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Technical Briefs

An Analysis of Higher Order Effects in the Half Power Method for Calculating Damping

[+] Author and Article Information
Ivan Wang

Department of Mechanical Engineering and Material Science, Duke University, 144 Hudson Hall, Durham, NC 27708ivan.wang@duke.edu

J. Appl. Mech 78(1), 014501 (Oct 08, 2010) (3 pages) doi:10.1115/1.4002208 History: Received September 17, 2009; Revised July 21, 2010; Posted July 23, 2010; Published October 08, 2010; Online October 08, 2010

The half power method is a technique commonly used for calculating the system damping using frequency response curves. Past derivations typically assume a small damping ratio but do not keep track of the order of magnitude when simplifying results and focus mainly on displacement frequency response curves. This paper provides two separate and rigorous derivations of the half power bandwidth for displacement and acceleration frequency response functions. The exact expressions are simplified systematically using binomial expansions to include third order effects. The third order and classical approximations are compared with the exact expressions, and the truncation errors are presented for both displacement and acceleration cases. The high order effects are more apparent and the truncation errors are greater for the acceleration case. The classical method is sufficiently accurate for many practical cases where the damping ratio is less than 0.1 but higher order corrections may be used to reduce truncation error for systems where the damping ratio is higher.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Calculated versus exact damping for displacement FRF

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Figure 2

Calculated versus exact damping for acceleration FRF

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Figure 3

Difference relative to exact result for displacement FRF

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Figure 4

Difference relative to exact result for acceleration FRF

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