Abstract
The scattering phenomena of the fundamental antisymmetric Lamb wave mode with a horizontal notch enabling the partial energy transfer (PET) option is addressed in this paper. The PET functionality for a given waveguide is realized using the material interface. The energy scattering coefficients are identified using two methods, namely, a hybrid approach, which utilizes the finite element method (FEM) and the general orthogonality relation, and the semi-analytical approach, which combines the modal expansion technique with the orthogonal property of Lamb waves. Using the stress and displacement continuity conditions on the present (sub)waveguide interfaces, one can explicitly derive the global scattering matrix, which allows detailed analysis of the scattering process across the considered interfaces. Both methods are then adopted on a simple representation of a surface breaking crack in the form of a vertical notch, of which a certain section enables not only the reflection of the incident energy, but also its nonzero transfer. The presented results show very good conformity between both utilized approaches, thus leading to further development of an alternative technique.
Highlights
The scattering phenomena of Lamb waves [1,2] on various types of discontinuities [3,4] in elastic waveguides remains an attractive topic with a direct relationship to numerous applications in nondestructive testing or structured health monitoring
Progressive development of computer technology has enabled the use of the finite element method (FEM) or, alternatively, the boundary element method (BEM) [12,13,14,15]
A pioneering work within this area is the method published by Torvik [19], which addressed the reflection of the Lamb wave modes from the free plate end, and discussed the importance of modes with complex and pure imaginary wavenumbers in the computational process
Summary
The scattering phenomena of Lamb waves [1,2] on various types of discontinuities [3,4] in elastic waveguides remains an attractive topic with a direct relationship to numerous applications in nondestructive testing or structured health monitoring. In 2002, a novel approach was published by Pagneux et al [24,25], which incorporated a mode matching technique in conjunction with the biorthogonality relation [26] and the stress and displacement discontinuities at the corresponding waveguide sections Using this method, it is possible to explicitly derive the scattering matrix, which links the incident Lamb wave modes with the scattered wave modes. The energy transmission and reflection coefficients with respect to the incident mode were obtained using two methods—the PET approach and a hybrid method combining FEM and the general orthogonality relation [16] Obtained results from both approaches show very good mutual agreement and provide promising applicability to many complex geometries in terms of their shape, including the study of the effect of multipoint contact between the crack faces or even partially opened/closed cracks.
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