Design of piezocomposite materials and piezoelectric transducers using topology optimization.

Abstract

Piezoelectric materials are widely used in electromechanical sensors and actuators, in electronic equipment as resonators, and in acoustic applications as ultrasonic transducers and hydrophones for generating and detecting sound waves. Their development has been based on the use of simple analytical models, test of prototypes, and analysis by the finite element method (FEM), usually limiting their design to a parametric optimization. By changing the topology of these devices or their components, we may obtain new kinds of piezocomposites and transducers with better performance characteristics. This dissertation describes the application of topology optimization combined with the homogenization method and FEM for designing piezocomposite materials and piezoelectric transducers. The optimized solution is obtained using Sequential Linear Programming. Three problems are discussed: design of piezocomposite materials, design of resonators and ultrasonic transducers, and design of piezoelectric actuators. The performance characteristics of piezocomposite materials can be improved by designing new topologies of microstructures (or unit cells) for these materials. The topology of the unit cell (and the properties of its constituents) determines the effective properties of the piezocomposite. By changing the unit cell topology, performance characteristics can be vastly improved in the piezocomposite. Hydrophone (low-frequency) and ultrasonic transducer (high-frequency) applications are considered. A general homogenization method applied to piezoelectricity was implemented using FEM to calculate the effective properties of a unit cell with complex topology. This method has no limitations regarding volume fraction or shape of the composite constituents. The main assumption is the periodicity of the unit cell. The performance characteristics are improved by orders of magnitude comparing with common configurations of piezocomposite unit cells, as confirmed by results of experiments conducted with manufactured prototypes of some optimized piezocomposites. In the design of resonators and ultrasonic transducers, three kinds of objectives are specified: maximize the energy conversion for a specific mode or a set of modes; design a transducer with specified frequencies; and design a transducer with narrow-band or broadband response. The results show new transducer configurations with better performance. In the design of piezoelectric actuators, we focus on the low-frequency flextensional actuators which consist of a piezoceramic connected to a coupling structure that converts and amplifies the piezoceramic output displacement. By designing new kinds of coupling structure, flextensional actuators for different tasks can be obtained. Transducer designs were obtained that conform to the desired design requirements and have better performance characteristics than other common configurations.