NUMERICAL DIMENSION-REDUCTION METHODS FOR NON-LINEAR SHELL VIBRATIONS

A number of methods are investigated for obtaining a low-dimensional dynamical system from a set of partial differential equations describing the non-linear vibrations of a shallow cylindrical panel under periodic axial forcing. In these approaches an initial (high-dimensional) spatial discretization of a (possibly irregular) domain is performed and a subsequent procedure is used to further reduce the resulting set of ordinary differential equations. In particular the results suggest that a numerical method based upon inertial manifold approximation is possible, but for the specific case studied, no advantage could be discerned over more direct dimension-reduction techniques.