Design of piezoelectric transducers using topology optimization

Among other applications piezoelectric transducers are widely used for acoustic wave generation and as resonators. These applications require goals in the transducer design such as high electromechanical energy conversion for a certain transducer vibration mode, specified resonance frequencies and narrowband or broadband response. In this work, we have proposed a method for designing piezoelectric transducers that tries to obtain these characteristics, based upon topology optimization techniques and the finite element method (FEM). This method consists of finding the distribution of the material and void phases in the design domain that optimizes a defined objective function. The optimized solution is obtained using sequential linear programming (SLP). Considering acoustic wave generation and resonator applications, three kinds of objective function were defined: maximize the energy conversion for a specific mode or a set of modes; design a transducer with specified frequencies and design a transducer with narrowband or broadband response. Although only two-dimensional plane strain transducer topologies have been considered to illustrate the implementation of the method, it can be extended to three-dimensional topologies. Transducer designs were obtained that conform to the desired design requirements and have better performance characteristics than other common designs.