Optimal design of 1-3 composite piezoelectrics

An optimal design problem for piezoelectric composite hydrophones is considered. The hydrophone consists of parallel piezoelectric rods embedded in a poroustransversely isotropic polymer matrix. We find the shape, volume fraction, and spatial arrangement of the piezoceramic rods, and the structure of the matrix material that maximizes the hydrophone performance characteristics. We found that the optimal composite consists of a hexagonal array of rods with small volume fraction, in a highly anisotropic matrix that is characterized by negative Poisson's ratios in certain directions. The performance characteristics of hydrophones with such a matrix are significantly higher than those with anisotropic polymer matrix. The results can be viewed as theoretical upper bounds on the hydrophone performance.