Theoretical and experimental studies on vibration control in cantilever beams using DC magnets

This paper describes the investigations that have been carried out on vibration control in cantilever beams using a DC magnet actuator. A repulsive type DC magnet configuration is postulated and its force characteristics are investigated, as a function of the air gap, the strength of the magnetic field, and its location on the beam. A strategy is developed to deal with inherent nonlinearity in the magnetic force effect. A modal formulation of the structural dynamics is used so that the method can be applied to any type of beam and some generic trends can be deduced. These results show that it is possible to arrive at a general configuration of a repulsion type magnetic actuator, which renders the beam axis as a stable equilibrium point, with reference to the restoring force from the magnets. Further, for a given air gap, this restoring force is a nonlinear function of the normalized disturbance, with a hardening type of behavior. Next, the vibration control problem is formulated using DC magnets, in the form of a SIMULINK(C) block diagram. The results concerning reduction in tip deflection are generated to quantify the extent of vibration suppression in the first vibration mode. Finally, a limited experimental study is carried out on a uniform cantilever beam to validate some of the assumptions of the theoretical study.