Active and Passive damping of Euler-Bernoulli beams and their interactions have been studied using the beam’s exact transfer function model without mode truncation or finite element or finite difference approximation. The combination of viscous and Voigt damping is shown to map the open-loop poles and zeros from the imaginary axis in the undamped case into a circle in the left half plane and into the negative real axis. While active PD collocated control using sky-hooked actuators is known to stabilize the beam, it is shown that the derivative action using proof-mass (reaction-mass) actuators can destabilize the beam.
Active and passive Damping of Euler-Bernoulli Beams and Their Interactions
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Pang, S. T., Tsao, T., and Bergman, L. A. (September 1, 1993). "Active and passive Damping of Euler-Bernoulli Beams and Their Interactions." ASME. J. Dyn. Sys., Meas., Control. September 1993; 115(3): 379–384. https://doi.org/10.1115/1.2899113
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