Dynamic modelling and control of a rotating Euler–Bernoulli beam

Flexible motion of a uniform Euler–Bernoulli beam attached to a rotating rigid hub is investigated. Fully coupled non-linear integro-differential equations, describing axial, transverse and rotational motions of the beam, are derived by using the extended Hamiltonʹs principle. The centrifugal stiffening effect is included in the derivation. A finite-dimensional model, including couplings of axial and transverse vibrations, and of elastic deformations and rigid motions, is obtained by the finite element method. By neglecting the axial motion, a simplified modelling, suitable for studying the transverse vibration and control of a beam with large angle and high-speed rotation, is presented. And suppressions of transverse vibrations of a rotating beam are simulated with the model by combining positive position feedback and momentum exchange feedback control laws. It is indicated that an improved performance for vibration control can be achieved with the method.