Particle distributions in Lamb wave based acoustofluidics

Acoustic streaming enabled by a Lamb wave resonator(LWR)is efficient for particle trapping and enrichment in microfluidic channels.However,because Lamb waves combine the features of bulk acoustic waves and surface acoustic waves,the resulting acoustic streaming in the LWR occurs in multiple planes,and the particle flow behavior in this acoustofluidic system is largely unknown.Reported here are numerical simulations and laboratory experiments conducted to investigate the boundary conditions for particle motion inside a microvortex induced by an LWR.Upon dynamic capture,the particles’trajectories become orbital paths within an acoustic vortex.The suspended particles encounter two distinct acoustic phenomena,i.e.,the drag force resulting from acoustic streaming and the acoustic radiation force,which exert forces in various directions on the particles.When the acoustic radiation force and the fluid drag force are dominant for large and small particles in a mixed solution,respectively,the large particles reside within the vortex while the small particles remain at its periphery.Conversely,when the acoustic radiation force is dominant for both types of particles,the distribution pattern is reversed.

Application of Nonlinear Lamb Wave Mixing Method for Residual Stress Measurement in Metal Plate

Harmonic nonlinear ultrasound can offer high sensitivity for residual stress measurements;however,it cannot be used for local stress measurements at a point in space and exhibits nonlinear distortions in the experimental system.This paper presents a feasibility study on the measurement of residual stress in a metal plate using a nonlinear Lamb wave-mixing technique.The resonant conditions for two Lamb waves to generate a mixing frequency wave are obtained via theoretical analysis.Finite element simulations are performed to investigate the nonlinear interactions between the two Lamb waves.Results show that two incident A0 waves interact in regions of material nonlinearity and generate a rightward S0 wave at the sum frequency.Residual stress measurement experiments are conducted on steel plate specimens using the collinear Lamb wave-mixing technique.By setting different delays for two transmitters,the generated sum-frequency component at different spatial locations is measured.Experimental results show that the spatial distribution of the amplitude of the sum-frequency component agrees well with the spatial distribution of the residual stress measured using X-rays.The proposed collinear Lamb wave-mixing method is effective for measuring the distribution of residual stress in metal plates.

Micro-Sized Pinhole Inspection with Segmented Time Reversal and High-Order Modes Cluster Lamb Waves Based on EMATs

Pinhole corrosion is difficult to discover through conventional ultrasonic guided waves inspection,particularly for micro-sized pinholes less than 1 mm in diameter.This study proposes a new micro-sized pinhole inspection method based on segmented time reversal(STR)and high-order modes cluster(HOMC)Lamb waves.First,the principle of defect echo enhancement using STR is introduced.Conventional and STR inspection experiments were conducted on aluminum plates with a thickness of 3 mm and defects with different diameters and depths.The parameters of the segment window are discussed in detail.The results indicate that the proposed method had an amplitude four times larger than of conventional ultrasonic guided waves inspection method for pinhole defect detection and could detect micro-sized pinhole defects as small as 0.5 mm in diameter and 0.5 mm in depth.Moreover,the segment window location and width(5-10 times width of the conventional excitation signal)did not affect the detection sensitivity.The combination of low-power and STR is more conducive to detection in different environments,indicating the robustness of the proposed method.Compared with conventional ultrasonic guided wave inspection methods,the proposed method can detect much smaller defect echoes usually obscured by noise that are difficult to detect with a lower excitation power and thus this study would be a good reference for pinhole defect detection.

New Developments in Structural Health Monitoring Based on Diagnostic Lamb Wave

Structure health monitoring based on diagnostic Lamb waves has been found to be one of the most promising techniques recently. This paper has a brief review of the new developments on this method including the basic novel of the method, fundamentals and mathematics of Lamb wave propagation, narrowband and wideband Lamb wave excitation methods, optimization of excitation factors and diagnostic Lamb wave interpretation methods.

Quantitative damage imaging using Lamb wave diffraction tomography

In this paper, we investigate the diffraction tomography for quantitative imaging damages of partly through-thickness holes with various shapes in isotropic plates by using converted and non-converted scattered Lamb waves generated nu- merically. Finite element simulations are carried out to provide the scattered wave data. The validity of the finite element model is confirmed by the comparison of scattering directivity pattern （SDP） of circle blind hole damage between the finite element simulations and the analytical results. The imaging method is based on a theoretical relation between the one-dimensional （1D） Fourier transform of the scattered projection and two-dimensional （2D） spatial Fourier transform of the scattering object. A quantitative image of the damage is obtained by carrying out the 2D inverse Fourier transform of the scattering object. The proposed approach employs a circle transducer network containing forward and backward projections, which lead to so-called transmission mode （TMDT） and reflection mode diffraction tomography （RMDT）, respectively. The reconstructed results of the two projections for a non-converted SO scattered mode are investigated to illuminate the influence of the scattering field data. The results show that Lamb wave diffraction tomography using the combination of TMDT and RMDT improves the imaging effect compared with by using only the TMDT or RMDT. The scattered data of the converted A0 mode are also used to assess the performance of the diffraction tomography method. It is found that the circle and elliptical shaped damages can still be reasonably identified from the reconstructed images while the reconstructed results of other complex shaped damages like crisscross rectangles and racecourse are relatively poor.

