| Piezoelectric transducers are widely used since the piezoelectric effect can induce the conversion between mechanical and electrical energy. In this dissertation, an optimization of electrode shape for piezoelectric composite transducers is studied to improve actuator performance. Towards this goal, strong form and weak form of equations of motion for different types of transducer structures are derived based on different approaches. In addition to the derivations, rigorously convergent approximation schemes are presented for the finite element approximation of the governing equations. To obtain the optimal electrode shape, two optimization methodologies are investigated based on the theory. One is a straightforward ad hoc algorithm and the other is an algorithm that is consistent with the corresponding theory. Numerical examples of both methodologies are given that illustrate the convergence of the approximate methods and verify the theory. Both methodologies obtain the same optimal electrode shapes that are easy for fabrication. The second algorithm turns out to be an effective method to solve the oscillation phenomenon in the shape optimization procedure. |
