Experimental and numerical investigation of the interaction of the first four SH guided wave modes with symmetric and non-symmetric discontinuities in plates

The interaction of the SH0, SH1, SH2 and SH3 guided wave modes on a metal plate with a thickness discontinuity is numerically and experimentally investigated. Two different geometries were evaluated, namely symmetric and non-symmetric discontinuities, relative to the plate longitudinal mid-plane. Experiments were performed with periodic permanent magnet array EMATs as transmitters and receivers. Mode separation in transmission and reception was experimentally and numerically performed by dual transduction and by modal decomposition post-processing techniques, respectively. The reflection and transmission coefficients at the discontinuity for each of the investigated SH modes was calculated. It has been experimentally confirmed that when interacting with symmetric discontinuities, only modes that share the same symmetry as the incident mode are created by mode conversion, whereas mode conversion to modes of different symmetry can occur with non-symmetric discontinuities. Experimental and numerical data show good agreement, revealing that the higher the order of the incident mode, the more complex the behaviour of the reflection coefficient is, as a function of the discontinuity depth. For the same incident mode, symmetric discontinuities impose less complexity than non-symmetric ones

Proper contractions and invariant subspaces

Let T be a contraction and A the strong limit of {T∗nTn}n≥1. We prove the following theorem: if a hyponormal contraction T does not have a nontrivial invariant subspace, then T is either a proper contraction of class 00 or a nonstrict proper contraction of class 10 for which A is a completely nonprojective nonstrict proper contraction. Moreover, its self-commutator [T*,T] is a strict contraction

Mode selectivity of SH guided waves by dual excitation and reception applied to mode conversion analysis

SH guided waves, generated by periodic permanent magnet arrays have been used previously in non-destructive evaluation of metal plates and pipes. When an SH guided wave interacts with a defect or change in sample thickness, the incident SH wave may undergo mode conversion. Analysis of mode conversion is complicated, due to the interference of several propagating modes in the received signal, that can often temporally overlap. This paper proposes a mode selection technique to help understand the interaction of SH guided waves with changes in sample thickness. Using an understanding of the propagation characteristics of the guided waves, SH guided waves are sequentially generated and detected on both surfaces of the plate, capturing four distinct waveforms. By superposition of the detected signals, symmetric modes can be clearly separated from antisymmetric modes in the processed, received signals. For this method to work well, the transducers used should have very similar responses and be precisely positioned on exactly opposite positions either side of the plate. Finite element simulations are also performed, mirroring the experimental measurements, and the results correlate well with the experimental observations made on an 8 mm thick plate with a region of simulated wall thinning machined into the sample