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Open AccessArticle

Scattering of Surface Waves by a Three-Dimensional Cavity of Arbitrary Shape: Analytical and Experimental Studies

School of Mechanical Engineering, Changwon National University, Changwon 51140, Korea
Institute of Theoretical and Applied Research, Duy Tan University, Hanoi 100000, Vietnam
Institute of Mechanics, Vietnam Academy of Science and Technology, Hanoi 100000, Vietnam
Faculty of Civil Engineering, Ho Chi Minh City University of Technology and Education, Ho Chi Minh City 700000, Vietnam
School of Mechanical Engineering, Pusan National University, Busan 46241, Korea
Authors to whom correspondence should be addressed.
Appl. Sci. 2019, 9(24), 5459;
Received: 20 October 2019 / Revised: 30 November 2019 / Accepted: 8 December 2019 / Published: 12 December 2019
(This article belongs to the Special Issue Surface Waves for Monitoring of Materials at Different Scales)
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. View Full-Text
Keywords: surface wave; half-space; three-dimensional cavity; reciprocity surface wave; half-space; three-dimensional cavity; reciprocity
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Lee, J.; Ngo, V.; Phan, H.; Nguyen, T.; Dao, D.K.; Cho, Y. Scattering of Surface Waves by a Three-Dimensional Cavity of Arbitrary Shape: Analytical and Experimental Studies. Appl. Sci. 2019, 9, 5459.

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