On the influence of the magnetic field on the eigenmodes of thin laminated cylindrical shells containing magnetorheological elastomer

Laminated cylindrical sandwich shells composed by embedding magnetorheological elastomers (MREs) between elastic layers is the subject of this investigation. Physical properties of the magnetorheological (MR) layers are assumed to be functions of the magnetic field induction and curvilinear coordinates. A system of differential equations with complex variable coefficients depending upon the magnetic field and based on both the assumptions of the generalized kinematic hypothesis for the whole sandwich and experimental data for MREs is used as the governing one. To analyze damping capabilities of adaptive materials, free vibrations of a three-layered circular cylinder containing MRE core layer are studied at different levels of the magnetic field. Using the asymptotic approach, eigenmodes of free vibrations of a laminated cylindrical shell with variable physical characteristics of MRE are constructed in the form of functions decaying far from the weakest plot on the shell structure. It has been shown that applying constant magnetic field may result in localization of eigenmodes corresponding to low-frequency spectrum of three-layered circular thin cylinder with embedded nonuniform MRE layer. Dependencies of natural frequencies, damping decrement and parameter characterizing the power of the eigenmode localization on the intensity of applied magnetic field are analyzed.