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ABSTRACT
An incompressible, isotropic and homogeneous damaged Ogden material cylindrical tube is considered. The tube is kept under constant inflation pressure, and the respective small amplitude radial oscillations are studied. Ogden material model is based on experimental data and whose special cases are Mooney-Rivlin and the neo-Hookean. Stability and bifurcation analysis are the main topics of this work. Rubber material tube is mimicked as an incompressible damaged Ogden cylindrical material tube, and the stability results are interpreted. The study carried for the virgin case exhibits bifurcation for some thickness, whereas for the damaged case it depends both on the thickness and the extent of damage the material has experienced in its time history. Universal relations are obtained for a damaged Ogden cylindrical membrane. The analysis above carried for the Ogden material may be reduced to its special cases for Mooney-Rivlin and neo-Hookean as well. All the results are depicted graphically.
Notes
1. A long cylindrical cavity is defined as the state of a cylindrical tube wherein the tube inner radius becomes negligible as compared to its outer radius.