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Research Papers

Estimating Damping Parameters in Multi-Degree-of-Freedom Vibration Systems by Balancing Energy

[+] Author and Article Information
B. F. Feeny

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824feeny@egr.msu.edu

J. Vib. Acoust 131(4), 041005 (Jun 05, 2009) (7 pages) doi:10.1115/1.2980372 History: Received April 28, 2007; Revised July 01, 2008; Published June 05, 2009

A method of estimating damping parameters for multi-degree-of-freedom vibration systems is outlined, involving a balance of dissipated and supplied energies over a cycle of periodic vibration. The power is formulated as the inner product between the velocity and force terms and integrated over a cycle. Conservative terms (mass and stiffness) drop out of the formulation. The displacement response and the input are measured, and the damping coefficients are estimated without knowledge of the mass and stiffness, which can be nonlinear, as illustrated in one example. The identification equations are also obtained with a modal reduction based on proper orthogonal decomposition. The method can be applied with a harmonic motion assumption or by simple numerical integration. The method is illustrated with linear and quadratic damping, in simulations of a four degree-of-freedom system, and in a string with and without noise.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Animated steady-state vibration of the four mass system, with nondimensional a=1 and with nondimensional axial displacements plotted transversally. The mass deflections are connected with lines for visualization of the instantaneous configurations. The masses are indexed with labels 1–4 (mass locations). Mass label 5 indicates the right wall. The solid and dashed lines distinguish forward (upward) and return strokes.

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Figure 2

Displacements of mass 4 versus mass 1 show the asynchronicity of the steady-state response. The loop in the plot indicates asynchronicity.

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Figure 3

Animated steady-state vibration of the nonlinearly damped string, with nondimensional c=0.4, d=0.5, and a=32. The sensor index numbers indicate the locations of sensed nondimensional displacements on the string. These are plotted and connected with lines to visualize the rest of the string. Sensor label 9 indicates the right wall. The solid and dashed lines distinguish forward (upward) and return strokes.

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Figure 4

The first two proper orthogonal modes of the string response, normalized to unity and then scaled by the root-mean-squared modal amplitude (square root of the POV)

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