Modeling and boundary control of translational and rotational motions of nonlinear slender beams in three-dimensional space
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Do, Khac Duc
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Do, K.D. 2017. Modeling and boundary control of translational and rotational motions of nonlinear slender beams in three-dimensional space. Journal of Sound and Vibration. 389: pp. 1-23.
Journal of Sound and Vibration
Department of Mechanical Engineering
Equations of motion of extensible and shearable slender beams with large translational and rotational motions under external loads in three-dimensional space are first derived in a vector form. Boundary feedback controllers are then designed to ensure that the beams are practically K8-exponentially stable at the equilibrium. The control design, well-posedness, and stability analysis are based on two Lyapunov-type theorems developed for a class of evolution systems in Hilbert space. Numerical simulations on a slender beam immersed in sea water are included to illustrate the effectiveness of the proposed control design.
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