Dynamic Modeling and Optimal Control of Rotating Euler-Bernoulli Beams

[+] Author and Article Information
W. D. Zhu

Department of Mechanical Engineering, University of North Dakota, Grand Forks, ND 58202

C. D. Mote

Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720

J. Dyn. Sys., Meas., Control 119(4), 802-808 (Dec 01, 1997) (7 pages) doi:10.1115/1.2802393 History: Received August 01, 1995; Online December 03, 2007


The nonlinear integro-differential equations, describing the transverse and rotational motions of a nonuniform Euler-Bernoulli beam with end mass attached to a rigid hub, are derived. The effects of both the linear and nonlinear elastic rotational couplings are investigated. The linear couplings are exactly accounted for in a decoupled Euler-Bernoulli beam model and their effects on the eigensolutions and response are significant for a small ratio of hub-to-beam inertia. The nonlinear couplings with a resultant stiffening effect are negligible for small angular velocities. A discretized model, suitable for the study of large angle, high speed rotation of a nonuniform beam, is presented. The optimal control moment for simultaneous vibration suppression of the beam at the end of a prescribed rotation is determined. Influences of the nonlinearity, nonuniformity, maneuver time, and inertia ratio on the optimal control moment and system response are discussed.

Copyright © 1997 by The American Society of Mechanical Engineers
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