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

Abstract

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.

Modelling piezoelectric excitation in waveguides using the semi-analytical finite element method

“…To achieve this, one might use a higher-order analytical theory, such as the Mindlin plate theory [9] or employ hybrid techniques, e.g. the coupling between the finite element method and normal modes expansion [10]. A paper by Raghavan and Cesnik [11] discusses a model based on an integral transform solution to the full 3-D elasticity equations with the external forcing approximated using the pin-force assumption.…”

Lamb Wave Detection of Delaminations in Large Diameter Pipe Coatings

“…Assuming that the coatings are linear viscoelastic layers, for the time harmonic case, elastic and viscoelastic solutions are identical with the exception that the viscoelastic material constants are complex and frequency dependent [47]. By inserting the real and complex material parameters for the layers into the model through the transfer matrix method [38], the global matrix method [42], or a hybrid finite element-normal modes expansion method [43,45] we can obtain dispersion curves for the propagating Lamb wave modes. Through these methods it is apparent that there is the emergence of a decaying exponential term that causes attenuation of the propagating waves in the viscoelastic material due to the complex roots of the dispersion relations.…”

“…Moulin et al presented work starting in 2000 modeling the generation of Lamb waves using a coupled finite element-normal modes expansion method [43,44]. In 2004 Duquenne et al took this coupled method and extended it to the modeling of viscoelastic materials showing the attenuation of some modes in these layers [45].…”

Semi-analytical modelling of piezoelectric excitation of guided waves

“…14,15 Various hybrid techniques employing full FE for modelling piezoelectric excitation and other techniques such as normal modes expansion or Local Interaction Simulation A pproach (LISA) for wave propagation have also been developed. 16,17 The wide range of models briefly recalled above serves many purposes well in NDT/SHM applications, but has certain limitations both from the viewpoint of assumptions made and the model development (ability to model multi-component waveguides). Moreover, there are many applications such as removal of surface accretions using structural waves, where the actuators may operate close to their resonance frequencies and be of a similar to the host structure thickness which violates the quasi-static assumption.…”