A 3D shell model for static and free vibration analysis of multilayered magneto-elastic structures

Abstract

In this paper, an exact 3D coupled magneto-elastic shell model for static and free vibration analysis of multilayered piezomagnetic smart structures is presented. The introduction of the mixed curvilinear orthogonal reference system (α,β,z) allows investigations of plates, cylindrical shells, cylinders and spherical shells as actuators or sensors and also in free vibration conditions. The present exact 3D coupled shell model is composed of four second-order differential equations whose primary variables are the three displacements u, v and w and the magnetic potential ψ. Displacements, stresses, strains, magnetic potential, magnetic induction and circular frequency values are computed to understand the behaviour of piezomagnetic smart structures. The resolution method adopted for the present 3D magneto-elastic problem is based on harmonic forms in α and β in-plane directions and the exponential matrix method in the z direction. Simply supported one-layered/multilayered structures with 0° or 90° orthotropic angles have been analyzed. The results section is divided into a first part related to the validation of the proposed 3D model and a second part where new benchmark cases are presented and discussed. Different lamination schemes, load boundary conditions, geometries and materials are studied. Magneto-elastic coupling, thickness and material layer effects are discussed for thin and thick structures. The main novelty of the present exact 3D coupled magneto-elastic shell model stands in the ability to analyze several geometries and multilayered configurations embedding piezomagnetic materials under the action of different boundary loads via a general mathematical formulation.