Galerkin's solution to a severely non-linear problem of finite elastodynamics

Large amplitude free radial oscillations of a thick-walled circular shell are analysed on the basis of a rigorous finite-deformation theory of elasticity. The governing equation derived in two papers by Knowles is solved using the Galerkin procedure and the principle of conservation of energy. The material of the tube is considered incompressible and eventually specialized to the Mooney-Rivlin type. It is shown that the approximate solution, in the interval of interest, differs negligibly from that furnished by the rigorous theory and displays the same hard-spring behavior of oscillations. In the case of non-linear oscillations of a thin shell and of small oscillations of a thick-walled shell both solutions coincide.