Modeling and Application of Eddy Current Damper for Suppression of Membrane Vibrations

Abstract

Inflatable space-based structures have become increasingly popular over the past three decades due to their minimal deployed mass and launch volume. To facilitate packaging of the satellite in the shuttle bay, the optical or antenna surface is in many cases a thin-film membrane. Additionally, because the structure holding the membrane is a lightweight and flexible inflated device, the membrane is subjected to a variety of dynamic loadings. For the satellite to perform optimally, the membrane structure must be free of vibration. However, due to the extreme flexibility of the membrane, the choice of applicable sensing and actuation methods to suppress the vibration is limited. The present study investigates the use of an eddy current damper to passively suppress the vibration of a thin membrane. Eddy currents are induced when a nonmagnetic conductive material is subjected to a timechanging magnetic flux. As the eddy currents circulate inside the conductor they are dissipated, causing energy to be removed from the system and thus allowing the system to function as a type of viscous damper. Using this concept, the ability to generate sufficient damping forces in the extremely thin-film membranes used in space is studied. First, a theoretical model of the interaction between the eddy current damper and the membrane is developed. The model is then validated through experiments carried out at both ambient and vacuum pressures. The results show that the model can accurately predict the damping of the first mode as the distance between the magnet and membrane is varied. Furthermore, the results of the experiments performed on the membrane at vacuum conditions show the functionality of the damping mechanism in space and indicate damping levels as high as 30% of critical at ambient pressure and 25% of critical at vacuum pressure. NomenclatureA = half the conductor's length B = magnetic flux density b = radius of the circular magnet C = damping matrix C b = damping matrix of beam c e = eddy current damping coefficient E = modulus of elasticity F = concentrated forces F = damping force f = distributed forces J = eddy current density K = stiffness matrix . Fellow AIAA. § Aerospace Engineer, Mail Stop 230, Structure Division, 4B West Taylor Street; w.k.belvin@larc.gov. Member AIAA. L= length of magnet L m = length of membrane l g = gap length between magnet and conductor M = mass matrix M 0 = magnetization P = axial load Q = external forces r (t) = temporal coordinate r c = equivalent radius of the conductor T = kinetic energy t = time U = potential energy V = volume v = velocity of conductor v z = velocity of beam in z direction w = displacement δ = thickness of conductor ζ = damping ratio μ 0 = permeability of free space ρ(x) = area density σ = conductivity φ(x) = assumed mode shapes φ e = magnitude of mode shape at location of eddy current damper

Modeling and experiments on eddy current damping caused by a permanent magnet in a conductive tube

“…This concept used the magnet's axial flux induced by two oppositely poled magnets and has been studied by previous researchers [1][2][3][4] because of the desirable traits that this method has for magnetic braking. Sodano et al [16][17][18] proposed a new concept using the eddy currents induced in a conductive plate which oscillates through the magnetic poling axis as shown in Fig. 1(b).…”

Non-Contact Eddy Current Excitation Method for Vibration Testing

“…While this configuration is effective for magnetic damping, it is not functional for use as an actuator for providing dynamic energy to a structure. However, Sodano et al [11,12] recently developed an eddy current damping scheme that functioned such that forces were generated in the poling axis of the magnet rather than perpendicular to it as previous studies had done. The study modeled and experimentally demonstrated the placement of a permanent magnet in close proximity to a conductive structure vibrating along the poling axis of the magnet could induce damping levels as high as 35% of critical.…”

“…Therefore the damping system developed by Sodano et al [11][12][13] can be modified to allow the permanent magnet to move relative to the structure such that forces are generated due to the motion of the magnet relative to the beam. The proposed eddy current excitation system will convert a traditional linear actuator into a non-contact actuator.…”

Vibration Suppression of a Cantilever Plate Using Magnetically Multimode Tuned Mass Dampers

“…The concept of the ECD used in the present study is presented in Figure 4 and is proposed by Sodano et al [14][15][16] and Bae et al [10]. The damping force ( ) in the (vertical) direction due to the eddy current in Figure 4 yields…”

“…Using this model, they have investigated the ECD damping characteristics and performed the simulation of the vibration suppression of a cantilever beam with Kwak's ECD. Sodano et al [14][15][16] proposed the new concept of ECD device to attenuate the vibration of a cantilevered beam. Cheng and Oh [17,18] studied multimode vibration suppression using a permanent magnet and a coil with a shunt circuit for semiactive control.…”