NUMERICAL ANALYSIS FOR VIBRATION CONTROL OF BEAMS WITH ACTIVE CONSTRAINED LAYER DAMPING TREATMENTS

The finite element method(FEM) is combined with the GHM(Golla Hughes McTavish) model of viscoelastic material to model a cantilever beam with active constrained layer damping (ACLD), which can avoid time consuming iteration for solving modal frequencies, modal damping rations and responses. But the resulting finite element model has too many degress of freedom from the point of control. Furthermore, it is not observable and controllable. So, a new model reduction procedure was proposed. Firstly, an iterativr dynamic condensation is performed in the physical space and Guyan condensation is taken as an initial approximation of the iteration. This results in a reduced order system with suitable size, but it is still not observable and controllable. So a kind of robust model reduction methods is utilized in the state space afterwards. The numerical example shows that the above model reduction procedure can not only reduce the size of the system greatly but also guarantee the stability, controllability and observability of the final reduced order system. Finally, a controller, is designed by LQG (Linear Quadratic Gaussian) method based on the final reduced order model. It shows that the vibration attenuation is obvious.