A study of the noncollinear ultrasonic-wave-mixing technique under imperfect resonance conditions

Abstract

Geometrical and material property changes cause deviations in the resonant conditions used for noncollinear wave mixing. These deviations are predicted and observed using the SV(ω1)+L(ω2)→L(ω1+ω2) interaction, where SV and L are the shear vertical and longitudinal waves, respectively, and ω1, ω2 are their frequencies. Numerical predictions, performed for the scattered secondary field in the far field zone, show three field features of imperfect resonance conditions: (1) rotation of a scattered beam, (2) decrease in the beam amplitude, and (3) beam splitting. The response of the nonlinear ultrasonic wave mixing technique is verified experimentally in two ways: (1) detection of a kissing bond between two polyvinyl chloride (PVC) plates, and (2) detection of subsurface micro-cracks in polymethyl methacrylate (PMMA). A predominant decrease in nonlinear wave energy is observed in both experiments. Beam rotation and splitting is observed in the kissing-bond experiment, while a minor increase in the nonlinear wave energy up to 100% is observed in the micro-cracked PMMA specimen.

2D finite element modeling of the non-collinear mixing method for detection and characterization of closed cracks

“…2, ensure constructive interferences of all nonlinear interactions within the interaction volume V . In [30], a study of the technique (in the case of SV and P waves interaction) under imperfect resonance conditions demonstrated that in the far field, a deviation of a few degrees from the ideal angle of incidence at resonance causes a rotation of the scattered beam, a decrease in the beam amplitude, and a beam splitting. In our study, a contact interface is considered on a closed crack.…”

“…The method is applied in the case of a closed crack embedded in an elastic solid which behavior is considered linear. The application of the non-collinear mixing method for a classical bulk nonlinearity (already studied and showed in [26,27,28,30]) is beyond the scope of this paper. In this study, the interface is modeled by a unilateral contact with Coulomb's friction and the resolution is evaluated in the time domain.…”

Non-collinear interaction of guided elastic waves in an isotropic plate

“…The non-collinear interaction has been studied for bulk waves in isotropic elastic media theoretically [4][5][6][7][8] as well as numerically [9,10], leading to the derivation of the so-called resonance condition for the occurrence of third waves, i.e., the ratio of driving frequencies, the angle of intersection, and the combination of the incident and third wave modes. The third waves generated by the non-collinear interaction were experimentally observed by Rollins et al [11], and the influence of applied stress on the generation behavior of third wave was investigated by Hirao et al [12].…”

Analytical and numerical modeling of non-collinear shear wave mixing at an imperfect interface

“…Non-collinear shear wave mixing has been reported to exhibit potential for assessing the excess nonlinearity caused by both bulk material degradation [1][2][3][4] and interface imperfections between solids [5][6][7][8]. When this technique is used to assess bulk nonlinearity, certain phase-matching resonance conditions must be satisfied so that nonlinear mixing of the two non-collinear shear waves can generate a third longitudinal wave with frequency and wave vector equal to the sum of the frequencies and wave vectors of the two interacting shear waves [9][10][11][12].…”