Research Article
Apr 1968
Upper and Lower Frequencies Tapered Beams
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VIEW THE REPLYAuthors: J.H. Gaines and Enrico Volterra, F.ASCEAuthor Affiliations
Publication: Journal of the Engineering Mechanics Division
Volume 94, Issue 2
Abstract
Two equations for obtaining lower bounds of the natural frequencies of lateral vibrations of beams are presented. The effects of shear and rotatory inertia are included. One of the equations is employed in conjunction with the Rayleigh-Ritz method to obtain upper and lower bounds for the three lowest natural frequencies of vibration of linearly tapered beams with free-free end conditions. For cases in which the effects of shear and rotatory inertia are small, the upper and lower bounds are in good agreement for all three modes of vibration. In cases in which the effects of shear and rotatory inertia are significant the upper and lower bounds are in good agreement for the first two modes; for the third mode, however, the percent deviation is, in some cases, about 20% for beams with small length to depth ratios.
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Published In
Journal of the Engineering Mechanics Division
Volume 94 • Issue 2 • April 1968
Pages: 465 - 488
Copyright
© 1968 American Society of Civil Engineers.
History
Published in print: Apr 1968
Published online: Feb 3, 2021
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J.H. Gaines
Asst. Prof. of Engrg. Mechanics, The Univ. of Texas at Arlington, Arlington, Tex.
Enrico Volterra, F.ASCE
Prof. of Engrg. Mechanics, The Univ. of Texas, Austin, Tex.
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ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.