Shape Optimization of Distributed Sensors and Actuators for Smart Structure 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 feedback the weighted integration of vibration velocity in the closed loop system through the application of distributed sensors and actuators made of smart materials. We model the beam by the Timoshenko beam model embedded with the distributed sensors and actuators to account for the shear and inertial effects on the structures. We propose an algorithm to find the optimal placement of the actuators and sensors 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 constraints. This approach can be generalized to cases of plate damping and active control of more complicated smart structures as well.