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Abstract Ultrasonic imaging is crucial in the fields of biomedical engineering for its deep penetration capabilities and non-ionizing nature. However, traditional techniques heavily rely on impedance differences within objects, resulting in poor contrast when imaging acoustically transparent targets. Here, we propose a compact spatial differentiator for underwater isotropic edge-enhanced imaging, which enhances the imaging contrast without the need for contrast agents or external physical fields. This design incorporates an amplitude meta-grating for linear transmission along the radial direction, combined with a phase meta-grating that utilizes focus and spiral phases with a first-order topological charge. Through theoretical analysis, numerical simulations, and experimental validation, we substantiate the effectiveness of our technique in distinguishing amplitude objects with isotropic edge enhancements. Importantly, this method also enables the accurate detection of both phase objects and artificial biological models. This breakthrough creates new opportunities for applications in medical diagnosis and nondestructive testing.

The imaging detection of ultrasonic guided waves in plates using arc sparse arrays is highly significant for weld scattering conditions. A novel approach for detecting welded plate structures using the left rank of ultrasonic guided waves in arc sparse arrays was proposed. The relationship between the receiving matrix and the left rank was analyzed, along with the connection between the arc sparse array with the left rank and the receiving aperture. The imaging mechanism of the ultrasonic guided waves in arc sparse arrays with left rank under weld scattering conditions was investigated. The results of imaging experiments demonstrated a downward trend in the gray and background gray of the multi-frame images. As the left rank reaches approximately 64% of the full rank, the slope of the image gray and background gray decreases gradually, leading to the appearance of an inflection point. With an increasing signal-to-noise ratio curve, the imaging improved during the multi-frame imaging process of ultrasonic guided waves for the arc sparse arrays with left rank under weld scattering conditions. This research showed that the multi-frame imaging of ultrasonic guided waves in welded structural plates using arc sparse arrays with left rank effectively characterized scattering information with millimeter-scale wavelength size. The experimental results validated the feasibility of the theoretical analysis. This research provides a crucial foundation for the further exploration and application of the multi-frame imaging detection of ultrasonic guided waves using irregular arrays in welded structural plates.

Nonlinear guided elastic waves have attracted extensive attention owing to their high sensitivity to microstructural changes. However, based on the widely used second harmonics, third harmonics and static components, it is still difficult to locate the micro-defects. Perhaps the nonlinear mixing of guided waves can solve these problems since their modes, frequencies and propagation direction can be flexibly selected. Note that the phenomena of phase mismatching usually occur due to the lack of precise acoustic properties for the measured samples, and they may affect the energy transmission from the fundamental waves to second-order harmonics as well as reduce the sensitivity to micro-damage. Therefore, these phenomena are systematically investigated to more accurately assessing the microstructural changes. It is theoretically, numerically, and experimentally found that the cumulative effect of difference- or sum-frequency components will be broken by the phase mismatching, accompanied by the appearance of the beat effect. Meanwhile, their spatial periodicity is inversely proportional to the wavenumber difference between fundamental waves and difference- or sum-frequency components. The sensitivity to micro-damage is compared between two typical mode triplets that approximately and exactly meet the resonance conditions, and the better one is utilized for assessing the accumulated plastic deformations in the thin plates.

The generation of second- and third-order combined harmonics induced by the interaction of two primary Lamb waves with different frequencies has been analyzed theoretically and observed experimentally in our previous research [W. Li et al., J. Appl. Phys. 124, 044901 (2018)]. However, only third-order combined harmonics were observed experimentally because in the experimental investigations, the conditions for both synchronism and the symmetric feature were not satisfied simultaneously for the generation of the second-order combined harmonics. In this paper, first, the numerical perspective of the second-order combined harmonic generation by the collinear interaction of two primary Lamb waves with different frequencies in an isotropic and homogeneous plate is investigated. The results indicate that the synchronism and symmetric feature of two primary Lamb waves selected significantly affect the generation of second-order combined harmonics at the mixing frequencies. Next, an experimental scheme is proposed to measure the second-order combined harmonics predicted theoretically and numerically, through which it is found that the experimental results agree well with that of the theoretical and numerical predictions. The numerical and experimental results in this paper provide a clear physical insight, not previously available, into the second-order combined harmonic generation induced by the collinear interaction of two primary ultrasonic Lamb waves.

