A power flow mode theory is developed to describe the natural power flow behaviour of a dynamic system based on its inherent damping distribution. The system's characteristic-damping matrix is constructed and it is shown that the eigenvalues and eigenvectors of this matrix identify natural power flow characteristics. These eigenvectors, or power flow mode vectors, are chosen as a set of base-vectors spanning the power flow space and completely describe the power flow in the system. The generalized coordinate of the velocity vector decomposed in this space defines the power flow response vector. A time-averaged power flow expression and theorems relating to its estimation are presented.<br/><br/>Based on this theory, power flow design approaches are proposed to identify energy flow patterns satisfying vibration control requirements. The mode control factor defines the measure of the correlation between a power flow mode and a natural vibration mode of the system. Power flow design theorems are presented providing guidelines to construct damping distributions maximizing power dissipation or to suppress/retain a particular vibration mode and/or a motion.<br/>The developed damping-based power flow mode theory is compared with a mobility-based power flow model. It is shown that the proposed power flow model provides insight into the power flow dissipation mechanisms in dynamic systems.<br/><br/>Examples are presented to demonstrate the applicability of the power flow mode theory and the power flow design approach. These examples demonstrate the generality of the theory, including non-symmetric damping matrices, and illustrate power flow design applications through modifications of the system's damping distribution using passive and/or active control components
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