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TECHNICAL PAPERS

Metric Damping of MDOF Systems in High Transient Motion

[+] Author and Article Information
A. Al Majid

Laboratoire de Dynamique des Machines et des Structures, UMR CNRS 5006,  INSA de Lyon, 69621 Villeurbanne, Franceahmad.almajid@insa-lyon.fr

A. Allezy

Laboratoire de Dynamique des Machines et des Structures, UMR CNRS 5006,  INSA de Lyon, 69621 Villeurbanne, Francearnaud.allezy@insa-lyon.fr

R. Dufour

Laboratoire de Dynamique des Machines et des Structures, UMR CNRS 5006,  INSA de Lyon, 69621 Villeurbanne, Franceregis.dufour@insa-lyon.fr

J. Vib. Acoust 128(1), 50-55 (Mar 23, 2005) (6 pages) doi:10.1115/1.2128638 History: Received June 25, 2003; Revised March 23, 2005

This paper deals with damping due to transient motion in the case of multi-degree-of-freedom (MDOF) system. The main aim of this research is to make the method presented by the authors in a previous paper available for MDOF systems. An method based on relativity concepts is developed in order to identify and evaluate a metric damping due to time-varying forcing frequency. An additional dimension for each degree of freedom (DOF) is introduced. The variational problem of the metric of a Riemannian space gives the geodesic equations, i.e., equations of motion that, after time integration carried out with several types of numerical schemes, permit one to predict the forced transient response of a 3-DOF system. The proposed metric approach makes the experimental results correspond with the simulated results.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Diagram of the experimental setup

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Figure 2

Excitation force (0–50Hz)

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Figure 3

Predicted response with a classical model (ODE113, dotted line) and measured response (solid line)

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Figure 4

Classical model. Zooms of the predicted response of three different algorithms: ODE23 (---), ODE45 (+++), ODE113 (엯엯엯)

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Figure 5

Displacement measured (solid line) and predicted with the metric model (dotted line)

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Figure 6

Zooms of displacement measured (solid line) and predicted with the metric model (dotted line)

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Figure 7

Modal damping coefficients predicted with the metric (solid line) and classical (dotted line) models

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Figure 8

Progression of θ(t) of the metric model (solid line) and Ωt of the classic model (dotted line)

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