THE MODELLING AND VIBRATION CONTROL OF BEAMS WITH ACTIVE CONSTRAINED LAYER DAMPING

Abstract

The finite element method (FEM) is combined with the Golla–Hughes–McTavish (GHM) model of viscoelastic materials (VEM) to model a cantilever beam with active constrained layer damping treatments. This approach avoids time-consuming iteration in solving modal frequencies, modal damping ratios and responses. But the resultant finite element (FE) model has too many degrees of freedom (d.o.f.s) from the point of view of control, nor is it observable and controllable. A new model reduction procedure is proposed. An iterative dynamic condensation is performed in the physical space, and Guyan condensation is taken as an initial iteration approximation. A reduced order model (ROM) of suitable size emerges, but it is still not observable and controllable. Accordingly, a robust model reduction method is then employed in the state space. A numerical example proves that this procedure reduces the model and assures the stability, controllability and observability of the final reduced order model (FROM). Finally, a controller is designed by linear-quadratic Gaussian (LQG) method based on the FROM. The vibration attenuation is evident