On the modelling of stability problems for thin cylindrical shells with two-directional micro-periodic structure. (1st November 2021)

• Record Type: Journal Article
• Authors: Tomczyk, Barbara; Bagdasaryan, Vazgen; Gołąbczak, Marcin; Litawska, Anna
• Is Part Of: Composite structures. Volume 275(2021)
• Publication Date: 2021-11-01
• Subjects: Micro-biperiodic cylindrical shells -- Stability problems -- Tolerance and asymptotic modelling -- Length-scale effect; Composite construction -- Periodicals; Composites -- Périodiques; 624.18
• DOI: 10.1016/j.compstruct.2021.114495
• Languages: English
• ISSNs: 0263-8223

Abstract

Abstract: Thin linearly elastic Kirchhoff-Love-type circular cylindrical shells having a micro-periodic structure in circumferential and axial directions (biperiodic shells) are considered. The aim of this paper is to investigate the effect of a periodicity cell size on the stationary and dynamical stability of such shells. In order to take into account the length-scale effect in some special stability problems, an averaged non-asymptotic biperiodic shell model derived by means of the known tolerance modelling procedure is applied. 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 Kirchhoff-Love second-order theory of thin elastic shells). The effect of a cell size on critical forces and on frequency equation being a starting point in the analysis of parametric vibrations and dynamical stability is studied. It will be shown that the micro-periodic heterogeneity of the shells leads to the fourth-order ordinary differential frequency equation, which can be treated as a certain generalization of the known Mathieu second-order equation. It reduces to the Mathieu equation provided that the length-scale effect is neglected.