Active vibration control of an axially moving beam using varying velocity method

In this paper, active vibration control method of a viscoelastic axially moving beam, using varying velocity approach, is investigated. The dynamic response of the moving beam is computed with a set of linear equations in state space, which are obtained by Galerkin finite-element method. Based on the approximated solution, the vibration energy is reformulated as a quadratic function. Lyapunov stability is employed to investigate the vibration energy. The varying velocity algorithm optimizing time of vibration suppression is achieved by using steepest descent method. Simulation results demonstrate the effectiveness of the control approach.