A closed-form solution to propagation of guided waves in a layered half-space under a time-harmonic load: An application of elastodynamic reciprocity

Haidang Phan; Younho Cho; Quang Hung Le; Chi Vinh Pham; Hoai T-L Nguyen; Phuong Thuy Nguyen; Tinh Quoc Bui

doi:10.1016/j.ultras.2019.03.015

A closed-form solution to propagation of guided waves in a layered half-space under a time-harmonic load: An application of elastodynamic reciprocity

Ultrasonics. 2019 Jul:96:40-47. doi: 10.1016/j.ultras.2019.03.015. Epub 2019 Mar 22.

Authors

Haidang Phan¹, Younho Cho², Quang Hung Le³, Chi Vinh Pham⁴, Hoai T-L Nguyen⁵, Phuong Thuy Nguyen⁵, Tinh Quoc Bui⁶

Affiliations

¹ Institute of Theoretical and Applied Research, Duy Tan University, 1 Phung Chi Kien, Hanoi 100000, Viet Nam. Electronic address: haidangphan.vn@gmail.com.
² School of Mechanical Engineering, Pusan National University, Pusan, South Korea.
³ Graduate University of Science and Technology, Vietnam Academy of Science and Technology, Viet Nam.
⁴ Faculty of Mathematics, Mechanics and Informatics, Hanoi University of Science, Hanoi, Viet Nam.
⁵ Institute of Physics, Vietnam Academy of Science and Technology, Hanoi, Viet Nam.
⁶ Department of Civil and Environmental Engineering, Tokyo Institute of Technology, Tokyo, Japan.

PMID: 30947073
DOI: 10.1016/j.ultras.2019.03.015

Abstract

This article is concerned with the application of reciprocity in computing guided wave motions generated by a time-harmonic load in a layer of uniform thickness joined to a half-space. Explicit expressions for free Rayleigh waves and Love waves propagating in the layered half-space are introduced. Exact solutions of Rayleigh waves and Love waves are derived from reciprocity relations between an actual state - guided waves generated by a time-harmonic line load and a virtual state - an appropriately chosen free wave traveling in the structure. Scattered amplitudes of the wave motions are thus determined. The validation of the reciprocity approach is shown through the computation of the lowest Rayleigh wave mode in the layered half-space, which approaches the calculation of the Rayleigh surface wave in the half-space once the layer thickness approaches zero in the limit.

Keywords: Guided waves; Layered half-space; Love waves; Rayleigh waves; Reciprocity.