Abstract
The scattering of surface waves by a three-dimensional shallow cavity of arbitrary shape at the surface of a homogenous, isotropic, linearly elastic half-space is theoretically investigated. A novel analytical approach based on a reciprocity consideration is introduced in this article to determine the particle displacements of the scattered wave field generated by the interaction between the surface waves and the cavity. In the usual manner, the scattered field was shown to be equivalent to the radiation from the distribution of tractions, calculated from the incident wave, on the surface of the cavity. The radiation of surface waves subjected to the computed tractions applied at a single location was found using reciprocity theorems. The field scattered by the cavity was subsequently obtained from the superposition of displacements due to all the forces applied on the cavity surface. Solutions for the scattering of surface waves by a spherical, a circular cylindrical (coin-shaped) and a square cylindrical cavity are presented in detail. We here derive the closed-form expressions of the displacement amplitudes, which represent the far-field scattered waves produced by each of the cavities. An experimental setup using the ultrasonic pulse-echo technique was then carried out to record the scattered echoes of surface waves from these cavities in order to provide practical validation of the analytical findings. The vertical displacements measured at a significant distance of about twenty-five wavelengths from the cavities of the same width and different depth were compared with the corresponding theoretical predictions. The comparisons show excellent agreement for the case of a spherical cavity and good agreement in the cases of a circular and a cylindrical cavity in terms of trends and magnitudes. It is followed by a discussion on the results of the comparison and the limitations of the proposed approach regarding the degree of smoothness and the size of cavity.
Highlights
Understanding the interaction of elastic waves with surface defects like cracks, corrosion pits, topographic irregularities, etc., is critical for the potential development of ultrasonic nondestructiveAppl
Most of the works in the literature are performed with the use of numerical methods, such as the finite element (FE) method [1], the boundary element (BE) method [2], or the finite element boundary integral (FE-BI) approach [3]
The shape application of reciprocity to the of surface three-dimensional cavity of arbitrary in an elastic half-space hasscattering been shown in this waves article. by
Summary
Understanding the interaction of elastic waves with surface defects like cracks, corrosion pits, topographic irregularities, etc., is critical for the potential development of ultrasonic nondestructive. We studied the general three-dimensional problem of surface wave scattering by a cavity of arbitrary shape on the surface of a half-space. The investigation is the very first theoretical approach for obtaining the solutions of the scattering of surface waves by a three-dimensional cavity of arbitrary shape. The approximation models can offer a much lower computational cost and time with a reasonable accuracy in comparison with the existing numerical methods They are able to provide insight into the physics of the scattering process that is important to solving inverse scattering problems. Major conclusions drawn from this investigation are given in Section 8.Section 8
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