Lamb waves are often used for non-destructive evaluation of composite plates. The wavelength of the Lamb waves used is of the same order of magnitude as the plate thickness. These wave packets propagate over long distances and can be used with conformal piezoelectric actuators/sensors that require low power, they may be suitable for online monitoring of the structure's health [1]. The development of wavelet analysis has allowed the intensive use of Lamb wave techniques for detecting defects in composite structures. This study continues the development of a damage detection methodology for composite structures by developing an improved wavelet-based signal processing technique [2]. This technique improves the resolution and interpretation of Lamb wave signals associated with defects in a composite plate [3]. In addition, a statistically rigorous damage classifier is developed to identify the wave propagation paths affected by damage. In addition, a new damage location algorithm is developed to determine the location of damage based on signal attenuation rather than time-of-arrival information. Lamb waves are characterized by significant dispersion [4]. As a result, their propagation through a solid volume often generates several modes of secondary Lamb waves. The dispersive nature of the waves means that the different frequency components of the Lamb waves propagate at different speeds and that the shape of the wave packet changes as it propagates through the solid. However, in practice, researchers for fault detection applications essentially limit the number of Lamb waves generated to two fundamental modes, namely the S0 and A0 modes. In subsequent steps, a less dispersive frequency region is selected to make the interpretation of the response signals easier. In this study, a Morlet wavelet with a narrow-band excitation frequency is developed as the input wave. The selection of an appropriate excitation frequency involves taking several factors into account. The first step in modulating the input frequency is to calculate the group velocity dispersion curve. Although the application of effective elastic properties in composite laminates is limited, it is often useful to derive such constants for an initial assessment of the laminate response. The presence of mechanical loading in the principal cross-sectional plane of quasi-isotropic laminates causes longitudinal isotropy. For this type of laminates, it is found that the effective Young's modulus, Poisson's ratio, and shear modulus are the same for any direction in the laminate plane.
The Lamb wave group velocity modes depend on the stiffness tensor of each layer for a fixed layer orientation angle to the general direction of the laminate. The transformed stiffness coefficients are then averaged over the laminate thickness, weighted by the thickness of each layer. The elements of the averaged stiffness tensor are related to the effective elastic properties by analogy with the isotropic stiffness tensor. The presence of a set of averaged stiffness tensor components allows one to determine the effective Young's modulus and Poisson's ratio of the composite plate. Based on the delamination detection technique, a dispersion curve was obtained that can be used to initially determine the frequency range where only the fundamental Lamb wave modes propagate and to search for any non-dispersive regions. The input signal frequency was chosen high enough to make the Lamb wavelength comparable to the scale of the local damage. On the other hand, the excitation frequency was chosen low enough to avoid the higher modes cluttering the fundamental symmetric (S0 ) and antisymmetric (A0) modes. The calculated numerical values of the group velocities of the S0 and A0 modes were in satisfactory agreement with known experimental studies on the propagation of wave packets in laminated composites. The dispersion curve is calculated for a macroscopically isotropic composite plate. In addition, the dispersion curve calculation ignores the attenuation effects in the composite plate. Therefore, the dispersion curve is used only as a guide, and several trial-and-error experiments are performed to adjust the optimum excitation frequency.
The propagation of the Lamb wave through the volume of the laminated composite is accompanied by the energy transfer between its kinetic and elastic potential components. When this transfer is not ideal due to heating, leakage and reflection of the wave, attenuation occurs. In particular, the attenuation increases due to the presence of delamination, and the energy of the input force flows from the excitation frequency to the neighboring frequency values. The appearance of microcracks in the laminated composite is accompanied by the energy loss, which leads to the excitation of high-frequency local modes. Based on these findings, the damage index was defined as a function of the signal attenuation for a limited period of time (the part of the signal corresponding to the first mode A0) and at a certain frequency (the input frequency of the signal). In all cases, the attenuation processes correlate with the amount of energy dissipated by the damage. It can be concluded that the proposed damage index measures the degree of energy dissipation of the test signal compared to the baseline signal, especially in the first mode A0 and at the input frequency value.
References:
1. Diamanti, K., & Soutis, C. (2010). Structural health monitoring techniques for aircraft composite structures. Progress in Aerospace Sciences, 46(8), 342-352. https://doi.org/10.1016/j.paerosci.2010.05.001
2. Lee, H., Lim, H. J., Skinner, T., Chattopadhyay, A., & Hall, A. (2022). Automated fatigue damage detection and classification technique for composite structures using Lamb waves and deep autoencoder. Mechanical Systems and Signal Processing, 163, 108148. https://doi.org/10.1016/j.ymssp.2021.108148
3. Lin, J., Gao, F., Luo, Z., & Zeng, L. (2016). High-resolution Lamb wave inspection in viscoelastic composite laminates. IEEE Transactions on Industrial Electronics, 63(11), 6989-6998. https://doi.org/ 10.1109/TIE.2016.2582735
4. Chen, Q., Xu, K., & Ta, D. (2021). High-resolution Lamb waves dispersion curves estimation and elastic property inversion. Ultrasonics, 115, 106427. https://doi.org/10.1016/j.ultras.2021.106427
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