Transient axisymmetric motions of a conical bar

R. W. Mortimer, R. J. Schaller, Joseph Lawrence Rose

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Abstract

Three bar-of-revolution theories are developed. The most inclusive theory is equivalent to the Mindlin-McNiven theory for circular bars in that it includes radial, axial shear, and longitudinal modes. By removing the axial shear mode in the foregoing, a theory equivalent to the Mindlin-Herrmann theory for circular bars is obtained. Finally, by eliminating all the radial effects in this latter theory, a simple theory incorporating only longitudinal effects is obtained. Each of these three theories is then specialized for a conical geometry and solved by the method of characteristics for the case of a longitudinal impact. The solutions for each of these theories are then compared to published surface meridional strain and internal strain data. In addition, the importance of impact pulse duration in establishing the validity of the approximate bar theories for impact problems is analytically indicated.

Original languageEnglish (US)
Pages (from-to)709-716
Number of pages8
JournalJournal of Applied Mechanics, Transactions ASME
Volume39
Issue number3
DOIs
StatePublished - Jan 1 1972

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All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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