Multilayer piezocomposite structures with piezoceramic volume fractions determined by mathematical optimisation

Piezocomposite materials are now widely used in broadband underwater sonar for ultrasound generation and detection because of their recognised advantages over piezoceramic devices. However, it is difficult to make single-layer piezocomposite devices to operate effectively at frequencies below 100 kHz. Instead, multilayer composite stacks can be used. If this solution is adopted, interesting effects can be achieved by choosing appropriate ceramic volume fractions for different layers in the stack, as volume fraction plays a key role in achieving the desired performance. In this paper we describe a theoretical study of 1-3 piezocomposite transducers with five layers each with a different volume fraction. Our work is based mainly on our own special purpose computer code which solves the one-dimensional wave equation by matrix manipulation, with additional support from the PZ Flex finite element analysis package. The choice of volume fractions is difficult because of the multifaceted nature of the problem, with a very large number of possible combinations and complex dependence of material properties, and hence transducer sensitivity and frequency response on the volume fractions. Therefore, we have used the stochastic optimisation technique of simulated annealing implemented in MATLAB code to determine the volume fraction of each layer. The optimisation cost function we have used is maximisation of gain-bandwidth product. We have found that significant increases in gain-bandwidth product can be achieved compared with the use of the same volume fraction in each layer, far exceeding the 35% reported previously with trial-and-error volume fraction adjustment. This suggests that improvements in practical device performance are possible.