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This paper numerically and experimentally investigates the resonant behavior of one-way Lamb and SH (shear horizontal) mixing method in thin plates with quadratic nonlinearity. When the primary S

Using the nonlinear interaction effect between ultrasonic Lamb waves and microcracks to detect and locate microcracks has the advantages of fast detection speed and high sensitivity. In this paper, a method for microcrack localization based on cross-shaped sensor clusters in a plate is proposed by combining nonlinear ultrasonic Lamb wave technology and time difference of arrival (TDOA) technology. The antisymmetric (A0) mode at low frequency is chosen as the primary Lamb wave to simplify the complication of the dispersion and multi-mode properties of Lamb waves. The selected mode pair (A0-s0) weakens the influence of the cumulative growth effect of higher harmonics induced by the inherent material nonlinearity on the microcrack characteristic signals. Pulse inversion technique and cross correlation function are used to extract the TDOAs of the nonlinear characteristic signals including microcrack information. The cross-shaped sensor clusters approach proposed for the first time can achieve reliable and fast microcrack localization without being affected by the duration of the excitation signal, and a priori knowledge of group velocities of primary wave modes or generated harmonics. Experimental and numerical results validate the proposed method in isotropic and anisotropic plates. This paper provides a new idea for nonlinear ultrasonic nondestructive evaluation and structural health monitoring of microcracks in plates.

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.

The appropriate mode pairs of primary and double-frequency circumferential guided waves (CGWs) have been investigated and selected for generation of the cumulative second harmonics, which are applicable for quantitative assessment of damage/degradation in a circular tube. The selection criteria follow the requirements: the higher efficiency of cumulative second-harmonic generation (SHG) of primary CGW propagation, and the larger response sensitivity of cumulative SHG to material damage/degradation [characterized by variation in the third-order elastic (TOE) constants]. The acoustic nonlinearity parameter β of CGW propagation and the change rate of normalized β versus the TOE constants of tube material are, respectively, used to describe the efficiency of SHG and its response sensitivity to damage/degradation. Based on the selection criteria proposed, all the possible mode pairs of primary and double-frequency CGWs satisfying the phase velocity matching have been numerically examined. It has been found that there are indeed some mode pairs of CGW propagation with the larger values both of β and the change rate of normalized β versus the TOE constants. The CGW mode pairs found in this paper are of practical significance for quantitative assessment of damage/degradation in the circular tube.

The experimental observation of acoustic radiation induced static component (SC) generation by Lamb wave propagation in an elastic plate is first reported. An experimental approach to directly detect the generated SC of primary Lamb wave propagation in an elastic plate is proposed, where a low-frequency wedge transducer is used to detect the SC pulse generated by primary Lamb wave tone-burst that is excited by a high-frequency wedge transducer. The basic requirements are that the group velocity of primary Lamb wave needs to be equal to that of the s0 mode at zero frequency (i.e., the SC), and that the central frequency of the low-frequency wedge transducer needs to be near the center of the main lobe frequency range of the generated SC pulse. For this purpose, the S4 mode whose group velocity is equal to that of the generated SC is selected as the primary Lamb wave, and then the specific mode pair S4-s0 is focused and analyzed. Accompanying propagation of the S4 mode tone-burst, the generated SC pulse detected with the low-frequency wedge transducer is clearly observed. Through respectively measuring the amplitudes of the S4 mode and the generated SC for different spatial separation between the transmitting and receiving wedge transducers, the quantitative relationship of the relative nonlinear acoustic parameter with propagation distance is obtained. The experimental results show that the proposed approach can be used to directly detect the generated SC of Lamb wave propagation, and that the said SC does have a cumulative growth effect with propagation distance.

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.

