Dynamic modeling and optimal control of rotating Euler-Bernoulli beams

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, maneuvering time, and inertia ratio on the optimal control moment and system response, are discussed.