Predicting the losses and the efficiency of a 1-3 piezo-composite transducer through a partial homogeneization method

The topic of this work is the theoretical study of a disc-shaped acoustic transducer made with a 1-3 piezoelectric composite material. This material consists of PZT ceramic rods embedded in a polymer matrix. A modeling of this ideal transversally periodic structure is proposed. It is based on a finite element approach derived from homogenization techniques mainly used for composite material studies. The analysis focuses on a representative unit cell with specific boundary conditions on the lateral surfaces taking accurately into account the periodicity of the structure. The first step proposed is the development of a three-dimensional Fortran code with complex variables, especially adapted for this problem. Using the principle of correspondence of Lee-Mandel, thus technique allows the prediction of the damping properties of the transducer from the complex modulus of the constituents. Both the versatility of the method and the rigorous character of the model are pointed out through various boundary conditions and mixed loadings. An interesting result is that, despite the lossy polymer matrix, a 1-3 composite can advantageously replace a much heavier massive transducer, in terms of efficiency and loss factor.