Finite difference modeling of piezoelectric composite transducers with 0-3 connectivity

The mechanical and electrical properties of transducers are modelled by finite-difference representations of the relevant physical equations and the numerical problems are discussed. The theory is applied to a transducer consisting of a calcium-modified lead titanate (PTCa) ceramic mixed with the polymer P(VDF-TrFE), and comparison of ∈₃₃ with experimental values is found to be good. The introduction of ceramic into the mix has an immediate effect on the voltage, and s₁₁ and s₁₂. d₃₁ is not much affected by the presence of the ceramic until it reaches 70% of the mixture whereas d₃₃ changes sign rather quickly and then increases more slowly. A second transducer having the ceramic PZT5 mixed with P(VDF-TrFE) is also modelled and the characteristics of the 0-3 structure are compared with those of the 1-3 structure of the same components modelled in an earlier paper. The 1-3 construction brings the effect of the ceramic in much faster than the 0-3 construction. For example, at 50% ceramic, e₃₃, d_3l and d₃₃ are roughly trebled compared to the 0-3 values.