Modeling of lamb waves generated by integrated transducers in composite plates using a coupled finite element-normal modes expansion method

Thin piezoelectric transducers attached to or embedded within composite structures could be used for in situ structural health monitoring. For plate-shaped structures, the useful ultrasonic vibration modes are Lamb waves. Preliminary testing has already demonstrated the suitability and practical feasibility of such integrated transducers, but better control of the generation of Lamb modes seems to be necessary. Therefore, an original modeling approach has been developed, which can be used to design and optimize these "sensitive materials." This modeling technique allows the determination of the amplitude of each Lamb mode excited in a composite plate with surface-bonded or bulk-embedded piezoelectric elements. The method consists of a coupling of the finite element method (FEM) and the normal modes expansion method. The limited finite element mesh of the transducer and its vicinity enables the computation of the mechanical field created by the transducer, which is then introduced as a forcing function into the normal modes equations. The adequacy and accuracy of this modeling method have been numerically and experimentally verified.