may influence the external input power into the master dynamic system which may interfere with the expected noise control. Indeed, the coupling may influence the external input power such that the expected beneficial noise control may not materialize. Examples of these kinds of noise control reversals are cited.