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Vibration of open cylindrical shells: A three-dimensional elasticity approach

Journal of the Acoustical Society of America, ISSN: 0001-4966, Vol: 104, Issue: 3 I, Page: 1436-1443
1998
  • 26
    Citations
  • 0
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  • 13
    Captures
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Metrics Details

  • Citations
    26
    • Citation Indexes
      26
  • Captures
    13

Article Description

The three-dimensional elastic analysis of the vibration of open cylindrical shells are presented. Transverse normal stress usually neglected in plate and shell higher, order theories has been considered. The natural frequencies and vibration mode shapes have been obtained via a three- dimensional displacement-based extremum energy principle. Excessive requirements for memory and computational effort have been overcome, without sacrificing numerical accuracy, by (i) decoupling the three-dimensional displacements into the product of a set of beam and shell shape functions; and (ii) classifying the vibration modes. The effects of subtended angle and aspect ratio have been concluded for shells with various boundary conditions. Typical vibration mode shapes demonstrating the dependence of vibration characteristics on boundary constraints are presented. A study of the free vibration characteristics of thick and open cylindrical shells is conducted using a three-dimensional displacement-based extremum energy principle. The spatial integrals for strain, with transverse normal stress, and kinetic energy components are formulated. A Ritz energy functional is defined and minimized to derive a governing eigenvalue equation. Two-dimensional p-Ritz functions are generalized to three-dimensional functions by associating the two-dimensional functions with one-dimensional p-Ritz admissible function. Convergence of vibration frequencies are examined and favorable comparison with finite-element solutions is observed.

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