Dynamics of a chain of permanent magnets
Unité de Mécanique (UME), ENSTA Paristech - 828 Boulevard des Maréchaux, 91762 Palaiseau cedex, France
Received: 1 September 2014
Accepted: 28 January 2015
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.
PACS: 45.50.-j – Dynamics and kinematics of a particle and a system of particles / 45.20.Jj – Lagrangian and Hamiltonian mechanics / 41.20.Gz – Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems
© EPLA, 2015