Power flow between two continuous one-dimensional subsystems : a wave solution

Abstract The power flow between two point-coupled wave-bearing subsystems is determined by using a wave approach. The subsystems are one dimensional in that each supports just one wave mode, and are described by a reflection coefficient from which, in certain circumstances, the modal overlap and modal density can be defined as continuous functions of frequency. The coupling element is described by a reflection coefficient, and attention is focused on the case of conservative coupling. Time harmonic point forces or “rain-on-the-roof” excitations may act on the subsystems. Uncertainty exists in the properties of the subsystems, which are assumed to be drawn from ensembles of similar subsystems. The exact power flow and the ensemble statistics are seen to depend on the magnitudes of the subsystem and coupling reflection coefficients. For some particular cases the maximum and minimum power flows are examined, together with the ensemble mean and geometric mean, the cumulative probability distribution and the probability density function. For a given power incident upon the coupling the ensemble mean power flow through the coupling is always less than that expected from a normal SEA wave approach due to power re-radiation. The differences are largest when the damping is light and the coupling strong. For a given level of excitation power re-radiation effects are also apparent for the ensemble mean power flow from an infinite subsystem to a finite subsystem. In the opposite case the ensemble mean power flow from a finite to an infinite subsystem is greater than that between two infinite subsystems due to power re-injection. The differences are largest for light damping and for weak coupling. Finally, the case where there is uncertainty in one subsystem only is considered.

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