NUMERICAL DIMENSION-REDUCTION METHODS FOR NONLINEAR SHELL VIBRATIONS

A number of methods are investigated for obtaining a low-dimensional d ynamical system from a set of partial differential equations describin g the non-linear vibrations of a shallow cylindrical panel under perio dic axial forcing. Tn these approaches an initial (high-dimensional) s patial discretization of a (possibly irregular) domain is performed an d a subsequent procedure is used to further reduce the resulting set o f ordinary differential equations. In particular the results suggest t hat a numerical method based upon inertial manifold approximation is p ossible, but for the specific cases studied, no advantage could be dis cerned over more direct dimension-reduction techniques. (C) 1998 Acade mic Press.