Abstract
The partial-wave method takes advantage of the Christoffel equation’s generality to represent waves within a waveguide. More specifically, the partial-wave method is well known for its usefulness when calculating dispersion curves for multilayered and/or anisotropic plates. That is, it is a vital component of the transfer-matrix method and the global-matrix method, which are used for dispersion curve calculation. The literature suggests that the method is also exceptionally useful for conceptual interpretation, but gives very few examples or instruction on how this can be done. In this paper, we expand on this topic of conceptual interpretation by addressing Rayleigh waves, Stoneley waves, shear horizontal waves, and Lamb waves. We demonstrate that all of these guided waves can be described using the partial-wave method, which establishes a common foundation on which many elastodynamic guided waves can be compared, translated, and interpreted. For Lamb waves specifically, we identify the characteristics of guided wave modes that have not been formally discussed in the literature. Additionally, we use what is demonstrated in the body of the paper to investigate the leaky characteristics of Lamb waves, which eventually leads to finding a correlation between oblique bulk wave propagation in the waveguide and the transmission amplitude ratios found in the literature.
Highlights
In this paper, we demonstrate how the partial-wave method, as first introduced by Solie and Auld [1], can be used to gain a new perspective on guided waves
The most well-known example of this is that the two-part Lamb wave characteristic equation shows that all of the Lamb waves can be divided into two types: symmetric and anti-symmetric
This paper exploits the Christoffel equation, slowness curves, and the partial-wave method to establish a foundation on which guided waves can be analyzed, compared, and explained
Summary
We demonstrate how the partial-wave method, as first introduced by Solie and Auld [1], can be used to gain a new perspective on guided waves. Our understanding of guided waves is primarily informed by the derivation of characteristic equations and dispersion curve solutions. Sci. 2018, 8, 966 cover the calculation of dispersion curves, attenuation, energy loss, or anisotropic materials Neither will it cover the derivation of characteristic equations for various guided waves. These sections give special attention to the diction used and the assumptions made, as they are pertinent to how the interpretation presented in this paper deviates from the literature. It discusses in detail how the slowness curve solutions of the Christoffel equation can be used to interpret the characteristics of most guided waves, and the Lamb wave solutions in particular. A correlation between the amount of acoustic leakage and the refraction qualities of obliquely travelling bulk waves in the guided wave is identified
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