Interaction of Lamb Wave Modes with Weak Material Nonlinearity: Generation of Symmetric Zero-Frequency Mode

Investigation of the Zero-Frequency Component of Nonlinear Lamb Waves in a Symmetrical Undulated Plate

When an ultrasonic pulse propagates in a thin plate, nonlinear Lamb waves with higher harmonics and a zero-frequency component (ZFC) will be generated because of the nonlinearity of materials. The ZFC, also known as the static displacement or static component, has its unique application on the evaluation of early-stage damages in the elastic symmetrical undulated plate. In this study, analysis of the excitation mechanism of the ZFC and the second harmonic component (SHC) was theoretically and numerically investigated, and the material early-stage damage of a symmetrical undulated was characterized by studying the propagation of nonlinear Lamb waves. Both the ZFC and SHC can be effectively employed in monitoring the material damages of the undulated plate in its early stage. However, several factors must be considered for the propagation of the SHC in an undulated plate because of the geometric curvature and interference between the second harmonics during propagation, preventing efficient application of this technique. If the fundamental wave can propagate in the plate regardless of the plate boundary conditions, an accumulative effect always exists for the ZFC in a thin plate, indicating that the ZFC is independent of the structural geometry. This study reveals that the ZFC-based inspection technique is more efficient and powerful in characterizing the damages of a symmetrical undulated plate in the early stage of service compared to the second harmonic method.

Characterization of interfacial property of a two-layered plate using a nonlinear low-frequency Lamb wave approach

This work investigates the feasibility of using a nonlinear low-frequency Lamb wave approach for characterizing the interfacial property of a two-layered plate. Compared with the case of the exact phase-velocity matching, the approximate phase-velocity matching in the low-frequency region can still guarantee the cumulative second-harmonic generation (SHG) of primary Lamb wave propagation, which overcomes the drawbacks arising from the inherent dispersion and multimode features of Lamb wave propagation. For a given two-layered plate, the appropriate mode pair at low frequency consisting of primary Lamb wave and double-frequency Lamb wave (DFLW), which satisfies the approximate phase-velocity matching and nonzero energy flux, is selected to ensure that the amplitude of the generated second harmonic grows within the maximum cumulative distance (MCD). Meanwhile, the numerical analyses indicate that the variation of the SHG efficiency is maximized at the MCD during the interfacial degradation. Using the nonlinear ultrasonic measurement-based experimental setup, the time-domain signal of the second harmonic generated at different propagation distances is conveniently extracted, and then the relative nonlinear acoustic parameter curve consistent with the theoretical prediction is obtained. For examining the influence of interfacial property on the SHG effect of low-frequency Lamb wave propagation, the different annealing cycles of the thin adhesive layer (acrylics) are used to simulate minor changes in the interfacial property of the given two-layered plate. It is found that the relative nonlinear acoustic parameter at the MCD decreases monotonically and sensitively with the increment of annealing cycle number, which verifies the quantitative correlation between the SHG efficiency of low-frequency Lamb wave propagation and the degree of the interfacial degradation. The consistency between the numerical analysis and the experimental measurement shows the potential of using the SHG effect of low-frequency Lamb wave propagation to characterize a minor change in the interfacial properties of a layered composite plate.

Microcrack localization based on static component induced by a primary A0 Lamb wave in a thin plate

A microcrack localization method based on a static component (SC) induced by a primary A0 Lamb wave is proposed. Based on the bilinear stress-strain constitutive model, a two-dimensional finite element model is built to investigate the interaction between microcracks and Lamb waves. The A0 Lamb wave at low frequency is selected to be the primary Lamb wave, which is beneficial to microcracks localization. Based on the time of flight of the generated SC pulse, an indicator named normalized amplitude index is defined for finding the location and number of microcracks. Simulation results show that one or multiple microcracks can be effectively located.

Modeling and simulation of static component generation of Lamb wave propagation in a layered plate

Modeling of the acoustic-radiation-induced static component (SC) generation of primary Lamb wave tone burst propagating in a layered plate is conducted. Accompanying the propagation of primary Lamb wave tone burst, there are the finite-duration SC bulk driving force in the interior of the layered plate, and the finite-duration SC traction stress on each surface/interface. According to the modal analysis approach for waveguide excitation, the function of the finite-duration SC bulk driving force and traction stress is to generate the finite-duration SC of primary Lamb wave tone burst. Compared with the second harmonic (SH) generation of Lamb wave propagation in a layered plate, the phase velocity matching is no longer required for the generation of the SC with a cumulative growth effect. Based on modeling of the finite-duration SC generation, it is found that the integrated amplitude of the finite-duration SC generated by propagation of the primary Lamb wave tone burst does grow with propagation distance. Meanwhile, the numerical analyses and the finite element (FE) simulations are conducted to investigate the effect of the said SC generation. It is found that, although the interfacial layer of the layered plate considered is quite thin compared with the upper and lower layers, the numerical analyses indicate that the influence of the interfacial property on the cumulative growth effect of the SC of primary Lamb wave is significant. Furthermore, the FE simulations demonstrate that the cumulative SC of primary Lamb wave tone burst will exhibit a monotonic and sensitive response to the degree of interfacial degradation. This investigation provides an physical insight not previously available into the process of the SC generation of Lamb wave propagation in a layered plate.

Static component generation and measurement of nonlinear guided waves with group velocity mismatch

This study focuses on static component generation (SCG) and its measurement wherein a group velocity mismatch (GVM) exists between the primary guided wave and the generated static component (SC). The SCGs by primary S0, A0, and SH0 waves are investigated. It is confirmed that the SCs are S0 mode. The GVM causes the temporal waveforms of the SCs to tend to increase in width with propagation distance. A feasible method is proposed accordingly for measurement of SCG with GVM using only lead zirconic titanate based transducers, wherein the SCs generated by two counter-propagating primary waves are modulated and superposed on each other.

Experimental and Numerical Study of Nonlinear Lamb Waves of a Low-Frequency S₀ Mode in Plates with Quadratic Nonlinearity

This paper investigates the propagation of low-frequency S₀ mode Lamb waves in plates with quadratic nonlinearity through numerical simulations and experimental measurements. Both numerical and experimental results manifest distinct ultrasonic nonlinear behavior which is mainly presented by the second harmonics. Meanwhile, we find that both the acoustic nonlinearity parameter and dispersion distance show the exponential decay trend with the increase of frequency-thickness. Moreover, the results reveal that the frequency is key to affect the acoustic nonlinearity parameter and dispersion distance with the same frequency-thickness. This study theoretically and experimentally reveals that nonlinear Lamb waves of the low-frequency S₀ mode are feasible to quantitatively identify material weak nonlinearity in plates.