ON MEMBRANE FREQUENCIES FOR SPHERICAL SHELL VIBRATIONS

Abstract

The membrane solutions for non-symmetric vibration of a spherical dome are studied. The solutions are written in a convenient form, and it is shown how these reduce to the familiar membrane and inextensional solutions in the static limit. This information enables one to perceive several difficulties in finding inextensional frequencies by numerical means and to suggest ways around these difficulties. Also membrane frequencies are found for circumferential wave numbers up through eight by direct calculation and compared with several different approximations. One type of approximation, due to Jeffreys and Jeffreys, gives quite good results. It is seen that earlier work agrees well with these results except for a few frequencies which are not found at all in the present calculations.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1967
Accession Number
AD0651475

Entities

People

  • Edward W. Ross Jr.

Organizations

  • United States Army Soldier Systems Center

Tags

DTIC Thesaurus Topics

  • Asymptotic Series
  • Classification
  • Continuum Mechanics
  • Differential Equations
  • Elastic Shells
  • Equations
  • Frequency
  • Legendre Functions
  • Mechanics
  • Membranes
  • Physics
  • Resonant Frequency
  • Security
  • Spatial Distribution
  • Transitions
  • Vibration
  • Waves

Fields of Study

  • Physics

Readers

  • Structural Dynamics.
  • Theoretical Analysis.