Metals which are widely used in many types of industries are usually subjected to fatigue and surface corrosion. There is a demand to detect the surface damage caused by fatigue and corrosion at an early stage to ensure the structural integrity. In this paper, a novel nonlinear ultrasonic technique based on the measure of third-order combined harmonic generation, is proposed to detect and locate the surface damage in 6061 aluminum alloy. Third-order combined harmonic generation caused by non-collinear mixing of one longitudinal wave and one transverse wave at different frequencies, is firstly analyzed and experimentally observed. An experimental procedure of nonlinear scanning is proposed for the damage detection and location by checking the variation of frequency nonlinear response. The correlations of nonlinear frequency mixing responses and surface damage in the specimens are obtained. Results show that the nonlinear response caused by fatigue damage and surface corrosion can be identified and located by this method. In addition, this approach can exclude the nonlinearity induced by the instruments and simplify the signal processing.

Human tumors exhibit plasticity and evolving capacity over time. It is difficult to study the mechanisms of how tumors change over time in human patients, in particular during the early stages when a few oncogenic cells are barely detectable. Here, we used a Drosophila tumor model caused by loss of scribble (scrib), a highly conserved apicobasal cell polarity gene, to investigate the spatial-temporal dynamics of early tumorigenesis events. The fly scrib mutant tumors have been successfully used to model many aspects of tumorigenesis processes. However, it is still unknown whether Drosophila scrib mutant tumors exhibit plasticity and evolvability along the temporal axis. We found that scrib mutant tumors displayed different growth rates and cell cycle profiles over time, indicative of a growth arrest-to-proliferation transition as the scrib mutant tumors progress. Longitudinal bulk and single-cell transcriptomic analysis of scrib mutant tumors revealed that the MAPK pathway, including JNK and ERK signaling activities, showed quantitative changes over time. We found that high JNK signaling activity caused G2/M cell cycle arrest in early scrib mutant tumors. In addition, JNK signaling activity displayed a radial polarity with the JNKhigh cells located at the periphery of scrib mutant tumors, providing an inherent mechanism that leads to an overall decrease in JNK signaling activity over time. We also found that ERK signaling activity, in contrast to JNK activity, increased over time and promoted growth in late-stage scrib mutant tumors. Furthermore, high JNK signaling activity repressed ERK signaling activity in early scrib mutant tumors. Together, these data demonstrate that dynamic MAPK signaling activity, fueled by intratumor heterogeneity derived from tissue topological differences, drives a growth arrest-to-proliferation transition in scrib mutant tumors. This article has an associated First Person interview with the joint first authors of the paper.

This study experimentally and numerically investigated the nonlinear behavior of the resonant bulk waves generated by the two-way collinear mixing method in 5052 aluminum alloy with micro-crack damage. When the primary longitudinal and transverse waves mixed in the micro-crack damage region, numerical and experimental results both verified the generation of resonant waves if the resonant condition ωL/ωT=2κ/(κ−1) was satisfied. Meanwhile, we found that the acoustic nonlinearity parameter (ANP) increases monotonously with increases in micro-crack density, the size of the micro-crack region, the frequency of resonant waves and friction coefficient of micro-crack surfaces. Furthermore, the micro-crack damage in a specimen generated by low-temperature fatigue experiment was employed. It was found that the micro-crack damage region can be located by scanning the specimen based on the two-way collinear mixing method.

In this paper, characterization of the orientation of a microcrack is quantitatively investigated using the directivity of second harmonic radiated by the secondary sound source (SSS) induced by the nonlinear interaction between an incident ultrasonic transverse wave (UTW) and a microcrack. To this end, a two-dimensional finite element (FE) model is established based on the bilinear stress–strain constitutive relation. Under the modulation of contact acoustic nonlinearity (CAN) to the incident UTW impinging on the microcrack examined, the microcrack itself is treated as a SSS radiating the second harmonic. Thus, the directivity of the second harmonic radiated by the SSS is inherently related to the microcrack itself, including its orientation. Furthermore, the effects of the stiffness difference between the compressive and tensile phases in the bilinear stress–strain model, and the UTW driving frequency, as well as the radius of the sensing circle on the SSS directivity are discussed. The FE results show that the directivity pattern of the second harmonic radiated by the SSS is closely associated with the microcrack orientation, through which the microcrack orientation can be characterized without requiring a baseline signal. It is also found that the SSS directivity varies sensitively with the driving frequency of the incident UTW, while it is insensitive to the stiffness difference between the compressive and tensile phases in the bilinear stress–strain model and the radius of the sensing circle. The results obtained here demonstrate that the orientation of a microcrack can be characterized using the directivity of the SSS induced by the interaction between the incident UTW and the microcrack.

Lamb wave-based structural health monitoring techniques have the ability to scan a large area with relatively few sensors. Lamb wave imaging is a signal processing strategy that generates an image for locating scatterers according to the received Lamb waves. This paper presents a Lamb wave imaging method, which is formulated as a weighted structured sparse reconstruction problem. A dictionary is constructed by an analytical Lamb wave scattering model and an edge reflection prediction technique, which is used to decompose the experimental scattering signals under the constraint of weighted structured sparsity. The weights are generated from the correlation coefficients between the scattering signals and the predicted ones. Simulation and experimental results from an aluminum plate verify the effectiveness of the present method, which can generate images with sparse pixel values even with very limited number of sensors.

