Power flow between two coupled beams

Abstract The coupling power between two end-coupled beams is determined by applying results from references [1, 2], in which a general wave solution was found for the energy flow between two coupled subsystems. Time-harmonic excitations of varying frequency are applied to one beam over a range of frequencies. The beams are described by reflection coefficients. For a constant power in the direct field at the coupling, peaks in the coupling power are identified with particular values of the phases of the subsystem reflection coefficients. When the coupling is weak enough, coupling power peaks occur approximately at the natural frequencies of the uncoupled subsystems, and when it is stronger they occur at the natural frequencies of the coupled system. A critical frequency where the behaviour changes qualitatively is determined from a critical value of the coupling reflection coefficient. The effects of uncertainty in the ratio of the lengths of the beams are examined and seen to be most significant when the beams are of nearly equal length. “Rain-on-the-roof” and point force excitations are considered, and in the latter case uncertainty exists in the point of application of the force. For “rain-on-the-roof” excitation, the power in the direct field at the coupling depends on the characteristic impedance of, and dissipation within, the excited subsystem. For point force excitation additional dissipation and interference effects are apparent. These depend on the point of application of the force. Averaging over a band of frequencies generally removes most of the interference effects, except for application points close to the far boundary, the remaining dependence on the application point being equivalent to the effects of mode shape coherence.