Nonlinear guided wave has been recognized as a potential means to characterize the state of material microstructures in solids. However, nonlinear guided wave approaches based on second harmonic generation or combined harmonic generation induced by counter-directional wave mixing, are applicable only under the condition that transmitters and receivers are placed at two different ends of the tested structures. These approaches are not effective for characterization of the structures with only one accessible end. In this paper, modeling of the backward combined harmonic at difference frequency induced by one-way mixing of two primary co-directional guided waves is investigated in a circular pipe, where the transmitters and receivers are placed at the same end of the pipe. The backward combined harmonic, generated at difference frequency and propagating in the direction opposite to that of two primary co-directional guided waves, is successfully observed numerically. A strong frequency mixing response characterized by a cumulative growth effect of the generated backward combined harmonic is demonstrated. The use of the generated backward combined harmonic for localized material degradation characterization and location is numerically examined in the given pipe. The obtained results indicate that the use of the backward combined harmonic can locate and characterize the localized material degradations in the given pipe by controlling the mixing zone of two primary co-directional guided waves. This study provides a promising means for characterization of localized degradations in pipes.

When a longitudinal wave (bulk wave) propagates in elastic solids with randomly distributed micro-cracks, the acoustic nonlinear behavior including the zero-frequency component and higher harmonics can be generated due to the clapping and slipping behavior of micro-cracks. In this paper, the analytical solution based on the bi-linear stiffness model of micro-cracks and the numerical simulation with random micro-crack modeling are implemented to investigate the behavior of the zero-frequency component. The theoretical and numerical results both show that the zero-frequency component of bulk waves can be generated by the micro-cracks, which is more sensitive than the conventional second harmonics. Meanwhile, we find that the acoustic nonlinearity parameter based on the zero-frequency component increases linearly with the crack density, the length of the micro-crack region and the fundamental frequency in the low-frequency region. Moreover, the zero-frequency component of the reflected waves is also investigated, indicating it can be used to locate the micro-crack region.

This work investigates modeling of the frequency mixing response (FMR) induced by two counter-propagating Lamb waves with different frequencies in a two-layered plate, and then numerically simulates and analyzes the influences of interfacial properties on the effect of FMR. Based on a perturbation approach and a normal-mode-expansion technique for waveguide excitation, the second-order bulk driving forces and surface/interface stresses at the mixing frequency, originated from the interaction of two counter-propagating Lamb waves within the wave mixing zone, can be regarded as the excitation sources for generation of a series of combined harmonics. It is found that, under the internal resonance condition including the phase matching and nonzero energy flux, the magnitude of the combined harmonic generated increases with increase in the length of mixing zone of the two counter-propagating Lamb waves, and tends to be stable outside the wave mixing zone. Due to the relatively short mixing zone of the two counter-propagating Lamb waves, the effect of FMR has attracted considerable attention because it can enhance the accuracy of location of the local interfacial degradation in the given layered plate. Both the numerical analyses and finite element (FE) simulations performed show that the local interfacial degradation in the two-layered plate may be assessed and located by spatial scanning of wave mixing zone of the two counter-propagating Lamb waves. Through modeling and FE simulations, this paper provides an insight into the physical process of FMR of the two counter-propagating Lamb waves in a two-layered plate, and meanwhile shows a potential for assessment and location of the local interfacial degradation by using the effect of FMR of the two counter-propagating Lamb waves.

The effect of second-harmonic generation (SHG) by primary ultrasonic guided wave propagation is analyzed, where the nonlinear elastic, piezoelectric, and dielectric properties of the piezoelectric plate material are considered simultaneously. The formal solution of the corresponding second-harmonic displacement field is presented. Theoretical and numerical investigations clearly show that the SHG effect of primary guided wave propagation is highly sensitive to the electrical boundary conditions of the piezoelectric plate. The results obtained may provide a means through which the SHG efficiency of ultrasonic guided wave propagation can effectively be regulated by changing the electrical boundary conditions of the piezoelectric plate.

