Session: 17-01-01: Research Posters

Paper Number: 150434

150434 - Influence of Skew Angle on Ultrasonic Guided-Wave Beam Solutions in Anisotropic Composite Plates 

Composite materials are frequently utilized to improve strength while reducing weight. Mechanically, they exhibit anisotropic properties. In the ultrasonic testing of plates, guided-wave testing is anticipated to be an effective method because guided waves propagate long distances with low attenuation. These guided waves have the properties of multi-modal and dispersion. Therefore, a dispersion analysis of the anisotropic materials is necessary for guided-wave testing of composite materials.

 

Guided waves in elastic isotropic plates have been studied extensively by various researchers. In most of these studies, measurement data are analyzed using two-dimensional(2D) theory. Similarly, for anisotropic elastic plates, the 2D guided-wave theory is commonly used to analyze measurement data. Employing 3D dispersion theory would appear to be a natural approach to understanding the properties of guided waves in practical plates with finite width. However, the 3D theory generates numerous propagation modes of guided waves, even in the low-frequency range. This complexity makes the analysis of measurement data and the optimization of incident excitation challenging when based on 3D theory. In this context, ultrasonic beam solutions have been developed for guided waves in isotropic elastic plates, where the beam is a low-diffracting wave with high directivity. The beam solutions are based on 2D dispersion theory (i.e., Lamb and shear SH waves), with the amplitude function of the guided wave governed by the 2D Helmholtz equation. Therefore, the beam solutions for Lamb and SH waves can be formulated within the same framework as the 2D Helmholtz equation. Since wave fields generated by an ultrasonic transducer are often modeled using beam solutions, the ultrasonic beam theory is valuable for optimizing incident excitation, a task traditionally investigated using 2D theory. In this study, we extend the ultrasonic beam theory of guided waves to anisotropic elastic plates.

 

The beam solution of wave fields has been extensively studied in optics. It is desirable that the formulation of ultrasonic guided-wave beams incorporates the knowledge gained from optics. In this study, we derive the paraxial beam solution for guided waves in general anisotropic elastic plates. The approximate integral form is derived from the angular spectrum representation, which is the exact integral form describing the superposition of plane guided waves concerning the angular-direction wavenumber. The approximation is based on that the beam solution consists of plane waves with small angles from the main wavenumber direction. To derive the amplitude function in the same form as its isotropic counterpart, we introduce an inclined coordinate system. Consequently, the amplitude function is governed by the 2D Helmholtz equation in the inclined coordinate system. Therefore, the construction of beam solutions can be achieved within the same framework as the 2D Helmholtz equation. In our proposed formulation, we find that the skew angle of guided waves is expressed by the wavenumber derivative. Furthermore, it is observed that diffraction effects on the ultrasonic beam strongly depend on the profile of the skew angle.

Presenting Author: Sumika Yamada Tokyo Institute of Technology

Presenting Author Biography: Sumika Yamada is a master’s student in the Department of Civil and Environmental Engineering, School of Environment and Society, Tokyo Institute of Technology, Japan. She graduated with a bachelor’s degree in 2024. Her research focuses on the guided wave theory in elastic plates with finite width for ultrasonic nondestructive evaluation.

Authors:

Sumika Yamada Tokyo Institute of Technology
Taizo Maruyama Tokyo Institute of Technology
Akira Furukawa Hokkaido University