In what follows, the analysis of Keane  for the energy flows around an arbitrary configuration of coupled multi-modal subsystems is extended to the case of non-conservative coupling. Here, the joints between any two subsystems are modelled by a spring and a damper, thus allowing for dissipation of energy to occur at the joint. The aim of this study is to give greater insight into the problem of energy flows through non-conservative couplings which has not been extensively discussed in the literature. Interest is focused on the effect of damping in the joints on the magnitudes of energy flows between, and energy levels in, each subsystem. The model derived is used to demonstrate the well known fact that selecting the correct level of damping in the joints surrounding a driven subsystem may cause a large percentage of the power input to the subsystem to be dissipated in these joints. This minimizes the overall power dissipated within the subsystems and thus the system total energy level. A Statistical Energy Analysis (SEA) model for non-conservatively coupled systems is then suggested, in which coupling damping loss factors are introduced into the main SEA energy balance equations to account for the energy dissipation in the joints. This model is shown to be exactly correct for the limiting case of weak coupling. Numerical examples which illustrate these various ideas are presented, with the use of parameters adopted in previous studies
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