The feasibility of fatigue damage evaluation has been investigated using nonlinear Lamb waves with group-velocity mismatching. To choose an efficient mode pair, a parameter is proposed to quantify the efficiency of cumulative second-harmonic generation (SHG) of Lamb waves based on the normal modal analysis. Experiments and simulations are performed to verify the proposed parameter, which demonstrates that whether the matching condition of group velocity is satisfied or not, the efficiency of cumulative SHG increases with the order of Lamb mode for the five low-order Lamb waves investigated. Then, S3-s6 mode pair with group-velocity mismatching is chosen to characterize the fatigue damage of an aluminium alloy for the high efficiency of cumulative SHG. Results show that S3-s6 mode pair is sensitive to fatigue damage evolution and the integrated amplitude of second harmonics increases by nearly 300% with fatigue cycles. Nonlinear Lamb waves with group-velocity mismatching are validated to be a candidate to efficiently evaluate the fatigue damage.

The feasibility of using the nonlinear effect of primary Circumferential Guided Wave (CGW) propagation for assessing accumulated damage in circular tubes has been investigated. For a given circular tube, an appropriate mode pair of fundamental and double frequency CGWs is chosen to enable that the second harmonic of the primary wave mode can accumulate along the circumferential direction. After the given circular tube is subjected to compression-compression repeated loading for different numbers of loading cycles, the corresponding ultrasonic measurements are conducted. It is found that there is a direct correlation between the acoustic nonlinearity parameter measured with CGWs propagating through one full circumference and the level of accumulated damage in the circular tube. The experimental result obtained validates the feasibility for quantitative assessment of the accumulated damage in circular tubes using the effect of second-harmonic generation by CGW propagation.

A nonlinear constitutive relationship was established to investigate nonlinear behaviors of ultrasonic wave propagation in plastically damaged media based on analyses of mixed dislocation evolution. Finite element simulations of longitudinal wave propagation in plastically deformed martensite stainless steel were performed based on the proposed nonlinear constitutive relationship, in which the contribution of mixed dislocation to acoustic nonlinearity was considered. The simulated results were validated by experimental measurements of plastically deformed 30Cr2Ni4MoV martensite stainless steels. Simulated and experimental results both reveal a monotonically increasing tendency of the normalized acoustic nonlinearity parameter as a function of plastic strain. Microscopic studies revealed that the changes of the acoustic nonlinearity are mainly attributed to dislocation evolutions, such as dislocation density, dislocation length, and the type and fraction of dislocations during plastic loading.

The cumulative second-harmonic analysis of ultrasonic Lamb wave has been performed to study the precipitation kinetics and microvoid initiation of ferritic Cr-Ni alloy steel during the ageing process. Ageing of ferritic Cr-Ni alloy materials have been done at 1223 K and 1173 K for different degradation time intervals and air cooled. The results show that the normalized acoustic nonlinearity of Lamb wave increases with the formation of fine precipitates at the early stage of ageing till about 1000 h and keeps as a plateau with the precipitates dynamic balance for a long-term ageing, and then decreases gradually at the final holding time with the coarsening of precipitates and initiation of microvoids. The results also show that the variation of nonlinear Lamb wave follows the same trend as that of hardness in materials. Therefore, the cumulative second-harmonic of ultrasonic Lamb waves has been found to be strongly sensitive to the precipitates behavior and microstructure evolution during the thermal ageing of ferritic Cr-Ni alloy steel.

A nonlinear Lamb wave approach is presented for characterizing the surface properties of a solid plate. This characterization approach is useful for some practical situations where ultrasonic transducers cannot touch the surfaces to be inspected, e.g. the inside surfaces of sealed vessels. In this paper, the influences of changes in the surface properties of a solid plate on the effect of second-harmonic generation by Lamb wave propagation were analyzed. A surface coating with the different properties was used to simulate changes in the surface properties of a solid plate. When the areas and thicknesses of coatings on the surface of a given solid plate changed, the amplitude–frequency curves both of the fundamental waves and the second harmonics by Lamb wave propagation were measured under the condition that Lamb waves had a strong nonlinearity. It was found that changes in the surface properties might clearly affect the efficiency of second-harmonic generation by Lamb wave propagation. The Stress Wave Factors (SWFs) in acousto-ultrasonic technique were used for reference, and the definitions of the SWFs of Lamb waves were introduced. The preliminary experimental results showed that the second-harmonic SWF of Lamb wave propagation could effectively be used to characterize changes in the surface properties of the given solid plate.