Theoretical analysis of wave packet propagation in structural elements such as beams, plates, and shells is of great importance in a number of non-destructive testing methods. Quite often, experimental non-destructive testing methods use acoustic waves. Acoustic emission testing has been frequently used as a method for testing the structural integrity of composite structures [1]. Non-destructive testing methods require knowledge of a large array of information on the generation and propagation of acoustic emission signals in structures containing laminated composites. For the case when the test specimen has the shape of a plate, far from the acoustic source, the propagating waves can be described by the homogeneous Lamb equation. The solutions of this equation are called Lamb waves. In the case of a thin plate, the velocities of the lowest symmetric (S0) and antisymmetric (A0) Lamb waves are reduced to plate wave solutions [2]. The two propagation modes are called longitudinal and flexural modes, respectively. These modes move at different speeds and exhibit dispersion characteristics. The presence of defects in laminar composites is localized based on the arrival time of wave packets at a number of transducers using known distances between transducers and volumetric longitudinal waves [3]. In turn, the arrival time is determined by acoustic threshold crossing methods. For example, the first threshold crossing can be defined as the time at which the envelope of the acoustic emission signal crosses a given threshold. It should be borne in mind that the acoustic emission pulse changes shape due to dispersion, as a result of which the accuracy of damage localization is significantly reduced. For wave propagation in dispersive media, the accuracy of source location can be improved by using the arrival time of a wave at a single frequency [4]. A frequently used method in this case is the cross-correlation method for determining the propagation time of a flexural wave in plates. The idea of this technique is that if one frequency component in the output waveform from each transducer can be determined, then the time differences caused by the propagation of this frequency component can be used for location analysis. Furthermore, in isotropic media, the dependence of wave velocity on the direction of propagation must be taken into account in the location analysis. Fourier transform is an effective tool for analyzing dispersive signals. Approximation of transient waves that propagate in a dispersive medium as a time-frequency series can be effectively realized using wavelet transforms.
The objective of this study is to analyze the feasibility of using the wavelet transform for the case of transient wave propagation in graphite/epoxy laminates. This model analysis was performed using a modification of the Gabor wavelet for the case of dispersive wave packets. In addition, the arrival time of the group velocity at each frequency can be extracted using the amplitude value of the wavelet transform. The experimentally measured flexural mode group velocities are compared with The theoretical flexural wave group velocities obtained from the Mindlin plate theory were compared with the experimentally measured values. For the computational methodology, the case of a planar source arrangement for anisotropic laminates was considered using frequency-dependent arrival times and direction dependence of the flexural mode velocities. Good agreement between the calculated and experimental values is observed for the case where the generated Lamb waves are low-frequency flexural waves. The flexural mode is an excellent defect detector in laminated composites. The arrival time of the flexural mode at a fixed frequency was used in the analysis of the local shear and stress locations. This frequency was chosen because spectral analysis showed that it is the frequency that is usually present in the trapped waveforms. The values of the wavelet transforms for a particular frequency correspond to the change in the component spectral intensities as a function of time. The peak corresponds to the arrival time of the group velocity at this frequency. The angular dependence of the flexural mode group velocities is also needed in the source location analysis. The calculation technique analyzed in this paper allows one to plot the dispersion curves of both phase and group velocities for unidirectional and quasi-isotropic laminates, respectively. It was found that the results of local defect source location on quasi-isotropic laminate are generally more accurate than on unidirectional laminate. Moreover, as the source point moves away from the mid-plane of the specimen cross-section, the error becomes larger. In this study, the application of wavelet transforms to time-frequency analysis of transient waves is analyzed in detail for the special case of wave packets propagating in dispersive, anisotropic media, particularly in laminated composites. The characteristics of the dispersive flexural wave in unidirectional and quasi-isotropic laminates can be used to accurately detect local mechanical shears.
References:
1. Brunner, A. J. (2018). Identification of damage mechanisms in fiber-reinforced polymer-matrix composites with Acoustic Emission and the challenge of assessing structural integrity and service-life. Construction and Building Materials, 173, 629-637. https://doi.org/ 10.1016/j.conbuildmat.2018.04.084
2. Werby, M. F., & Überall, H. (2002). The analysis and interpretation of some special properties of higher order symmetric Lamb waves: The case for plates. The Journal of the Acoustical Society of America, 111(6), 2686-2691. https://doi.org/ 10.1121/1.1473637
3. Kim, H., Kim, T., Morrow, D., & Jiang, X. (2019). Stress measurement of a pressurized vessel using ultrasonic subsurface longitudinal wave with 1–3 composite transducers. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 67(1), 158-166. https://doi.org/ 10.1109/TUFFC.2019.2941133
4. De Rosa, I. M., Santulli, C., & Sarasini, F. (2009). Acoustic emission for monitoring the mechanical behaviour of natural fibre composites: A literature review. Composites part a: applied science and manufacturing, 40(9), 1456-1469. https://doi.org/ 10.1016/j.compositesa.2009.04.030
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