Optimal Design of Distributed Sensors and Actuators Made of Smart Materials for Active Vibration Control

We describe a design technique for optimal control in active structural vibration damping using smart materials. The vibration of a cantilever beam is stabilized by using distributed sensors and actuators. We model the beam by the Timoshenko beam model together with the distributed sensors and actuators. A control law using the weighted integration of vibration velocity is incorporated in the closed loop system. We propose a method to find the optimal layout design of the smart material so as to maximize the damping effect. An objective functional is defined based on the vibration energy of the system. The optimal shapes of the sensor and actuator are determined through minimizing the energy functional of the beam over the admissible shape function space subject to certain geometric constraints. An algorithm has been developed to determine the optimal sensor and actuator layout. This method can be generalized to the plate damping problem and more complicated structures as well.