On effects of perforated domains on parameter-dependent free vibration

Free vibration characteristics of thin perforated shells of revolution vary depending not only on the dimensionless thickness of the shell but also on the perforation structure. All holes are assumed to be free, that is, without any kinematical constraints. For a given configuration there exists a critical value of the dimensionless thickness below which homogenisation fails, since the modes do not have corresponding counterparts in the non-perforated reference shell. For a regular g×g-perforation pattern, the critical thickness is reached when the lowest mode has an angular wave number of g∕2. This observation is supported both by geometric arguments and numerical experiments. The numerical experiments have been computed in 2D with high-order finite element method supporting Pitkäranta's mathematical shell model.