Magnetoelastic buckling of two nearby ferromagnetic rods in a magnetic field

The interactive effect of two nearby soft ferromagnetic rods on the magnetoelastic buckling is studied. The cantilevered rods are parallel to each other. The buckling is due to a uniform magnetic field normal to the axes of the rods, making an arbitrary angle with the plane through the axes of the rods. The buckling analysis is based upon a perturbation theory in which the final (or buckled) state of the system is considered as a small perturbation of an intermediate equilibrium state, for which the rigid-body state is taken. The unknown rigid-body and perturbed fields are solved with use of the theory of complex functions. The forces of magnetic origin on the deflected rods are calculated and the buckling problem is reduced to an eigenvalue problem. It is found that the interaction between the two rods considerably reduces the buckling magnetic field in case of two nearby rods. The buckling mode turns out to be symmetric. These theoretically predicted results are confirmed experimentally. Finally, the influences of the direction of the basic magnetic field and of the predeflection (before buckling) are discussed.