Mathematical optimisation of multilayer piezoelectric devices with non-uniform layer thicknesses by simulated annealing

We report a theoretical investigation of multilayer piezoelectric structures with non-uniform layer thicknesses. Our results come from a study of such structures using computer code based on solving the one-dimensional wave equation by matrix manipulation and validation using finite element analysis. We first show how structures with nonuniform layer thicknesses generate even harmonics in their frequency response as well as the odd harmonics generated by devices with uniform layer thicknesses. We have found that control can be exerted over the complete frequency response by appropriate choice of layer thickness. However, for most transducer configurations, the relationship between frequency response and layer thicknesses is very complicated. To overcome this, we have investigated the stochastic optimisation technique of simulated annealing. This allows a transducer configuration to be obtained with a desired frequency response expressed as a cost function. The cost function reported here maximises uniformity of the fundamental and second and third harmonics of output pressure, which we have achieved to approximately /spl plusmn/3%. The results are promising and may deliver additional bandwidth for applications in underwater sonar and biomedical imaging. To illustrate their potential, we also describe a three-layer 1-3 connectivity piezocomposite transducer with a strong response extending over the fundamental and first two harmonics.