Extended tolerance modelling of dynamic problems for thin uniperiodic cylindrical shells

Abstract

Dynamic problems of thin linearly elastic Kirchhoff–Love-type circular cylindrical shells having geometrical, elastic and inertial properties densely and periodically varying in circumferential direction (uniperiodic shells) are studied. In order to take into account the effect of a cell size on the global dynamic behaviour of such shells (the length-scale effect), a new mathematical averaged non-asymptotic model is formulated. This so-called the general tolerance model is derived by applying a certain extended version of the well-known tolerance modelling technique. Governing equations of this averaged model have constant coefficients depending also on a microstructure size, contrary to the starting exact shell equations with periodic, non-continuous and highly oscillating coefficients (the well-known governing equations of linear Kirchhoff–Love theory of thin elastic cylindrical shells). The effect of a cell size on the transversal free vibrations of an uniperiodic shell strip is studied. It will be shown that within this general tolerance model not only fundamental cell-independent, but also the new additional cell-dependent free vibration frequencies can be derived and analysed. The obtained results will be compared with the corresponding results derived from the knownnon-asymptotic standard tolerance model and from the asymptotic one.