Multimode control of a rotating, uniform, cantilever beam

Abstract

An investigation was undertaken to assess the performance of a saturation controller for vibration suppression at the tip of a rotating, uniform, cantilever beam. Previous investigations have shown that saturation controllers may be effective in suppressing the vibration of nonrotating, cantilever beams. However, in those investigations, the choice of natural modes to model the beam, and justify the effectiveness of the controller, eliminated any intermodal coupling. Therefore, it is not obvious that a saturation controller will be similarly effective for rotating beams. With both theoretical and numerical analyses, it is shown that in spite of signie cant intermodal coupling, the saturation controller is remarkably effective, even at moderately high rotation speeds. Nomenclature Aij = modal centrifugal stiffening ak = modal base acceleration dij = modal damping d31 = piezoelectric constant, m/V E = Young’ s modulus, Pa H = unit step function I = area moment of inertia, m 4 kij = modal stiffness