Preface

Numerical simulation of structures with embedded piezoelectric sensors and actuators for closed loop control of vibrations, radiated noise and surface shape is an important element in the computer aided design (CAD) of 'smart structures'. This area of research has seen much activity in the last decade and several papers have appeared in this journal as well as Computer Methods in Applied Mechanics and Engineering, International Journal for Numerical Methods in Engineering, American Institute of Aeronautics and Engineering Journal, American Society of Mechanical Engineering - Journal of Vibrations and Acoustics, Journal of Sound and Vibration, Journal of the Acoustical Society of America, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control as well as conference proceedings papers especially from the SPIE Symposium on Smart Materials and Structures - Mathematics, Control and Modeling. Further research is needed until simulation methods become well enough established to be included in commercial FEM packages. At the present time, there are limited modules available for modeling piezoelectric materials in packages such as ABAQUS. Use is restricted to open loop models and because of their reliance on brick elements to model devices as well as large structural regions, they result in computational models that are artificially large and stiff.

An important requirement for the numerical modeling of these problems is a finite element formulation for piezoelectric materials. Most authors revert to the original paper by Allick and Hughes (Int. J. Num. Meth. Eng. 1970 2 151) who presented a finite element formulation for coupled elastodynamic-electric field problems. The earliest applications of this formulation were for the performance simulation of ultrasonic transducers used in hydrophones, biomedical imaging and NDE. Here, the complexity introduced by a transducer mounted on a structure was absent since such transducers are in contact with a fluid. Most early papers assumed that the voltage applied across the electrodes of the piezoelectric device resulted in a constant electric field because the distance between the electrodes was assumed to be small and the frequencies considered were in the resonance region of the piezoelectric wafer or rod specimen. Once it became necessary to model structures containing sensors and actuators, there was a need to model these devices at the resonance frequencies of the structure and not the device. The coupling of the devices to the structure had to be modeled accurately and models had to be developed to describe the devices (relatively small) and the structure (relatively large) to the required degree of detail. Closed loop simulation relating the output of the sensors to the actuators via control algorithms became necessary to provide full simulation of a smart structure. The first challenge is that FEM results in second order PDEs whereas control theory relies on first order ODEs using a state space formulation. Recently several papers have appeared where there has been an efficient interface of the two in modal state space. In addition, new developments in control theory are continually finding their way into models for smart structures.

In this special issue devoted to modeling and numerical simulation, there are four groups of papers. The first group deals with control issues for vibration and noise suppression using simple models for the structure. The second group deals with finite element simulation of closed loop and open loop models where the emphasis is on accurate modeling of the structure and devices but feedback control is achieved using a simple gain factor. The third group of papers is on so-called laminated smart composites which are an offshoot of numerical models developed for thin plate structures. In these papers, it is assumed that the sensor and actuator layers cover the entire structure and thin plate assumptions are made for the active layers also resulting in the omission of several mechanical and electric field components. The merit of this approach is that the extant literature in mechanical composites can be extended to so-called smart laminates, but further work is needed to establish the approximations of the model and the practicality of implementing this for real structures. They, nevertheless, provide a useful approach for better understanding of smart structure behavior. The fourth group consists of two papers in the evolving field of topological optimization which can be used to optimally design the micro-geometry of piezoelectric layers used for sensing and actuation. An important issue addressed in these models is the contrast in the stiffness of ceramic piezoelectric materials preferred in applications because of their large electro-mechanical coupling strength and the lower stiffness of many structures that they are embedded in. Optimizing the compliance of the transducer while maximizing its electromechanical efficiency is the objective of these papers.

Not addressed in any of the papers in this issue are nonlinear control, modeling of other active materials such as shape memory alloys, relaxor ferroelectrics, etc. This special issue may suffice to give the reader a glimpse of what is happening with respect to the modeling, control and simulation of active structures for vibration and noise control.