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This paper is devoted to the derivation and the analysis of vibrations of shallow spherical shell subjected to large amplitude transverse displacement. The analog for thin shallow shells of von KármánÕs theory for large deflection of plates is used. The validity range of the approximations is assessed by comparing the analytical modal analysis with a numerical solution. The specific case of a free edge is considered. The governing partial differential equations are expanded onto the naturaldoi:10.1016/j.ijsolstr.2004.10.028 fatcat:fg5igraaqrg2fggj2hjccl7hze