Nonlinear mixing of non-collinear guided waves at a contact interface

Modeling and simulation of zero-group velocity combined harmonic generated by guided waves mixing

In this paper, modelling and numerical perspective of zero-group velocity (ZGV) combined harmonic generated by guided waves mixing are investigated. The conditions for the generation of the ZGV combined harmonic are analyzed by S₀-S₀ and SH₀-SH₀ guided waves mixing in an isotropic plate, respectively. The generation of ZGV combined harmonics at sum frequency caused by counter-directional guided waves mixing is observed. It is confirmed that the ZGV combined harmonic with a considerable magnitude can be generated by this counter-directional guided waves mixing when both the internal resonant condition and non-zero power flux are satisfied. The application of generated ZGV combined harmonics for localized material degradation assessment is numerically examined in the given plate. The obtained results indicate that the generated ZGV combined harmonic induced by the counter-directional guided waves mixing can be used to assess the localized material degradation with improved signal-to-noise ratio. This study provides an insight into the physical process of the ZGV combined harmonic generation, and meanwhile offer a promising means for localized material degradation assessment by ZGV combined harmonics generated by guided waves mixing.

Spectral noise and data reduction using a long short-term memory network for nonlinear ultrasonic modulation-based fatigue crack detection

This paper presents a spectral noise and data reduction technique based on long short-term memory (LSTM) network for nonlinear ultrasonic modulation-based fatigue crack detection. The amplitudes of the nonlinear modulation components created by a micro fatigue crack are often very small and masked by noise. In addition, the collection of large amounts of data is often undesirable owing to the limited power, data storage, and data transmission bandwidth of monitoring systems. To tackle the issues, an LSTM network was applied to ultrasonic signals to reduce the noise level and the amount of data. The proposed technique offers the following benefits: (1) spectral noise reduction using the LSTM network for ultrasonic signals and (2) data reduction without compromising the spectral density amplitude of the existing nonlinear modulation components. Finally, the performance evaluation was conducted using the data obtained from complex geometry and real structure under external noises, indicating that the proposed method can be applied to various structures.

Microcrack localization using nonlinear Lamb waves and cross-shaped sensor clusters

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.

Experimental investigation on ball plate contact using ultrasonic reflectometry: From static to dynamic

Machine elements such as rolling element bearings are widely used in engineering and transportation areas. The life of a bearing is closely related to the stress state in the constituent components. Determining the stress state experimentally is difficult since the contact region is hidden inside the contacting bodies, making it difficult to characterize without altering the contact itself. This paper presents an experimental study to monitor static and dynamic ball-on-flat contacts, by using an ultrasonic reflectometry measuring technique, to demonstrate the concept of monitoring operating ball-bearing conditions in a non-invasive manner. By using an ultrasonic focusing probe and a 64-element ultrasonic array, contacts between a nitrile ball and a Perspex plate as well as contact between a steel ball and a grooved steel plate were characterised under both static and dynamic conditions. Both contact size and distribution of contact stress can be visualized in 2-dimensional plots. In this paper, the capability of ultrasonic reflectometry for non-invasive characterisation of contact conditions are demonstrated, and more importantly the development of multiple measuring mechanisms to realize real-time contact monitoring from static to dynamic conditions is illustrated. The proposed technique in the study is expected to characterise dynamic contacts of bearings in various scenarios from small mechanical systems (e.g., micro motors) to large civil infrastructures (e.g., wind turbines).

Low-frequency Lamb wave mixing for fatigue damage evaluation using phase-reversal approach

Fatigue damage is difficult to detect and evaluate non-destructively, specifically at its early stages (before the macro-crack formation). In this study, fatigue damage is evaluated based on the growth rate of the combinational harmonics generated by mixing of two fundamental symmetric mode (S₀) of Lamb waves in the low frequency range. The incorporation of the phase reversal approach to the wave mixing method could potentially improve the evaluation of the combinational and second harmonics and avoid the influence of other undesirable harmonics. A series of parametric case studies are carried out using the three-dimensional (3D) finite element (FE) method to investigate the effects of the excitation frequencies and time delay of the incident waves in wave mixing on the transient response of a weakly-nonlinear material. The numerical results and experimental results show that the sum combinational harmonic and second harmonics are sensitive to weak material nonlinearities. Further experiments on damaged samples by cyclic loading demonstrate that the sum combinational harmonic has much better sensitivity to the progressive fatigue damage than the the second harmonics. In general, the outcomes of this study indicate that the damage evaluation of early stage fatigue damage is feasible and effective with the wave mixing method using the S₀ waves generated at low frequency, and the phase-reversal approach improves considerably the quality of experimental results in the fatigue damage evaluation.

Nonlinear generation of a zero group velocity mode in an elastic plate by non-collinear mixing

Zero Group Velocity (ZGV) modes are peculiar guided waves that can exist in elastic plates or cylinders, and have proved to be very sensitive tools in characterizing materials or thickness variations with sub-percent accuracy at space resolutions of about the plate thickness. In this article we show theoretically and experimentally how such a mode can be generated as the sum-frequency interaction of two high amplitude primary waves, and then serve as a local probe of material non-linearity. The solutions to the phase matching condition, i.e. condition for a constructive non-linear effect, are obtained numerically in the mark of classical, quadratic non-linearity. The coupling coefficients that measure the transfer rate of energy as a function of time from primary to secondary modes are derived. Experiments are conducted on an aluminum plate using piezo-electric transducers and a laser interferometer, and explore the interaction for incident symmetric and anti-symmetric fundamental Lamb modes. In an experiment operated without voltage amplifier we demonstrate that the resonant nature of these ZGV modes can be leveraged to accumulate energy from long excitations and produce detectable effects at extraordinarily low input power even in such weakly non-linear material.

A Feasibility Study for a Nonlinear Guided Wave Mixing Technique

Ultrasonic non-destructive testing is an effective means of examining objects without destroying them. Among such testing, ultrasonic nonlinear evaluation is used to detect micro-damage, such as corrosion or plastic deformation. In terms of micro-damage evaluation, the data that comes from amplitude comparison in the frequency domain plays a significant role. Its technique and parameter are called ultrasonic nonlinear technique and nonlinearity. A certain portion of nonlinearity comes from the equipment system, while the other portion of nonlinearity comes from the material. The former is system nonlinearity, while the latter is material nonlinearity. System nonlinearity interferes with interpretation, because its source is not from the material. In this study, in order to minimize system effects, a mixing technique is implemented. To use the large area inspection ability of the guided wave, the main research issue in this paper is focused on the guided wave mixing technique. Moreover, several bulk wave mixing theory equations become good concepts for guided wave mixing theoretical study, and the conventional nonlinear technique and guided wave mixing experimental results are compared in this study to confirm the reliability. This technique can play an important role in quantitatively discriminating fine damage by minimizing the nonlinearity of the equipment system.

Experimental and Numerical Investigation of the Micro-Crack Damage in Elastic Solids by Two-Way Collinear Mixing Method

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.