Optimal Design of Multiple Vibration Controllers for Elastic Beams

An optimization technique of multiple vibration controllers is presented in this study. In the technique, the characteristics of the vibration controllers are optimized by use of the property of the optimal control force obtained by the optimal control theory and the placement is optimized by the steepest descent method, under a criterion consisting of the mean squared bending stress and the transmitted forces of the controller. And a stationary Gaussian colored noise is used as such a random input as a seismic wave. Straight beam structures of a cantilever and a simply-supported beam, and a bent beam structure with various input directions are treated as application examples. The characteristics of the controlled structures, the relationship between the transmitted force and the reduction effect, the optimal allocation, etc. were investigated and as a result the importance of the optimization was pointed out especially in the bent beam structure.