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The response and control of the transverse vibration of an axially moving free-free beam with high speed subjected to the thermal shock is studied. Considering the thermal shock and the control force, the transverse vibration equation and boundary conditions are formulated by the Hamilton principle. The instant linearized equations are set up based on Galerkin' s method for the approximation solution. Considering the thermal shock, the displacement responses are calculated, where the axially speed is 2 Ma. Then the controller is designed based on LQR method. The optimal Q and R matrices are selected by the weighting coefficient method. The displacement responses for the control method are simulated by a numerical example. The results show that the control method can suppress the transverse vibration effectively [ABSTRACT FROM AUTHOR]

The control of the transverse vibration of an axially moving cantilever beam is studied and two control methods are presented in the paper. The transverse vibration equation and boundary conditions are formulated by the Hamilton principle. The instant linearized equations are set up based on Galerkin method for the approximation solution. The controllers for active vibrator and active force are designed based on LQR method. The optimal Q and R matrices are selected by the weighting coefficient method. The two control methods are simulated by a numerical example. The results show that the two control methods can all suppress the transverse vibration effectively. The control result of the latter method is better than that of the active vibrator method, but the active vibrator is more realizable than the former in practice. [ABSTRACT FROM AUTHOR]

Abstract: An H∞ method for the vibration control of an iron cantilever beam with axial velocity using the noncontact force by permanent magnets is proposed in the paper. The transverse vibration equation of the axially moving cantilever beam with a tip mass is derived by D''Alembert''s principle and then updated by experiments. An experimental platform and a magnetic control system are introduced. The properties of the force between the magnet and the beam have been determined by theoretic analysis and tests. The H∞ control strategy for the suppression of the beam transverse vibration by initial deformation excitations is put forward. The control method can be used for the beam with constant length or varying length. Numerical simulation and actual experiments are implemented. The results show that the control method is effective and the simulations fit well with the experiments. [Copyright &y& Elsevier]