Haidang Phan

Love waves are horizontally polarized shear waves guided by a surface layer and are highly sensitive to near-surface properties. While their behavior in isotropic media is well established, closed-form solutions for orthotropic layered structures under external excitation remain limited. This study presents closed-form solutions for both propagation and excitation of Love waves in an orthotropic elastic layer bonded to an orthotropic half-space. The dispersion relation is first derived within the framework of anti-plane shear motion using surface and interfacial boundary conditions. The elastodynamic reciprocity theorem is then applied to obtain explicit expressions for modal amplitudes generated by time-harmonic loading. Numerical results illustrate the dispersive characteristics and excitation behavior of the waves, highlighting the dependence of modal amplitudes on the frequency–thickness parameter. The proposed formulation provides a unified and efficient analytical framework for guided-wave analysis in anisotropic layered media.

Ultrasonic guided waves have become a key tool in nondestructive evaluation of pipelines, as they can travel long distances with low attenuation while maintaining high sensitivity to defects. Accurate modeling of their dispersion characteristics is essential for inspection design and signal interpretation. This study presents a finite element (FE) framework that advances beyond conventional eigenvalue-based analyses by directly simulating a realistic multichannel acquisition process. A pitch-catch configuration, consisting of a ring actuator and a linear receiver array, is modeled, and dispersion spectra are reconstructed through two-dimensional Fourier transforms—closely mirroring experimental practice. The reconstructed spectra show excellent agreement with analytical solutions, thereby validating the approach. By bridging numerical modeling and experimental acquisition, this FE framework delivers realistic datasets that facilitate advanced signal processing, imaging algorithms, and pipeline inspection strategies.

The elastodynamics of an orthotropic half-space coated by a thin orthotropic layer is theoretically investigated in this article. We newly propose explicit expressions of free Rayleigh waves in a layered half-space that are dependent on only one unknown constant representing amplitude. The main contribution is on deriving, in a simple manner, the theoretical predictions of far-field Rayleigh wave motion arising from time-harmonic loads using elastodynamic reciprocity theorems. These are the very first closed-form exact solutions found for the forced motion of Rayleigh waves in a layered half-space of orthotropic materials. To demonstrate the theoretical results, computation of Rayleigh wave motion in a jointed rock, including a layer of quartz-schist and a half-space of soil, is considered. We present the phase and group dispersion curves superimposed with the amplitude spectra that provide useful information on wave modes, frequencies, and displacement amplitudes. The inclusion of the amplitude spectra in the dispersion curves is a significant improvement over other dispersion curves currently available in the literature. The analytical predictions are compared with numerical results found by finite element analysis, and they show excellent agreement for the cases of a uniform distributed load and a varying distributed load both applied over a strip on the layer surface. The calculations obtained in the current study could generally be very useful for applications in seismology and materials characterization of coated structures.