Dynamics of a chain of permanent magnets

The dynamics of a straight chain of cylindrical neodymium magnets is considered. We showed that this system exhibits a behavior which is similar to that of a beam where the elastic rigidity acts like a restoring force. By using a Lagrangian approach, a linear model, accounting for different sets of boundary conditions, is derived. Specifically for the clamped-free case, eigenfrequencies and eigenmodes are determined. These theoretical results are compared to experiments. A good agreement is found, the discrepancies being attributed to the accumulation of defaults in the contact surface between the magnets. In the last part of the article, the equivalent beam behavior is sought by defining an equivalent flexural rigidity induced by magnetic dipoles interactions.