Distributed Modal Identification and Vibration Control of Continua: Theory and Applications

Conventional transducers and actuators are "discrete" in nature, i.e., they usually measure and control spatially discrete locations. These discrete devices become useless when they are placed at modal nodes or lines. In this paper, a generic "distributed" modal identification and vibration control theory for sensing and control of continua, e.g., shells, plates, cylinders, beams, etc., is proposed. The generic theory is derived for a thin shell coupled with two electroded piezoelectric layers. One piezoelectric layer serves as a distributed sensor and the other a distributed actuator. The sensor output, or a reference signal, is processed, amplified, and fed back into the distributed actuator. Due to the converse effect, the injected high voltage induces in-plane strains which result in counteracting moments used to suppress the shell oscillation. System dynamic equations and state equations are also derived. The theory shows that the distributed sensor can identify all vibration modes and the distributed actuators also control all modes. Simplification of the generic theory to other geometries is also demonstrated.