Using the Partial Wave Method for Wave Structure Calculation and the Conceptual Interpretation of Elastodynamic Guided Waves

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.

Ultrasonic Guided-Waves Sensors and Integrated Structural Health Monitoring Systems for Impact Detection and Localization: A Review

“…Moreover, mode conversion can occur when the ultrasonic guided waves travel across a discontinuity of acoustic properties in the planar structure, for example, a change in thickness or material composition. In general, the wave shape of the impact generated UGW is complex, but a list of features supported by theoretical modelling developed by Hakoda et al [ 52 ] based on the phase velocity analysis can be derived. It is worth noticing that the propagation velocity analysis, in general, is more complex for a composite three-dimensional structure than the simpler case shown in Figure 2 ; even the example of time domain signals generated on an aluminum plate reported in Figure 3 is a simplified scenario with respect to real-life cases.…”

On the Use of Oblique Acoustic Leakage to Measure the Wavenumber Spectrum of Propagating Lamb Waves

“…For the case of a Lamb wave travelling within an aluminum plate (as shown in Figure 2), where the plate’s surface is normal to the z-axis, Figure 1 still applies because Lamb waves are representable as a superposition of the Christoffel equation solutions [25]. In this context, the phase velocity of the Lamb wave is equal to ω/kx.…”

Dichotomy property of dispersion equation of guided waves propagating in anisotropic composite plates

“…The solving process of the Rayleigh-Lamb equation is achieved by dividing the whole solution domain into three regions, i.e., region 1 of 𝑣 < 𝑐 𝑇 , region 2 of 𝑐 𝑇 < 𝑣 < 𝑐 𝐿 and region 3 of 𝑣 > 𝑐 𝐿 , where 𝑣 is the phase velocity, and 𝑐 𝑇 and 𝑐 𝐿 are the velocities of transverse and longitudinal modes, respectively. Then in each region, the complex-valued Rayleigh-Lamb equation is derived to be a real one such that any standard root-finding algorithm can be easily called to solve it (see [33] and ch. 6.3 of [28]).…”