Lamb wave signal selective enhancement by an improved design of meander-coil electromagnetic acoustic transducer

In this paper, we investigate a method of selectively enhancing the single mode signal of a Lamb wave by using a meander-coil electromagnetic acoustic transducer （EMAT） with a new magnetic configuration. We use the Lamb antisym- metric （A0） mode and symmetric （SO） mode as an example for analysis. The analytical expression of the magnitude of the spatial Fourier transform of the Lorentz force generated by different meander coils is used to determine the optimal driving frequency for single mode generation. The numerical calculation is used to characterize the new magnetic configuration and the conventional EMAT magnet. Experimental examinations of each meander coil in combination with the conventional and new magnetic configuration show that the Lamb wave signal can be selectively enhanced by choosing the appropriate driving frequency and coil parameters through using the improved meander-coil EMAT.

Micro-crack detection of nonlinear Lamb wave propagation in three-dimensional plates with mixed-frequency excitation

We propose a nonlinear ultrasonic technique by using the mixed-frequency signals excited Lamb waves to conduct micro-crack detection in thin plate structures.Simulation models of three-dimensional(3D)aluminum plates and composite laminates are established by ABAQUS software,where the aluminum plate contains buried crack and composite laminates comprises cohesive element whose thickness is zero to simulate delamination damage.The interactions between the S0 mode Lamb wave and the buried micro-cracks of various dimensions are simulated by using the finite element method.Fourier frequency spectrum analysis is applied to the received time domain signal and fundamental frequency amplitudes,and sum and difference frequencies are extracted and simulated.Simulation results indicate that nonlinear Lamb waves have different sensitivities to various crack sizes.There is a positive correlation among crack length,height,and sum and difference frequency amplitudes for an aluminum plate,with both amplitudes decreasing as crack thickness increased,i.e.,nonlinear effect weakens as the micro-crack becomes thicker.The amplitudes of sum and difference frequency are positively correlated with the length and width of the zero-thickness cohesive element in the composite laminates.Furthermore,amplitude ratio change is investigated and it can be used as an effective tool to detect inner defects in thin 3D plates.

Second Harmonic Generation of Lamb Wave in Numerical Perspective

The influences of phase and group velocity matching on cumulative second harmonic generation of Lamb waves are investigated in numerical perspective. Finite element simulations of nonlinear Lamb wave propagation are performed for Lamb wave mode pairs with exact and approximate phase velocity matching, with and without group velocity matching, respectively. The evolution of time-domain second harmonic Lamb waves is analyzed with the propagation distance. The amplitudes of primary and second harmonic waves are calculated to characterize the acoustic nonlinearity. The results verify that phase velocity matching is necessary for generation of the cumulative second harmonic Lamb wave in numerical perspective, while group velocity matching is demonstrated to not be a necessary condition.

Cumulative second-harmonic generation of Lamb waves propagating in a two-layered solid plate

The physical process of cumulative second-harmonic generation of Lamb waves propagating in a two-layered solid plate is presented by using the second-order perturbation and the technique of nonlinear reflection of acoustic waves at an interface. In general, the cumulative second-harmonic generation of a dispersive guided wave propagation does not occur. However, the present paper shows that the second-harmonic of Lamb wave propagation arising from the nonlinear interaction of the partial bulk acoustic waves and the restriction of the three boundaries of the solid plates does have a cumulative growth effect if some conditions are satisfied. Through boundary condition and initial condition of excitation, the analytical expression of cumulative second-harmonic of Lamb waves propagation is determined. Numerical results show the cumulative effect of Lamb waves on second-harmonic field patterns.

Time-domain analysis of second-harmonic generation of primary Lamb wave propagation in an elastic plate

Within the second-order perturbation approximation, this paper investigates the physical process of generation of the time-domain second harmonic by a primary Lamb wave waveform in an elastic plate. The present work is performed based on the preconditions that the phase velocity matching is satisfied and that the transfer of energy from the primary Lamb wave to the double frequency Lamb wave is not zero. It investigates the influences of the difference between the group velocities of the primary Lamb wave and the double frequency Lamb wave, the propagation distance and the duration of the primary Lamb wave waveform on the envelope shape of the time-domain second harmonic. It finds that the maximum magnitude of the envelope of the second-harmonic waveform can grow within some propagation distance even if the condition of group velocity matching is not satisfied. Our analyses also indicate that the maximum magnitude of the envelope of the second-harmonic waveform is kept constant beyond a specific propagation distance. Furthermore, it concludes that the integration amplitude of the time-domain second-harmonic waveform always grows with propagation distance within the second-order perturbation. The present research yields new physical insight not previously available into the effect of generation of the time-domain second harmonic by propagation of a primary Lamb wave waveform.

