An Analysis of the Free Vibration of a Shallow Spherical Membrane Shell.

Abstract

The free vibration of a shallow spherical membrane shell is analyzed using the thin-shell theory developed by Kraus. The secular equation giving the lowest resonant frequencies of such a shell is derived. The normal and tangential modal displacement functions corresponding to these resonant frequencies are found for the case when the shallow spherical shell has a free edge. In addition, an approximate secular equation is derived for the shallow spherical membrane shell with a free edge by using the Rayleigh-Ritz method. Suitable approximate modal displacement functions, corresponding to the resonant frequencies that are determined using this approximate secular equation and satisfying the free-edge boundary condition, are found. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1978
Accession Number
ADA061259

Entities

People

  • Anthony J. Rudgers

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Bending Moments
  • Bessel Functions
  • Boundaries
  • Cartesian Coordinates
  • Coordinate Systems
  • Curvature
  • Differential Equations
  • Differential Geometry
  • Equations
  • Equations Of Motion
  • Frequency
  • Geometry
  • Military Research
  • Resonant Frequency
  • Transducers
  • Variational Equations
  • Vibration

Readers

  • Calculus or Mathematical Analysis
  • Structural Dynamics.