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TECHNICAL PAPERS

Dynamics of Flexible Structures With Nonlinear Joints

[+] Author and Article Information
Sunetra Sarkar, Kartik Venkatraman, B. Dattaguru

Aeroservoelasticity Laboratory, Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India 560 012

J. Vib. Acoust 126(1), 92-100 (Feb 26, 2004) (9 pages) doi:10.1115/1.1596548 History: Received August 01, 2001; Revised December 01, 2002; Online February 26, 2004
Copyright © 2004 by ASME
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References

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Bowden,  M., and Dugundji,  J., 1990, “Joint Damping and Nonlinearity in Dynamics of Space Structures,” AIAA J., 28(4), pp. 740–749.
Foelsche,  G. A., Griffin,  J. H., and Bielak,  J., 1988, “Transient Response of Joint-dominated Space Structures: A New Linearization Technique,” AIAA J., 26, pp. 1278–1285.
Gelb, A., and Vander Velde, W. E., 1968, Multiple-Input Describing Functions and Nonlinear Systems Design, McGraw-Hill Book Co., New York.
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Urabe,  M., 1965, “Galerkin’s Procedure for Nonlinear Periodic Systems,” Arch. Ration. Mech. Anal., 20, pp. 120–152.
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Figures

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(a) Single joint two beam model. (b) Nonlinear restoring force as a function of joint rotational degree of freedom
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(a) Two joint three beam model. (b) Nonlinear symmetric restoring force
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Example 1—Convergence of Fourier-Galerkin solution—Time history of 1st degree of freedom; ω̄=1.0,k̄1=0.15,k̄2=0.4,α=0.35
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Example 1—Converged Fourier-Galerkin solution with 14 and 20 harmonics compared with direct time integration result—Phase plot of 1st degree of freedom; ω̄=1.0,k̄1=0.15,k̄2=0.4,α=0.35
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Example 1—Maximum displacement of 4th degree of freedom at each period of excitation; k̄1=0.15,k̄2=0.4,α=0.35
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Example 1—The phase plot with the Poincaré points for 4th degree of freedom; ω̄=4.5,k̄1=0.15,k̄2=0.4,α=0.35
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Movement of Floquet multiplier with ω̄,k̄1=0.15,k̄2=0.4,α=0.35
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Example 1—Time history of 4th degree of freedom at ω̄=8.0,k̄1=1.5,k̄2=4.0,α=0.35
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Example 1—Maximum response of 4th degree of freedom at each period of excitation; k̄1=1.5,k̄2=4.0,α=0.35
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Example 1—Maximum response of 4th degree of freedom at each period of excitation; k̄1=0.15,k̄2=0.4,α=0.005
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Example 1—Movement of Floquet multiplier with ω̄;k̄1=0.15,k̄2=0.4,α=0.005
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Example 2—Maximum response at each period for 1st degree of freedom; k̄=0.1,α=0.1
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Example 2—Maximum response at each period for 4th degree of freedom; k̄=0.1,α=0.1
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Example 2—The amplitude versus frequency plot for the equivalent linear system for 1st freedom; k̄=0.1,α=0.1
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Example 2—The amplitude versus frequency plot for the equivalent linear system for 4th degree of freedom; k̄=0.1,α=0.1
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Example 2—The maximum displacement of 1st degree of freedom; k̄=1.0,α=0.1
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Example 2—The maximum displacement of 4th freedom; k̄=1.0,α=0.1

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