A piezoelectric laminate theory that uses the piezoelectric phenomenon to effect distributed control and sensing of structural vibration of a flexible plate has been used to develop a class of distributed sensor/actuators, that of modal sensors/actuators. The one-dimensional modal sensors/actuator equations are first derived theoretically and then examined experimentally. These modal equations indicate that distributed piezoelectric sensors/actuators can be adopted to measure/excite specific modes of one-dimensional plates and beams. If constructed correctly, actuator/observer spillover will not be present in systems adopting these types of sensors/actuators. A mode 1 and a mode 2 sensor for a one-dimensional cantilever plate were constructed and tested to examine the applicability of the modal sensors/actuators. A modal coordinate analyzer which allows us to measure any specific modal coordinate on-line real-time is proposed. Finally, a way to create a special two-dimensional modal sensor is presented.

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BOOK REVIEWS principles, invariance under translation and fundamental solutions, integral representation theorem, finite difference methods, finite element methods, Petrov-Galerkin finite element methods and boundary element methods. Various special iterative methods for the finite difference equations are also discussed. Chapter 4: "Dissipative Systems". The numerical methods considered in Chapter 3 are revised to deal with the advection-diffusion type equations. Nonstandard methods such as upstream weighting, solution pathology at sharp fronts, and alternating direction methods are also introduced in this chapter. Chapter 5: "Nondissipative Systems" deals with transport equations such as the Euler equations, the Burger's equation, and the wave equation. Methods of characteristic, conservative finite-difference schemes, and nonstandard Galerkin finite element methods are considered. Chapter 6: "High-Order, Nonlinear, and Coupled Systems," considers special problems such as the biharmonic equation, nonlinear diffusion equations and compositional flows in porous media. The oil reservoir modeling is discussed at great length. The above list is not complete, merely representative of the topics covered in the book.

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