THE STATISTICS OF POWER FLOW BETWEEN 2 CONTINUOUS ONE-DIMENSIONAL SUBSYSTEMS

The power flow between two continuous subsystems is examined using a wave solution [1]. One of the subsystems is excited by time-harmonic forces, and both subsystems can support only one power-transmitting wave mode. Uncertainty exists in the subsystems, which are assumed to be drawn at random from ensembles. Those ensembles members that have a natural frequency at the excitation frequency are determined. The particular members that are resonant are seen to depend on the strength of coupling. The statistics of power flow are considered; in particular, the maximum, minimum, ensemble arithmetic and geometric means, the variance and the cumulative probability distribution of the power flow. The maximum power flow undergoes a qualitative change at a particular coupling strength. For weak coupling the peak power flows occur at the uncoupled natural frequencies, while for stronger coupling they occur at the coupled frequencies. The ensemble average power flow may be significantly less than that expected from a "normal" SEA approach due to power re-radiation, especially for a lightly damped receiving subsystem and strong coupling. Conversely, it may be much greater due to power re-injection, which occurs particularly for a lightly damped excited subsystem and weak coupling. The power flow variance is largest for small damping and weak coupling, under which circumstances the cumulative probability distribution has an infrequent but dominant tail of very large power flows. © 1992.