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TECHNICAL PAPERS

Apparently First Closed-Form Solution for Frequencies of Deterministically and/or Stochastically Inhomogeneous Simply Supported Beams

[+] Author and Article Information
S. Candan

Laboratoire de Recherches et Applications en Mécanique Avançée, Institute Français de Mécanique Avançee, Aubière F-63175, France

I. Elishakoff

Department of Mechanical Engineering, Florida Atlantic University, Boca Raton, FL 33431e-mail: ielishak@me.fau.edu

J. Appl. Mech 68(2), 176-185 (Sep 07, 2000) (10 pages) doi:10.1115/1.1355034 History: Received May 25, 1998; Revised September 07, 2000
Copyright © 2001 by ASME
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References

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Köylüoğlu, H., Cakmak, A. S., and Nielsen, S. A. K., 1994, “Response of Stochastically Loaded Bernoulli-Euler Beams with Randomly Varying Bending Stiffness,” Structural Safety and Reliability, G. I. Schuëller, M. Shinozuka, and J. T. P. Yao, eds., pp. 267–274.
Elishakoff,  I., Ren,  Y. J., and Shinozuka,  M., 1995, “Some Exact Solutions for Bending of Beams With Spatially Stochastic Stiffness,” Int. J. Solids Struct., 32, pp. 2315–2327 (Corrigendum: 33 , p. 3491, 1996).
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Figures

Grahic Jump Location
Probability density functions of variables B1 and B2, and the probability distribution function FB1 for ω02≤σ2(α−δ), leading to zero reliability
Grahic Jump Location
Probability density functions of variables B1 and B2, and the probability distribution function FB1 for β−ω022≥δ; reliability is given by expression (80)
Grahic Jump Location
Probability density functions of variables B1 and B2, and the probability distribution function FB1 for α−ω022≥γ and γ≤β−ω022≤δ; reliability is given in Eq. (81)
Grahic Jump Location
Probability density functions of variables B1 and B2, and the probability distribution function FB1 for β−ω022≤γ; leading to unity reliability
Grahic Jump Location
Case when length β−α of B1 interval is smaller than the length of B2 interval; reliability is given in Eq. (83)
Grahic Jump Location
Case when length β−α of B1 interval is bigger than the length of B2 interval; reliability is given in Eq. (84)

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