Free vibration of perforated cylindrical shells of revolution: Asymptotics and effective material parameters

Abstract

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. For any given configuration there exists a critical value of the dimensionless thickness below which homogenisation fails. The failure occurs when the modes do not have corresponding counterparts in the non-perforated reference shell. Within the admissible range of thicknesses the uniform effective material parameters are derived with a minimisation process. During the process every observed mode is matched with a corresponding reference one using a problem-specific characterisation. The performance of the derived effective material parameters and hence the minimisation process is demonstrated with an extensive set of numerical experiments. Limitations of the proposed approach are reflected in relation to idealised trommel screen configurations.