LAMB WAVE GROUP VELOCITY ANALYSIS IN REINFORCED COMPOSITES - Наукові конференції
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LAMB WAVE GROUP VELOCITY ANALYSIS IN REINFORCED COMPOSITES

17.09.2025 19:28

[3. Технічні науки]

Автор: Alexander Pysarenko, associate professor, PhD, Odessa State Academy of Civil Engineering and Architecture



The study of Lamb waves is a promising method for monitoring large structures made of reinforced composite material. A traditional ultrasonic test allows for the inspection of only a local part of a structure, which is located under and near the transducers. This method involves the use of transducers over the entire surface of a large structure to perform a structural test. Such an inspection process can be laborious and time-consuming.

Recently, techniques based on Lamb waves have been used for the simultaneous inspection of large areas. However, such methods are more complex than traditional ultrasonic tests because Lamb waves have dispersive characteristics, meaning the wave velocity changes depending on the frequency, mode, and plate thickness. Experimentally measured Lamb wave group velocities in composite materials with anisotropic characteristics do not match the theoretical group velocities, which are calculated using the Lamb wave dispersion equation. This discrepancy is explained by the fact that in anisotropic materials, there is an angle between the direction of the group velocity and the direction of the phase velocity. Until now, group velocities have been calculated from the dispersion curves of Lamb waves in an anisotropic plate without considering the direction and magnitude of propagation.

In this study, a numerical analysis of experimental data on the measured group velocities of Lamb waves in composite materials was conducted. In a composite plate with anisotropic features due to fiber arrangement, the direction of the wave vector differs from the direction of energy flow, with the exception of the direction along the principal axis. It is necessary to consider the propagation of waves in composite materials with anisotropic features, taking into account not only the direction but also the magnitude.

There are many experimental confirmations of the presence of a fundamental symmetric mode (S0), which shows less dispersion when the product of the low frequency and the thickness of the composite sample is small. A set of experiments indicates a difference in directions between the group and phase velocity. This difference was found using the S0 mode in unidirectional laminated composite plates. The research showed that the direction of energy flow coincides with the direction of the fibers, except for the perpendicular direction. The group velocity of the S0 symmetric mode at a frequency below the cut-off is approximately used as the phase velocity due to the less dispersive region, and then the group velocity is recalculated from the slowness surface, which is built on the inverse value of the phase velocities.

This study presents the dispersion curves of the S0 mode for phase velocity using Lamb wave equations for unidirectional, bidirectional, and quasi-isotropic composite plates. The phase velocity dispersion curves were used to calculate the theoretical group velocity in the composite material. The calculation method made it possible to analyze the group velocity curve, i.e., the curve by which the magnitude and value of the group velocity direction are newly modified along the entire surface of the composite sample. A difference was found between the known experimental values of the group velocity and the group velocity calculated from the dispersion curves. This difference is caused by the direction and magnitude of the wave vector and the direction of the energy flow.

The equation for the dispersion of Lamb waves in an anisotropic material can be calculated using a numerical method, such as the bisection method [1]. The characteristic modes of Lamb waves are symmetric and anti-symmetric modes relative to the center line. The change in the phase velocity dispersion curve for the S0 mode is quite sharp for the direction that coincides with the propagation direction in a unidirectional composite plate [2]. The direction of the group velocity indicates the normal direction of the slowness surface, and the direction of the phase velocity indicates the line connecting the origin and a point on the slowness surface. From the geometrical relationship between the phase velocity direction and the X-axis, the following relationship can be obtained to calculate the angle. The results of the calculation method indicate the presence of more than two group velocities in the fiber directions. The result of the transformed group velocity can be obtained using the magnitude and direction of the group velocity calculated from the slowness surface for a single point. The recalculated group velocity corresponded to the measured group velocities, with the exception of the fiber direction, regardless of the composite plate thickness.

In this study, Lamb wave dispersion curves were obtained by considering the dispersion equation in composite plates. The method is based on the procedure of choosing a numerical value of the phase velocity from the analysis of dispersion curves and recalculating the group velocity, taking into account the magnitude and direction of the propagation of vibrational waves for monitoring the state of the reinforced composite. An analysis of the features of the application of the calculation method showed that the difference between the known experimentally measured group velocities and the theoretically calculated group velocity from the Lamb wave dispersion curves is the result of the direction and magnitude between the wave vector and the direction of the energy flow. It should be noted that the direction of wave propagation calculated from the dispersion equation indicates the direction of the phase velocity. 

References:

1. Pant, S., Laliberte, J., Martinez, M., Rocha, B., & Ancrum, D. (2015). Effects of composite lamina properties on fundamental Lamb wave mode dispersion characteristics. Composite Structures, 124, 236-252. https://doi.org/ 10.1016/j.compstruct.2015.01.017

2. Zhao, G., Jiang, M., Luo, Y., Li, W., & Sui, Q. (2023). Comparison of sensitivity in nonlinear ultrasonic detection based on Lamb wave phase velocity matching mode. Nondestructive Testing and Evaluation, 38(2), 297-312. https://doi.org/ 10.1080/10589759.2022.2121394



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