Regular Article
POWER FLOW ANALYSIS OF COMPLEX COUPLED SYSTEMS BY PROGRESSIVE APPROACHES

https://doi.org/10.1006/jsvi.2000.3159Get rights and content

Abstract

A generalized mobility/impedance-power flow mathematical model is developed to analyze the dynamical behaviour of a complex coupled system consisting of any number of substructures with various configurations and multiple interaction interfaces. The coupled system is subject to multiple excitations and selected boundary conditions. Generalized mobility/impedance matrix formulations for three-dimensional rigid and elastic structures of general configuration are first derived allowing the construction of equivalent mobility (EMM) and equivalent impedance (EIM) matrices to describe the dynamical behaviour of a substructure or a subsystem assembled from several inter-connected substructures within the overall system. Based on these two proposed matrices, two progressive approaches are developed to predict the force vectors and velocity response vectors as well as the power flows into and transmission between substructures in the complex coupled system. The developed mathematical model avoids the generalized inverse process associated with rectangular matrices when dealing with multi-input/multi-output (MIMO) systems in which the dimensions of input and output are different. It is also very flexible and conveniently extended if additional substructures are further connected to the original dynamic system without involving much additional computational effort. The proposed methods are shown to reduce the complexity of the power flow analysis applied to complex dynamic coupled systems and they are applicable to a very large class of dynamical systems in engineering. To illustrate and demonstrate their usage, the dynamics of a flexible raft vibration isolation system is investigated; this comprises two machines, flexible raft, and flexible foundation with connecting isolator attachments.

References (42)

  • P.E. CHO et al.

    Energy flow analysis of coupled beams

    Journal of Sound and Vibration

    (1998)
  • W.L. LI et al.

    Prediction of power flows through machine vibration isolators

    Journal of Sound and Vibration

    (1999)
  • T.Y. LI et al.

    Structural power flow analysis for a floating raft isolation system consisting of constrained damped beams

    Journal of Sound and Vibration

    (1997)
  • J.C. SNOWDON

    Mechanical four-pole parameters and their applications

    Journal of Sound and Vibration

    (1971)
  • J.Y. HA et al.

    Analysis of MIMO mechanical systems using the vectorial four pole parameter method

    Journal of Sound and Vibration

    (1995)
  • R.H. LYON

    Statistical Energy Analysis of Dynamic Systems

    (1975)
  • W.G. PRICE et al.

    Statistical energy analysis

    Philosophical Transactions of the Royal Society of London

    (1994)
  • A.J. KEANE et al.

    A Statistical Energy Analysis: An Overview with Application in Structural Dynamics

    (1997)
  • F.J. FAHY et al.

    IUTAM Symposium on Statistical Energy Analysis

    (1999)
  • B.L. CLARKSON

    Estimation of the coupling loss factor of structural joints

    Journal of Mechanical Engineering Science

    (1991)
  • Cited by (0)

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