Simulation of the Vibrations of a Piezoelectric Transducer with a Wrapped Electrode Using the Spectral Element Method

The paper presents an approach to the modelling of the dynamic behavior of a piezoelectric transducer of a complex shape in a three-dimensional case based on the spectral element method. The proposed mathematical model will be a part of the hybrid approach to the modelling of the guided waves excitation and sensing in an elongated structure in a three-dimensional case. Different types of electrodes of piezoelectric transducers as well as various boundary value conditions for the modelling of the actuation and sensing operations are considered. Unknown displacements are approximated with Lagrange polynomials at the Gauss-Legendre-Lobatto nodal points and the system of linear algebraic equations is obtained in terms of the displacement vector and electric potential at the nodal points. The results are compared with the standard finite element calculations provided with the finite-element COMSOL Multiphysics software. The electro-mechanical characteristics of the dynamic behaviour of piezoelectric transducers are analysed depending on the operational conditions and the kind of electrodes. The eigenfrequencies of the piezoelectric transducers are calculated and the corresponding eigenforms are constructed and analysed.