A finite element formulation is applied to study Lamb wave scattering in homogeneous and sandwich isotropic plates. Dispersion curves are calculated in a simple and automatic way by solving a quadratic eigenproblem. A meshing criterion to obtain accurate results with linear and quadratic elements is provided. An absorbing boundary condition for semi‐infinite plates is derived from this formulation by means of a truncated normal mode expansion technique, where the finite element eigenvectors are used instead of the analytical expressions for the normal modes. This non‐reflecting boundary condition is directly applicable to study Lamb wave reflection by simple obstacles such as a flat edge. In order to tackle Lamb wave diffraction problems by defects with more complex geometries, a hybrid boundary element‐finite element formulation is developed. The validity and accuracy of both formulations are checked thoroughly with a series of test problems studied by other researchers. Copyright © 2001 John Wiley & Sons, Ltd.

Ultrasonic guided wave inspection of structures containing adhesively bonded joints requires an understanding of the interaction of guided waves with geometric and material discontinuities or transitions in the waveguide. Such interactions result in mode conversion with energy being partitioned among the reflected and transmitted modes. The step transition between an aluminum layer and an aluminum-adhesive-aluminum multi-layer waveguide is analyzed as a model structure. Dispersion analysis enables assessment of (i) synchronism through dispersion curve overlap and (ii) wavestructure correlation. Mode-pairs in the multi-layer waveguide are defined relative to a prescribed mode in a single layer as being synchronized and having nearly perfect wavestructure matching. Only a limited number of mode-pairs exist, and each has a unique frequency range. A hybrid model based on semi-analytical finite elements and the normal mode expansion is implemented to assess mode conversion at a step transition in a waveguide. The model results indicate that synchronism and wavestructure matching is associated with energy transfer through the step transition, and that the energy of an incident wave mode in a single layer is transmitted almost entirely to the associated mode-pair, where one exists. This analysis guides the selection of incident modes that convert into transmitted modes and improve adhesive joint inspection with ultrasonic guided waves.

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SUMMARYA ÿnite element formulation is applied to study Lamb wave scattering in homogeneous and sandwich isotropic plates. Dispersion curves are calculated in a simple and automatic way by solving a quadratic eigenproblem. A meshing criterion to obtain accurate results with linear and quadratic elements is provided. An absorbing boundary condition for semi-inÿnite plates is derived from this formulation by means of a truncated normal mode expansion technique, where the ÿnite element eigenvectors are used instead of the analytical expressions for the normal modes. This non-re ecting boundary condition is directly applicable to study Lamb wave re ection by simple obstacles such as a at edge. In order to tackle Lamb wave di raction problems by defects with more complex geometries, a hybrid boundary element-ÿnite element formulation is developed. The validity and accuracy of both formulations are checked thoroughly with a series of test problems studied by other researchers.

Two general and flexible numerical techniques based on the finite-element and boundary element methods developed by the authors in a previous paper are applied to study Lamb wave propagation in multilayered plates and Lamb mode conversion at free edges for frequencies beyond the first cutoff frequency. Both techniques are supported by a meshing criterion which guarantees the accuracy of the results when a condition is fulfilled. A finite-element formulation is directly applicable to study Lamb wave propagation and reflection by simple obstacles such as a flat edge. In order to tackle Lamb wave diffraction problems by defects with more complex geometries, a hybrid boundary element-finite-element formulation is used. This technique provides a major improvement with respect to the only previous boundary element application on Lamb waves: the connecting boundary might be placed as close to the reflector as desired, reducing greatly the requirement on mesh size. Two main application problems on practical metallic plates are studied and compared with reported numerical, theoretical, and experimental results: (1) Lamb wave propagation in degraded titanium diffusion bonds, and (2) Lamb mode conversion at inclined or perpendicular free edges of steel plates for frequencies beyond the first cutoff frequency.