Mathematical optimization of multilayer piezoelectric devices with nonuniform layers by simulated annealing

Multilayer ultrasonic transducers with layers of uniform design are in common use. It is also possible to devise such transducers in which the layer design is nonuniform. However, this adds many degrees of freedom to the transducer design, and conventional design techniques are inadequate to realize desired behavior or even to assess potential benefits. In this paper, a theoretical investigation of multilayer piezoelectric structures with nonuniform layers is reported. Results are presented from a study using computer code to solve the one-dimensional wave equation. It is first shown how multilayer structures with nonuniform layer thicknesses generate even and odd harmonics in their frequency response, suggesting that frequency response can be controlled by choice of layer thickness. However, this choice is complicated and it is impossible to analyze all possible combinations of layer thicknesses. Hence, use of the stochastic optimization technique of simulated annealing is reported. Two optimized transducer designs illustrate this. The first design maximizes uniformity of the fundamental, second, and third harmonics of pressure output, achieved to approximately +/-3%. The results suggest additional bandwidth can be achieved for practical applications, as the presence of a finite response at the second harmonic frequency avoids the null usually associated with this frequency. This is further illustrated with the second optimized transducer design in the form of a three-layer 1-3 connectivity piezo-composite transducer for underwater operation.