Smart Material Structures: Modeling, Estimation and Control

In this monograph, mathematical and computational investigations pertinent to scientific and engineering issues in the emerging field of smart materials are presented. A brief survey of basic mechanisms and questions related to various components (piezoelectric and electrostrictive elements, magnetostrictive transducers, ER fluids, shape memory alloys, fiber optics) of smart material structures is given. Attention is then focused on piezoceramic actuators and sensors. Care is given to the precise modeling of piezoceramic patch contributions (passive and active) in structures such as thin shells, plates and beams. Mathematical foundations for well-posedness, approximation, inverse problem and parameter estimation, and feedback control methodologies are discussed. Applications, including experimental validation of the efficacy of the ideas, are presented in the context of damage detection and characterization in structures, and in active control of structural vibrations and structure-borne noise. This treatise features rigorous mathematical presentation as well as discussion of implementation and experimental challenges. It provides substantial evidence to support the utility, indeed, the necessity of a distributed parameter system approach in the development of smart material structure methodologies. It thus substantiates the importance of the theoretical ideas for control and identification of distributed parameter systems presented in the research literature over the past several decades. The ideas discussed in this monograph should be useful to both applied mathematicians and engineers with an interest in the science of smart materials.