Location of micro-cracks in plates using time reversed nonlinear Lamb waves

A promising tool to detect micro-cracks in plate-like structures is used for generating higher harmonic Lamb waves.In this paper,a method combining nonlinear S0 mode Lamb waves with time reversal to locate micro-cracks is presented and verified by numerical simulations.Two different models,the contact acoustic nonlinearity(CAN)model and the Preisach-Mayergoyz(PM)model,are used to simulate a localized damage in a thin plate.Pulse inversion method is employed to extract the second and fourth harmonics from the received signal.Time reversal is performed to compensate the dispersion of S0 mode Lamb waves.Consequently,the higher harmonics generated from the damaged area can be refocused on their source.By investigating the spatial distribution of harmonic wave packets,the location of micro-cracks will be revealed.The numerical simulations indicate that this method gives accurate locations of the damaged area in a plate.Furthermore,the PM model is proved to be a suitable model to simulate the micro-cracks in plates for generation of higher harmonics.

Microcrack localization using a collinear Lamb wave frequency-mixing technique in a thin plate

A novel Lamb wave frequency-mixing technique is proposed for locating microcracks in a thin plate,which does not require the resonance condition of Lamb wave mixing and can accurately locate the microcracks through only one-time sensing.Based on the bilinear stress-strain constitutive model,a two-dimensional finite element(FE)model is built to investigate the frequency-mixing response induced by the interaction between two primary Lamb waves and a microcrack.When two primary Lamb waves of A0 and S0 modes with different frequencies excited on the same side of the plate simultaneously impinge on the examined microcrack,under the modulation of the contact acoustic nonlinearity,the microcrack itself can be deemed as the secondary sound source and it will radiate the Lamb waves of new combined frequencies.Based on the time of flight of the generated A0 mode at difference frequency,an indicator named normalized amplitude index(NAI)is defined to directly locate the multi-microcracks in the given plate.It is found that the number and location of the microcracks can be intuitively visualized by using the NAI based frequency-mixing technique.It is also demonstrated that the proposed frequency mixing technique is a promising approach for the microcrack localization.

FOULING DETECTION IN FOOD VESSELS USING INTERDIGITAL LAMB WAVE TRANSDUCER

Lamb waves are used to detect fouling in food vessels. The propagation of the Lamb waves in plates exhibits many modes and dispersion characteristics, which have great influence on fouling detection. The relative distribution of the in-plane and out-of-plane displacement of the mode across the thickness of the plate will determine the sensitivity of the mode to a particular loading condition. By considering the dispersion and multi-mode characteristics of guided waves, an interdigital polyvi- nylidene fluoride （PVDF） transducer is designed to realize the mode selection of gnided waves, and a single a0 mode is used for guided wave detection. Fouling detection experiments are conducted in the laboratory using epoxy adhesive on a thin plate. Using the interdigital PVDF transducer, three fouled areas are detected. Using one of the time-frequency analysis methods, the waveforms are further processed. This also demonstrates the validity of this method of fouling detection.

Interface-guided mode of Lamb waves in a two-dimensional phononic crystal plate

We investigate the interface-guided mode of Lamb waves in a phononic crystal heterostructures plate, which is com- posed of two different semi-infinite phononic crystal （PC） plates. The interface-guided modes of the Lamb wave can be obtained by the lateral lattice slipping or by the interface longitudinal gliding. Significantly, it is observed that the condition to generate the interface-guided modes of the Lamb wave is more demanding than that of the studied fluid-fluid system. The interface-guided modes are strongly affected not only by the relative movement of the two semi-infinite PCs but also by the thickness of the PC plate.

A time reversal damage imaging method for structure health monitoring using Lamb waves

This paper investigates the Lamb wave imaging method combining time reversal for health monitoring of a metallic plate structure. The temporal focusing effect of the time reversal Lamb waves is investigated theoretically. It demonstrates that the focusing effect is related to the frequency dependency of the time reversal operation. Numerical simulations are conducted to study the time reversal behaviour of Lamb wave modes under broadband and narrowband excitations. The results show that the reconstructed time reversed wave exhibits close similarity to the reversed narrowband tone burst signal validating the theoretical model. To enhance the similarity, the cycle number of the excited signal should be increased. Experiments combining finite element model are then conducted to study the imaging method in the presence of damage like hole in the plate structure. In this work, the time reversal technique is used for the recompression of Lamb wave signals. Damage imaging results with time reversal using broadband and narrowband excitations are compared to those without time reversal. It suggests that the narrowband excitation combined time reversal can locate and determine the size of structural damage more precisely, but the cycle number of the excited signal should be chosen reasonably.

