University of Illinois Urbana-Champaign

On vibration and stability of finitely inflated spherical and cylindrical elastic membranes

Chen, Lien-Yan; Shield, Richard T.

Permalink

https://hdl.handle.net/2142/112129

Description

Title
On vibration and stability of finitely inflated spherical and cylindrical elastic membranes
Author(s)
  • Chen, Lien-Yan
  • Shield, Richard T.
Issue Date
1974-12
Keyword(s)
  • Vibration
  • Stability
  • Finite Inflation
  • Spherical Elastic Membrane
  • Cylindrical Elastic Membrane
Abstract
"Two investigations on the behavior of inflated membranes composed of highly elastic material are included in this study. The first deals with the small vibrations of an inflated spherical membrane coupled with the motion of the gas internal and external to the membrane. The gas is assumed to be ideal and its motion is adiabatic. Solutions appropriate for both symmetric and non-symmetric modes of vibration are obtained. The frequency equation for symmetric modes is derived; the frequency equation for non-symmetric modes is the same as that for symmetric modes. Some numerical values for frequencies are presented for membranes composed of a rubber material with an empirical strain energy function and composed of steel. The second investigation examines the stability of a finitely inflated and extended cylindrical tube under overall axial compression. The critical load for tubes with closed-ends and with either simply-supported or fixed ends are determined. For a long tube the results are compared with the well-known Euler buckling load for struts in compression. An ""equivalent"" Young's modulus E is derived, and it is shown that the critical load can be obtained from the Euler buckling formula by using the dimensions of the inflated state and the ""equivalent"" Young's modulus."
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 397
  • 1974-6019
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112129
Sponsor(s)/Grant Number(s)
National Science Foundation, Grant GK 37539, 74/12
Copyright and License Information
Copyright 1974 Board of Trustees of the University of Illinois

Owning Collections

Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.