Rotational symmetry vs. axisymmetry in shell theory

This paper treats rotationally symmetric motions of nonlinearly axisymmetric shells that can suffer transverse shear as well as the usual flexure and base-surface extension and shear. It derives the governing equations in a convenient form and determines their mathematical structure. The complicated governing equations have the same virtue of the far simpler equations for axisymmetric motions that there is but one independent spatial variable. Consequently the constitutive equations enjoy convenient monotonicity properties. Besides deriving these equations, the main purposes of the paper are (i) to give a numerical illustration of the richness of rotationally symmetric motions caused by the coupling of the additional shearing modes with classical modes of deformation, and (ii) to discuss the subtle question of nonexistence of general axisymmetric motions of axisymmetric shells. The paper briefly treats spatially autonomous motions, which are governed by ordinary differential equations in time.