Due to the dispersive and multimode natures, only nonlinear Lamb waves with exact phase-velocity matching were generally used in previous studies to evaluate the evenly distributed microstructural evolution in the incipient stage of material degradation, because of the cumulative generation of second harmonics, which was also found within a significant propagation distance for mode pair S0-s0 with quasi phase-velocity matching at low frequency. To explore the feasibility of fatigue damage evaluation by using this mode pair and fully utilize its unique merits, the cumulative second harmonic analysis was performed on aluminum alloy specimens with various material damage produced by the continuous low cycle fatigue tests. Similar to mode pair S1-s2 with exact phase-velocity matching, a mountain shape curve between the normalized acoustic nonlinearity parameter and the fatigue life was also achieved with the peak point at about 0.65 fatigue life for mode pair S0-s0, even though a relatively higher sensitivity to fatigue damage was observed for mode pair S1-s2. The excited frequency selection was further analyzed in a certain frequency range, where the quasi phase-velocity matching condition was satisfied for mode pair S0-s0 owing to the less dispersive property. Results show that the fatigue damage can be effectively detected using the mode pair S0-s0, and a relatively lower excited frequency was preferred due to its higher sensitivity to microstructural evolution.

It is known that measurement and extraction of the tiny amplitude of second harmonic Lamb waves are the main difficulties for practical applications of the nonlinear Lamb wave technique. In this study, phase-reversal approaches and phase matching technique are combined to build up the second-harmonic generation (SHG) of Lamb waves. A specific Lamb wave mode pair, which satisfied phase matching conditions, is selected to ensure the generation of cumulative second harmonic waves. Lamb wave signals with the same frequency but in reverse phase, propagating in the given specimen, are added together to counteract the fundamental waves, and simultaneously to enhance the signals of the second harmonic generated. The obtained results show that the phase-reversal approach can enhance the signals of second harmonic Lamb waves, and effectively counteract that of the fundamental waves. The approach is applied to assess the thermal-induced material degradation in the stainless steel plates. Distinctions of the acoustic nonlinearity parameters under different degraded levels are clearly shown in an improved repeatable and reliable manner, while those of linear wave velocity in the specimens are neglectable. The experimental investigations performed indicate that the proposed approach can be taken as a promising alternative for assessment of material degradation in its early stages.

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.

The characterization of residual stress in complicated components is a tough issue. The method of Rayleigh surface wave-based V(z) curve is adopted in this work to evaluate the distribution of residual stresses in aeroengine blades. First, the velocity of Rayleigh surface wave in aeroengine blade was measured by the V(z) curve technique, which can be used to calculate the local residual stress because the change of velocity is thought to be correlated with the contribution from residual stress. Two kinds of plastic-deformed Ti-6Al-4V samples were fabricated by ball-gun shooting to artificially induce distribution of residual stress and then measured by the proposed method. The results indicate that the distribution of the residual stress in both of the samples displays a predictable symmetry. The error of the measured stress is much less than 10% of the yielding stress in Ti-6Al-4V (i.e., about 800 MPa). Finally, the measured residual stresses were verified by X-ray diffraction method, whose results correlate reasonably well with each other. The proposed V(z) curve method and its experimental set-up appear to be a potential in characterizing residual stress at a point-like region, such as in complicated components.

The symmetric zero-frequency mode induced by weak material nonlinearity during Lamb wave propagation is explored for the first time. We theoretically confirm that, unlike the second harmonic, phase-velocity matching is not required to generate the zero-frequency mode and its signal is stronger than those of the nonlinear harmonics conventionally used, for example, the second harmonic. Experimental and numerical verifications of this theoretical analysis are conducted for the primary S0 mode wave propagating in an aluminum plate. The existence of a symmetric zero-frequency mode is of great significance, probably triggering a revolutionary progress in the field of non-destructive evaluation and structural health monitoring of the early-stage material nonlinearity based on the ultrasonic Lamb waves.

This paper investigates the propagation of Rayleigh surface waves in structures with randomly distributed surface micro-cracks using numerical simulations. The results revealed a significant ultrasonic nonlinear effect caused by the surface micro-cracks, which is mainly represented by a second harmonic with even more distinct third/quadruple harmonics. Based on statistical analysis from the numerous results of random micro-crack models, it is clearly found that the acoustic nonlinear parameter increases linearly with micro-crack density, the proportion of surface cracks, the size of micro-crack zone, and the excitation frequency. This study theoretically reveals that nonlinear Rayleigh surface waves are feasible for use in quantitatively identifying the physical characteristics of surface micro-cracks in structures.