Modeling of piezoelectric smart structures for active vibration and noise control applications

Active vibration control and active structural acoustic control using piezoelectric sensors and actuators have recently emerged as a practical and promising technology. Efficient and accurate modeling of these structures bonded to or embedded with actuators and sensors is needed for efficient design of smart structures. This dissertation addresses the modeling of these structures and the associated control system design technique. Modeling of structures with both laminated and discrete type of actuators and sensors are addressed.; For piezoelectric laminates the governing equations of motion are derived using First Order Shear Deformation Theory (FSDT) and for the first time the dynamic response fields inside the laminate are obtained and compared with full elasticity solutions. This comparison brought out the effect of assumptions made with respect to the electric and mechanical fields using FSDT and Classical Laminate Theory (CLT) in previous work. It is expected that this analysis and the interior field estimations would help designers to understand the shortcomings of FSDT in modeling piezoelectric laminates, and help them to adopt this theory properly for use in FE or other numerical models.; For discrete patch actuators/sensors, the governing dynamic equation of motion for a plate is derived. The solution to this equation is obtained using a Fourier series method and the effect of passive stiffness and mass on the natural frequency is studied. The studies showed that ignoring the mass and the passive stiffness' of actuators/sensors leads to large errors in estimating the vibration characteristics of the smart plate. A Rayleigh-Ritz (RR) approach is then presented for studying the active vibration and transmitted noise control of a smart plate with discrete piezoelectric patches. Classical laminated plate theory is used to model the composite plate and electro elastic theory is used model the piezoelectric patches. The dynamic equations of motion for the coupled smart panel-cavity system are derived using Hamilton's principle. Close agreement between the present approach and the finite element and experimental results confirmed the validity of the approach. The RR approach is thus presented as a simple, computationally inexpensive approach when compared to the finite element method. The RR method also proved to be powerful method for modeling the adjacent acoustic medium and for the associated control system design. (Abstract shortened by UMI.)...