A power flow mode theory based on a system's damping distribution and power flow design approaches

Abstract

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 characteristicdamping 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 timeaveraged power flow expression and theorems relating to its estimation are presented.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.The developed damping-based power flow mode theory is compared with a mobilitybased power flow model. It is shown that the proposed power flow model provides insight into the power flow dissipation mechanisms in dynamic systems.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.

Novel Approach for Structural Dynamic Topology Optimizations Based on Power Flow Mode Theory

“…As is shown in [1], this characteristic damping matrix C plays a significant role in determining the system's power flow.…”

“…The power flow mode theory provides a new approach for vibration control applications through modifications of the system's damping distribution using passive and/or active control components. Interested readers can refer to the full paper published in the royal society proceedings [1] for more details.…”

“…In this Section, the developed damping-based power flow mode theory [1] is briefly reviewed to aid the understanding for readers. It describes the essential power flow behaviour of a dynamic system.…”

A novel model of dipteran flight mechanism

“…Further researches have been actively undertaken by the current authors in the following directions: (i) to develop the methodologies for the irrational nonlinear system to derive the dynamic responses under perturbations; (ii) to determine the analytical measures e.g., the construction of Melnikovian to predict the border of chaos; (iii) to investigate the energy transmission mechanism [38][39][40] using power flow approach for the irrational nonlinear dynamic systems.…”

Power flow analysis for a floating sandwich raft isolation system using a higher-order theory

“…The fundamental concept of power flow is discussed by Goyder and White [1] and Pinnington and White [2]. In recent years, this approach has been developed and applied to model complex structure [3][4][5][6][7][8][9][10][11][12] and to assess passive, active and vibration control system [8,[13][14][15][16][17]. Langley [3] presented the dynamic stiffness method to investigate forced vibration of a row of stiffened rectangular panels, simply supported along the longitudinal edges.…”