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TECHNICAL PAPERS

Modeling and Simulation of Elastic Structures with Parameter Uncertainties and Relaxation of Joints

[+] Author and Article Information
S. L. Qiao, V. N. Pilipchuk, R. A. Ibrahim

Wayne State University, Department of Mechanical Engineering, Detroit, MI 48202

J. Vib. Acoust 123(1), 45-52 (Aug 01, 2000) (8 pages) doi:10.1115/1.1325409 History: Received February 01, 2000; Revised August 01, 2000
Copyright © 2001 by ASME
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References

Ibrahim,  R. A., 1987, “Structural Dynamics with Parameter Uncertainties,” Appl. Mech. Rev., 40, pp. 309–328.
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Manohar,  C. S., and Ibrahim,  R. A., 1999, “Progress in Structural Dynamics with Stochastic Parameter Variations: 1987–98,” Appl. Mech. Rev., 52, No. 5, pp. 177–197.
Bickford, J. H., 1990, An Introduction to the Design and Behavior of Bolted Joints, 2nd ed., Marcel Dekker, New York.
Shinozuka,  M., and Astill,  C. J., 1972, “Random Eigenvalue Problems in Structural Analysis,” AIAA J., 10, No. 4, pp. 456–462.
Paez, T. L., Branstetter, L. J., and Gregory, D. L., 1985, “Modal Rondomness Induced by Boundary Conditions,” SAE Technical Paper 851930.
Watanabe,  T., 1978, “Forced Vibration of Continuous System with Nonlinear Boundary Conditions,” ASME J. Mech. Des., 11, pp. 487–491.
Lee,  W. K., and Yeo,  M. H., 1999, “Two-Mode Interaction of a Beam with a Nonlinear Boundary Condition,” ASME J. Vibr. Acoust., 121, pp. 84–88.
Liu, W. K., Belytschko, T., and Mani, A., 1985, “Probabilistic Finite Elements for Transient Analysis in Nonlinear Continua,” Advances in Aerospace Structural Analysis, Proc. ASME WAM, Miami Beach, Florida, O. H. Burnside and C. H. Parr, Eds., Vol. AD-09, pp. 9–24.
Liu,  W. K., Belytschko,  T., and Mani,  A., 1986, “Probabilistic Finite Elements for Nonlinear Structural Dynamics,” Comput. Methods Appl. Mech. Eng. 56, pp. 61–81.
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Brenner, C. E., 1994, “On Methods for Nonlinear Problems Including System Uncertainties,” Structural Safety and Reliability—Proceedings of ICOSSAR '93, Rotterdam, G. I. Schuëller, M. Shinozuka and J. T. P. Yao, Eds., Balkema, Rotterdam, pp. 311–317.
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Figures

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Time history records of excitation, responses for z=0.0 and with z=0.5075
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Power spectra of excitation and response for z=0.0 and with z=0.5075
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Conditional mean square response of the system for z=0.0 and z=0.5075
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Dependence of the response central frequency on the boundary condition uncertainty f=ωc/2πmL4/EI
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Response mean squares E[U12] on the boundary condition uncertainty
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Modified experimental residual preload versus the number of cycles (Bickford, 1990)
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Time evolution of the linear natural frequency and nonlinear coefficient (a) natural frequency (b) nonlinear coefficient
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Time history records under sinusoidal excitation for excitation amplitude fam=0.2, (a) direct numerical integration (b) one-step averaging
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Time history records under sinusoidal excitation for excitation amplitude fam=1.0, (a) direct numerical integration (b) one-step averaging
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Response spectrum (a), and amplitude time history for fam=0.2
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Response spectrum (a), and amplitude time history for fam=1.0
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Relaxation of the joint stiffness α(t) and response statistics for slope parameter λ=0.05 under excitation spectral density Sξ=0.2
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Relaxation of the joint stiffness α(t) and response statistics for slope parameter λ=0.1 under excitation spectral density Sξ=0.2
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Relaxation of the joint stiffness α(t) and response statistics for slope parameter λ=0.15 under excitation spectral density Sξ=0.2
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Response spectra estimated over short interval of time history record of duration 30 seconds each
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Relaxation of the joint stiffness α(t) and response statistics for slope parameter λ=0.1 under excitation spectral density Sξ=200
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Relaxation of the joint stiffness α(t) and response statistics for slope parameter λ=0.1 under excitation spectral density Sξ=2000

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