The design of piezoelectric transducers used for medical imaging or non destructive evaluation (NDE) requires powerful and flexible tools to accurately simulate complex combinations of materials exhibiting acoustic and dielectric losses, with a reliable representation of acoustic radiation in fluids. The periodicity of such probes has to be taken into account to correctly predict their capability to convert bulk vibrations into acoustic radiation. The present work is devoted to the development of finite element computation tools to address this issue. It is based on an harmonic analysis of the admittance (or of the impedance) of any piezoelectric transducer. It is associated with boundary element techniques to simulate acoustic radiation in different media assuming plane interfaces. Periodicity is taken into account using a standard periodic finite element approach and a Bloch-Floquet expansion for the radiation medium. Computations are performed for different kinds of piezoelectric ultrasonic transducers to illustrate the proposed approach.