Piezoelectric transducer parameter selection for exciting a single mode from multiple modes of Lamb waves

Excitation and propagation of Lamb waves by using rectangular and circular piezoelectric transducers surface- bonded to an isotropic plate are investigated in this work. Analytical stain wave solutions are derived for the two transducer shapes, giving the responses of these transducers in Lamb wave fields. The analytical study is supported by a numericM simulation using the finite element method. Symmetric and antisymmetric components in the wave propagation responses are inspected in detail with respect to test parameters such as the transducer geometry, the length and the excitation frequency. By placing only one piezoelectric transducer on the top or the bottom surface of the plate and weakening the strength of one mode while enhancing the strength of the other modes to find the centre frequency, with which the peak wave amplitude ratio between the SO and A0 modes is maximum, a single mode excitation from the multiple modes of the Lamb waves can be achieved approximately. Experimental data are presented to show the validity of the analyses. The results are used to optimize the Lamb wave detection system.

Propagation Properties of Backward Lamb Waves in Plate Investigated by Dynamic Photoelastic Technique

The dynamic photoelastic technique is employed to visualize and quantify the propagation properties of backward Lamb waves in a plate. Higher energy leakage of second-order symmetric backward wave mode S2b in contrast to third-order anti-symmetric backward mode A3b is shown by the dispersion curve of a plate immersed in water, and then verified by experiments. To avoid the considerable high leakage, the plate is placed in air, both group and phase velocities of modes S2b and A3b in the glass plate are experimentally measured. In comparison with the theoretical values, less than 5% errors are found in experiments.

Selective generation of ultrasonic Lamb waves by electromagnetic acoustic transducers

In this paper, we describe a modal expansion approach for the analysis of the selective generation of ultrasonic Lamb waves by electromagnetic acoustic transducers （EMATs）. With the modal expansion approach for waveguide excitation, an analytical expression of the Lamb wave＇s mode expansion coefficient is deduced, which is related to the driving frequency and the geometrical parameters of the EMAT＇s meander coil, and lays a theoretical foundation for exactly analyzing the selective generation of Larnb waves with EMATs. The influences of the driving frequency on the mode expansion coefficient of ultrasonic Lamb waves are analyzed when the EMAT＇s geometrical parameters are given. The numerical simulations and experimental examinations show that the ultrasonic Lamb wave modes can be effectively regulated （strengthened or restrained） by choosing an appropriate driving frequency of EMAT, with the geometrical parameters given. This result provides a theoretical and experimental basis for selectively generating a single and pure Lamb wave mode with EMATs.

Analysis of Second-Harmonic Generation of Low-Frequency Dilatational Lamb Waves in a Two-Layered Composite Plate

We analyze the effect of second-harmonic generation（SHG） of primary Lamb wave propagation in a two-layered composite plate, and then investigate the influence of interfacial properties on the said effect at low frequency. It is found that changes in the interfacial properties essentially affect the dispersion relation and then the maximum cumulative distance of the double-frequency Lamb wave generated. This will remarkably influence the efficiency of SHG. To overcome the complications arising from the inherent dispersion and multimode natures in analyzing the SHG effect of Lamb waves, the present work focuses on the analysis of the SHG effect of low-frequency dilatational Lamb wave propagation. Both the numerical analysis and finite element simulation indicate that the SHG effect of low-frequency dilatational Lamb wave propagation is found to be much more sensitive to changes in the interfacial properties than primary Lamb waves. The potential of using the SHG effect of low-frequency dilatational Lamb waves to characterize a minor change in the interfacial properties is analyzed.

Defect detection in brazed weldment with lattice structure using ultrasonic Lamb wave technique

In this paper, defects detection in brazed weldment with lattice structure is studied using ultrasonic Lamb wave. Based on the ultrasonic guided wave theory, the frequency dispersion curves for phase and group velocity of I Cr18Ni9Ti are obtained by solving the Rayleigh-Lamb equation. The incident angles of different modes are determined through theoretical calculation and experimental analyses. Artificial defects of through-wall slots with different dimensions are made and tested. Experimental scattering effects of the fundamental symmetric mode S2 and asymmetric modes A1 and A0 are analysed and compared. The results show that mode Ao is suitable for detecting artificial defect, and the amplitude of the received signals are in good agreement with the defect size. Brazed weldment specimen containing lack of brazing with certain dimensions is made. Using the same methodology, scattering effects produced by weld defects are measured. The results show that the clutter wave brought about by the filler metal will certainly disturbs the identification of defect signal. But, when the defect is 3.0 mm in width, the presented mode Ao could be used potentially.