On the Vibration and Stability of Finitely Inflated Spherical and Cylindrical Elastic Membranes
Lien-Yan Chen, Richard Thorpe Shield · Illinois Digital Environment for Access to Learning and Scholarship (University of Illinois at Urbana-Champaign) · 1974
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.