A new asymptotic-tolerance model of dynamic and stability problems for longitudinally graded cylindrical shells

Thin linearly elastic Kirchhoff-Love-type cylindrical shells of a heterogeneous microstructure which is periodic in the circumferential direction and slowly varying along the axial direction (composite shells with a space-varying periodic microstructure) are considered. Since macroscopic (averaged) properties of such shells are constant in circumferential direction but smoothly slowly varying in the axial one, then we deal with shells of a functionally (longitudinally) graded macrostructure. The aim of the contribution is to formulate and discuss a new mathematical averaged non-asymptotic model for the analysis of selected dynamic and stability problems for these shells. The model is derived by applying both the asymptotic and the tolerance non-asymptotic procedures which are combined together into a new modelling technique. The combined model equations include coefficients constant in periodicity direction and continuously slowly variable along axial coordinate. Since some of these coefficients depend on a cell size, then the model takes into account the effect of a microstructure size on the shells dynamics and stability. Moreover, it makes it possible to separate the macroscopic description of some problems from their microscopic description.