Random Response Relationships to Transfer Function and State-Space Properties

[+] Author and Article Information
Robin C. Redfield

Department of Engineering Mechanics, United States Air Force Academy, Colorado Springs, CO 80840Rob.Redfield@Usafa.Af.Mil

J. Vib. Acoust 129(5), 672-677 (Feb 22, 2007) (6 pages) doi:10.1115/1.2748458 History: Received June 16, 2005; Revised February 22, 2007

Output variables of dynamic systems subject to random inputs are often quantified by mean-square calculations. Computationally for linear systems, these typically involve integration of the output spectral density over frequency. Numerically, this is a straightforward task and, analytically, methods exist to find mean-square values as functions of transfer function (frequency response) coefficients. These formulations offer analytical relationships between system parameters and mean-square response. This paper develops further analytical relationships in calculating mean-square values as functions of transfer function and state-space properties. Specifically, mean-square response is formulated from (i) system pole-zero locations, (ii) as a spectral decomposition, and (iii) in terms of a system matrix transfer function. Direct, closed-form relationships between response and these properties are afforded. These new analytical representations of the mean-square calculation can provide significant insight into dynamic system response and optimal design/tuning of dynamic systems.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Decomposition of mean square

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Figure 2

2-DOF (quarter car) suspension model

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Figure 3

Modal contributions to normalized mean-square tire contact force



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