**5. Conclusions**

A parametric analysis was performed to study the effects of multiple key factors, including material parameters of epoxy layers, piezoceramic material types, and locations of piezoceramic rings, on the electromechanical characteristics of the radially layered cylindrical piezoceramic/epoxy composite transducer. The main results can be concluded as follow.

(1) Based on the presented three different epoxy materials that have the same Poisson's ratio, approximately equal density and the certain difference in Young's modulus, the transducer can present 27 sets of electromechanical characteristics by utilizing different material sequences. Furthermore, these electromechanical characteristics are mainly controlled by the Young's moduli of the epoxy layers, especially for that of the epoxy ring #2. This result demonstrates that only regulating the Young's modulus of the epoxy layers can realize the design and optimization of the electromechanical characteristics of the transducer.

(2) Among five commonly used piezoceramic materials (PZT-5H, PZT-4, EC-64, PZT-5A and BaTiO3), the transducer with the PZT-5A ring #2 has the minimum first resonance and anti-resonance frequencies as well as the maximum first electromechanical coupling factor; the transducer with the BaTiO3 ring #2 has the maximum first resonance and anti-resonance frequencies as well as the minimum first electromechanical coupling factor; the transducer with PZT-5H, PZT-4, EC-64 ring #2 has the similar first resonance and anti-resonance frequencies. That is to say, the selections of piezoceramic material types in the ring #2, the piezoceramic materials with the lager radial sound speed and plane electromechanical coupling factor can optimize the electromechanical characteristics of the transducer.

(3) The locations of piezoceramic rings have grea<sup>t</sup> effects on the electromechanical characteristics of the transducer, in particular, an appropriate location can be used to optimize the transducer design, making it have the maximum first resonance and anti-resonance frequencies as well as the first electromechanical coupling factor.

**Author Contributions:** J.W. established the modelling and performed the numerical analysis; J.W., L.Q. and W.S. fabricated the transducer; J.W. and L.Q. tested the transducer; J.W. and W.L. wrote the paper; and all the authors discussed the results.

**Funding:** This research was funded by the National Natural Science Foundation of China (51708025, 61671068) and the Fundamental Research Funds for the Central Universities (FRF-TP-16-069A1).

**Conflicts of Interest:** The authors declare no conflicts of interest.
