Harmonic Generation at a Nonlinear Imperfect Joint of Plates by the S0 Lamb Wave Incidence

Abstract

Nonlinear interaction of Lamb waves with an imperfect joint of plates for the incidence of the lowest-order symmetric (S0) Lamb wave is investigated by perturbation analysis and time-domain numerical simulation. The imperfect joint is modeled as a nonlinear spring-type interface, which expresses interfacial stresses as functions of the displacement discontinuities. In the perturbation analysis, under the assumption of weak nonlinearity, the second-harmonic generation at the joint is examined in the frequency domain by the thin-plate approximation using extensional waves. As a result, the amplitude of the second-harmonic extensional wave is shown to be in good agreement with the result of the S0 mode in a low-frequency range. However, it is found that the thin-plate approximation does not reproduce the amplification of the second-harmonic S0 mode, which occurs due to the resonance of the joint. Furthermore, the time-domain analysis is performed by the elastodynamic finite integration technique (EFIT). When the amplitude of the incident wave is relatively large, the fundamental wave and the second harmonic exhibit different behavior from the results by the perturbation analysis. Specifically, if the incident amplitude is increased, the peak frequency of the second-harmonic amplitude becomes low. The transient behavior of the nonlinear interaction is also examined and discussed based on the results for the weak nonlinearity.

Second-harmonic generation of the lowest-order antisymmetric Lamb wave at a closed parallel crack

“…It can also be obtained as a limiting case of a thin nonlinear elastic interphase layer, as discussed by An et al 40 and Zhang et al 41 It has been used in the analysis of the second-harmonic generation at contacting interfaces for normally incident waves 28,30 and for more general situations. 36,42 Similar models can be found in other works 27,29,31 on the contact acoustic nonlinearity. For the sake of brevity, the nonlinear effects of the closed crack are solely represented by the term by 2 ðx 1 ; tÞ 2 on the right-hand side of Eq.…”

“…8 are scaled by the non-dimensional parameter bA 0 , as shown in Eq. (36). The actual magnitudes of the second-harmonic components, which depend on both these quantities and bA 0 , can be significantly large at the peaks.…”

“…[30][31][32] For Lamb waves, the reflection and transmission at an imperfect joint of plates [33][34][35] and a closed crack in a plate 15 have been studied based on linear spring-type interface models. Recently, Mori et al 36 analyzed the secondharmonic generation of the fundamental symmetric Lamb wave at a nonlinear spring-type joint between two plates both in frequency and time domains. For closed cracks in plates, however, it still remains as an intriguing issue to analyze the nonlinear behavior of Lamb waves based on such models.…”

Localization and Imaging of Micro-Cracks Using Nonlinear Lamb Waves with Imperfect Group-Velocity Matching

“…In addition, mode pair S0-s0 was also used to detect closed defects or imperfect bonding interfaces that open and close as the waves pass across them. Mori et al [20] explored nonlinear interaction of S0 mode Lamb wave with an imperfect joint of plates by perturbation analysis and numerical simulation. Zhao et al [21] performed numerical simulations on the propagation of S0 Lamb waves in thin plates with randomly distributed micro-cracks to study the behavior of nonlinear Lamb waves.…”