Power flow mode theory and application to active vibration control of equipment mounted on travelling flexible ship excited by waves

Damping based power flow mode theory proposed is summarised and further investigated through a numerical simulation of an integrated system consisting of equipment, active/passive isolators and an elastic beam-like ship travelling in seaways. The system’s characteristic damping matrix is constructed and its eigenvalues and eigenvectors are calculated to identify the natural power flow characteristics of the system. These eigenvectors are defined as power flow mode vectors spanning the power flow space describing the power flow behaviour of the system. It reveals the system’s vibration energy dissipation mechanisms. The power flow design approach based on the system’s power flow characteristics is applied to design the system’s damping distributions to achieve the objectives to maximize the power dissipations to reduce vibration energy transmission to the equipment and to retain or suppress a particular vibration mode of the system. The simulation illustrates the power flow mode theory and power flow design concept through modifications of the system’s damping distribution using passive and / or active control means. This study provides an approach to design a dynamical system from the perspective of energy flow patterns.