Finite element simulation of Lamb wave generation with bonded piezoelectric transducers

Bonded piezoelectric transducers have been identified as a way to perform real time interrogation of a structure for Structural Health Monitoring (SHM) systems. It has been shown in previous work that these bonded piezoelectric sensors can perform Lamb wave generation and reception in both pulse-echo and pitch-catch modes of operation with results that are comparable to those of traditional ultrasonic transducers. It has also been demonstrated both analytically and experimentally that preferential generation of particular modes is possible by operating at an appropriate frequency for a particular combination of transducer and plate geometry. However, the prior work does not explicitly include the transducer characteristics in the analytic model. The current work uses transient dynamic Finite Element Modeling to examine the response of a plate to excitation by bonded piezoelectric transducers. This simulation includes an explicit finite element device model which solves the electromechanical equations resulting from the piezoelectric coupling effect. This allows direct comparison of the transducer responses in the model with those obtained from the experiment. Symmetry partitioning is used to split the displacement fields of the total response into the symmetric and anti-symmetric parts. This symmetry partitioning of the transverse and longitudinal displacement fields in the plate enables the calculation of the stress fields resulting from the superposition of the symmetric or anti-symmetric modes. When only S0 and A0 are present, it allows a complete separation of these modes. The photoelastic effect has been used to enable visualization of guided waves. These visualizations result in providing intensity contours of the difference between the transverse normal stress and the longitudinal normal stress. The symmetry splitting of the displacement field allows the calculation of the normal stress differences which would result from the symmetric or anti-symmetric modes. This allows the strength and propagation of these modes to be viewed independently. It also allows the relative strengths of these two mode types to be calculated and compared to the relative strengths predicted by the theory. Simulation results from several frequencies for a fixed transducer and plate geometry are presented and compared made with theoretical results.