An infinite number of closed-form solutions is reported for a deterministically or stochastically nonhomogeneous beam, for both natural frequencies and reliabilities, for specialized cases. These solutions may prove useful as benchmark solutions. Numerical examples are evaluated.
Apparently First Closed-Form Solution for Frequencies of Deterministically and/or Stochastically Inhomogeneous Simply Supported Beams
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, May 25, 1998; final revision, Sept. 7, 2000. Associate Editor: J. W. Ju. Discussion on the paper should be addressed to the Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Candan, S., and Elishakoff, I. (September 7, 2000). "Apparently First Closed-Form Solution for Frequencies of Deterministically and/or Stochastically Inhomogeneous Simply Supported Beams ." ASME. J. Appl. Mech. March 2001; 68(2): 176–185. https://doi.org/10.1115/1.1355034
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