Using FreeFEM Open Software for Modelling the Vibrations of Piezoelectric Devices

Modelling vibrations of piezoelectric transducers has been a topic discussed in the literature for many decades. The first models - so-called one-dimensional - describe the vibrations only near operating frequency and near its harmonics. Attempts to introduce two-dimensional models were related to the possibility of one transducer working at several frequencies, including both thickness vibrations and those resulting from the transducer horizontal dimensions. In recent decades, thanks to the use of the finite element method and its derivatives, and the progress related to the increase in processor speed and memory availability, the implementation of models based on three-dimensional modelling is possible using software on personal computers. As the implementation of finite element method algorithms is characterized by high complexity, several professional software packages have been created on the commercial market, among which only a few implement the piezoelectric equations. In this context, this article presents how to use open source software along with developed programming language for intuitive definition of piezoelectric equations and its solution.