On the harmonic magnetoelastic behavior of a composite cylinder with an embedded polynomial eigenstrain

This article presents closed-form solutions of displacement and stress components for a dynamic eigenstrain problem in a bi-layered coaxial cylinder. The cylinder could be axisymmetric and infinitely long with plane strain condition, or axisymmetric and thin with plane stress condition. The inner layer experiences a harmonic eigenstrain with cubic polynomial distribution in the radial direction. The layers are assumed to be imperfectly bonded and the cylinder is subjected to an external constant magnetic field. The harmonic governing differential equations including the Lorentz force effect are analytically solved. The results illustrate the effect of external magnetic field, cubic polynomial eigenstrain, and imperfect boundary conditions on the magnetoelastic response of the composite cylinders with plane strain and plane stress conditions.