In a previous study, a generalized power flow mode theory was proposed to describe the power flow behaviour of a dynamical system based on the inherent characteristics of the system's damping distribution. By extending this theory, a power flow design and control mathematical model is developed which allows control of energy flow patterns, thus reducing or retaining vibratory energy flow in a particular vibration mode of the system. This is achieved through analyzing energy flow characteristics and designing an appropriate damping distribution in the system to adjust its characteristic damping factors and power flow mode vectors. To meet different vibration control requirements, new design criteria are proposed so as to dissipate maximum vibration energy and/or to control power flow in a specific vibration mode of the system. This mathematical model is demonstrated through an example of a suspension system with two degrees of freedom for which the power flow dissipation corresponding to selected control cases are presented. This study provides a novel approach to design a dynamical system from the perspective of energy flow patterns.
Many types of engineering structures, such as ships and offshore structures, are subjected to high-frequency excitation, the sense that high modal densities are experienced in the high-frequency range. Typical examples include dynamic responses of various ship subject to explosion waves in sea, ship machinery foundations excited by engines and auxiliaries, etc. A power flow analysis provides a technique to describe the dynamical behaviour of various structures and coupled systems at medium to high values of frequency. It focuses on the flow of vibrational energy rather than the detailed spatial pattern of the structural response. The fundamental concept of power flow was discussed by Goyder and White (1980) and Pinnington and White (1981), with significant developments and advances reported by Fahy and Price (1999).