This thesis presents a theoretical analysis of active control of sound radiation from elastic plates with the use of piezoelectric transducers as actuators. A strain-energy model (SEM), based upon the conservation of strain energy, for a laminate beam with attached or embedded finite-length spatially distributed induced strain actuators was first developed to determine the induced strain distribution. The equivalent axial force and bending moment induced by the embedded or surface bonded actuators were also calculated. The one-dimensional SEM was then extended to a two-dimensional model by employing the classical laminate plate theory and utilizing Heaviside functions to integrate the actuator influence on the substructure. The mechanics model can determine the structural coupling effect and predict the structural response as a result of piezoelectric actuation.

A baffled simply-supported rectangular plate subjected to harmonic disturbances was considered as the plant. Piezoceramic materials bonded to the surfaces of the plate or point force shakers were applied as control actuators. Both microphones in the radiated far-field and accelerometers located on the plate were considered as error sensors. In addition, distributed sensors for pressure and structural motion were modelled. The cost function was formulated as the modulus squared of the error signal. Linear quadratic optimal control theory was then applied to minimize the cost function to obtain the optimal input voltages to the actuators. Both near-field and far-field pressure and intensity responses as well as plate displacement distributions were presented to show the effectiveness and mechanisms of control for various configurations of the actuators and sensors. Plate wavenumber analysis was also shown to provide a further insight into control technique. The results show that piezoelectric actuators perform very well as control sources, and that pressure sensors have many advantages over acceleration sensors while distributed sensors are superior to discrete sensors.

The optimal placement of multiple fixed size piezoelectric actuators in sound radiation control is also presented. A solution strategy is proposed to calculate the applied voltages to piezoelectric actuators with the use of linear quadratic optimal control theory. The location of piezoelectric actuator is then determined by minimizing an objective function, which is defined as the sum of the mean square sound pressure measured by a number of error microphones. The optimal location of piezoelectric actuators for sound radiation control is found so as to minimize the objective function and shown to be dependent on the excitation frequency. In particular, the optimal placement of multiple piezoelectric actuators for on-resonance and off-resonance excitation is presented. Results show that the optimally placed piezoelectric actuators perform far better in sound radiation control than arbitrarily selected. This work leads to a design methodology for adaptive or intelligent material systems with highly integrated actuators and sensors. The optimization procedure also leads to a reduction in the number of control transducers.