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

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.

Cubic nonlinearity parameter measurement and material degradation detection using nonlinear ultrasonic three-wave mixing

Early detection of accumulated damage or material degradation in structures is important to ensure their structural safety. Nonlinear ultrasonic techniques are widely used to measure the quadratic nonlinearity parameter that represents the third-order elastic constants of materials for material degradation detection. In addition, there are ongoing efforts to exploit both the third- and fourth-order elastic constants that describe the cubic nonlinearity parameter to detect material degradation. This study develops a nonlinear ultrasonic three-wave mixing technique to generate and measure third-order combined harmonics (TOCH) in plate-like structures and to measure cubic nonlinearity parameter. The proposed three-wave mixing technique generates three primary Lamb waves in the target structure and measures the TOCH produced by nonlinear cross-interaction of the primary Lamb waves. A theoretical model is developed to describe the generation of TOCH in a nonlinear elastic and homogeneous plate, and the effectiveness of the theoretical model is validated experimentally. Measurements of the TOCH are conducted for intact and degraded aluminum specimens with different degradation levels. Because inherent material nonlinearity and material degradation alter the third- and fourth-order elastic constants of a structure, the three-wave mixing technique for measuring the TOCH can be used to identify the inherent material nonlinearity and material degradation. In particular, the experimental results indicate that the proposed technique is more sensitive to early-stage material degradation than existing nonlinear ultrasonic techniques such as two-wave mixing, and third harmonic generation techniques.

Resonant activation of different intermodulation frequencies using dual excitations

In this paper, an analytical framework is presented to understand the generation of different intermodulation frequencies under dual excitation which is also verified with experiments. One single periodic frequency (SPF) excitation along with one variable frequency excitation, varying from local defect resonance (LDR) frequency and its superharmonics to subharmonic, are used. The flexural wave propagation in an orthotropic composite plate containing a delamination is analytically derived considering quadratic nonlinearity. Both analytical and experimental results are presented for glass fibre reinforced plastic (GFRP) plates with single and double delaminations. Two different types of intermodulation peaks are observed, that is local defect resonance intermodulation (LDRI) and single periodic frequency intermodulation (SPFI), out of which SPFI is found to be generated only during superharmonics and subharmonic excitation. At LDR frequency excitation, only its higher harmonics are found and no SPFI peaks are observed. The acoustic nonlinearity parameters are found increase with order of harmonics and delamination diameter.

A Microcrack Location Method Based on Nonlinear S0 Mode Lamb Wave and Probability Scan Positioning Imaging Matrix

Early damage, such as microcrack, occupies most of the fatigue life of materials, and timely detection of early damage and positioning has great engineering and economic value. In this paper, a matrix scanning and positioning imaging method based on a probabilistic algorithm is proposed. Cooperating with the single-mode (S0) lamb wave, the microcrack in the thin plate material can be efficiently positioned. Taking the S0 mode lamb wave as the fundamental wave can effectively reduce the influence of the dispersion effect on the signal analysis. Meanwhile, in order to reduce the noise interference, the signal is reconstructed by empirical mode decomposition (EMD) to achieve the filtering effect. Then, the ABAQUS finite element simulation software is used to compare the positioning results under different locations of microcrack and different arrangements of probe. Finally, the feasibility of the localization algorithm is verified by the RAM-5000 SNAP nonlinear ultrasound system. The experimental results are consistent with the simulation theory, and the microcrack is effectively positioned. This facilitates our timely remedial action or further assessment of the remaining value of the material.