Thin laminated cylindrical shells containing magnetorheological elastomers: Buckling and vibrations

The paper focuses on the problems of buckling and free vibrations of thin laminated cylindrical shells containing layers made of magnetorheological elastomers (MREs). The equivalent single layer model based on the generalized kinematic hypotheses of Timoshenko is used to derive the governing equations with complex coefficients depending on the magnetic field induction. Circular and non-circular cylinders with simply supported edges with and without diaphragms are considered. For shells with diaphragms at their edges, solutions of the boundary-value problems are found in an explicit form,whereas for shells without diaphragms eigenmodes are constructed in the form of superposition of functions corresponding to the main stress state and non-classical edge effect integrals. If the shell is non-circular and/or loading is inhomogeneous, both natural and buckling modes are sought in the form of functions localized in the neighbourhood of some generatrix. We show that an applied magnetic field results in increasing the total stiffness of a laminated package and leads to growing the critical buckling load (external pressure, axial compression) and natural frequencies as well. If buckling or natural modes are localized near some line, then an applied magnetic field results in increasing the rate of this localization.