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TECHNICAL PAPERS

Discrete Frequency Models: A New Approach to Temporal Analysis

[+] Author and Article Information
Douglas E. Adams

School of Mechanical Engineering, Purdue University, 1077 Ray W. Herrick Laboratories, West Lafayette, IN 47907-1077

Randall J. Allemang

Structural Dynamics Research Laboratory (UC-SDRL), University of Cincinnati, Cincinnati, OH 45221-0072

J. Vib. Acoust 123(1), 98-103 (Aug 01, 2000) (6 pages) doi:10.1115/1.1320815 History: Received November 01, 1999; Revised August 01, 2000
Copyright © 2001 by ASME
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References

Figures

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An illustration of the three fundamental model types and the relationships between them. The discrete frequency model represents a new temporal analysis approach.
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Venn diagram illustration of the variation in linear and nonlinear dynamics with environmental test conditions
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Illustration of nonlinear feedback within a duffing oscillator. Two forces act on the underlying linear system: the external force and a cubic nonlinear function of the response.
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Forced response of the system in Eq. (1) to three sinusoidal excitations with unity amplitudes and different frequencies: (Top) ω0=Ω/2=k/4m, (Middle) ω0=Ω, (Bottom) ω0=2Ω.
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Forced response of the system in Eq. (1) to two sinusoidal excitations at approximately three times the underlying resonant frequency: (Top) F0=1 N,ω0=3.3Ω=3.3k/m, (Bottom) F0=5 N,ω0=3.3Ω where Ω=3.9 Hz.
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Forced response spectrum of the system in Eq. (1) to a sinusoidal excitation at 1.5Ω=1.5k/m and 0.8 N amplitude: (—) True response spectrum, (○○○) DFM estimates from Eq. (13).
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Forced response spectrum of the system in Eq. (1) to a sinusoidal excitation at 1.5Ω=1.5k/m and 1.2 N amplitude: (—) True response spectrum, (○○○) DFM estimates from Eq. (17).
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Estimates of the frequency response function of the underlying system in Eq. (1) and the residual autocorrelation of these estimates: (Left) Linear system estimate and residual autocorrelation, μ=0(1/m2), (Right) Nonlinear system estimate and residual autocorrelation, μ=7e5(1/m2).

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