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 ◽  
Vol 96 ◽  
pp. 40-47 ◽  
Author(s):  
Haidang Phan ◽  
Younho Cho ◽  
Quang Hung Le ◽  
Chi Vinh Pham ◽  
Hoai T.-L. Nguyen ◽  
...  
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Guided Waves ◽  
Closed Form Solution ◽  
Form Solution ◽  
Harmonic Load ◽  
Time Harmonic ◽  
Layered Half Space

scholarly journals A THEORETICAL STUDY ON PROPAGATION OF GUIDED WAVES IN A FLUID LAYER OVERLYING A SOLID HALF-SPACE

2018 ◽  
Author(s):  
Haidang Phan
Keyword(s):  
Half Space ◽  
Guided Waves ◽  
Fluid Layer ◽  
Elastic Solid ◽  
Wave Mode ◽  
Ultrasonic Guided Waves ◽  
Harmonic Load ◽  
Closed Form Solutions ◽  
Time Harmonic ◽  
Potential Applications

Ultrasonic guided waves propagating in a fluid layer of uniform thickness bonded to an elastic solid half-space is theoretically investigated in this article. Based on the boundary conditions set for the joined configuration, a characteristic dispersion equation is found and new expressions for free guided waves are introduced. Closed-form solutions of guided waves generated by a time-harmonic load are derived by the use of elastodynamics reciprocity theorems. Through calculation examples, it is shown that the obtained computation of the lowest wave mode approaches the result of the Rayleigh wave in the solid half-space as the layer thickness approaches zero. The aim of the present work is to improve the understanding of wave motions in layered half-spaces for potential applications in the area of bone quantitative ultrasound

Exact closed-form solutions for Lamb’s problem—III: the case for buried source and receiver

2020 ◽  
Vol 224 (1) ◽  
pp. 517-532
Author(s):  
Xi Feng ◽  
Haiming Zhang
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Closed Form Solution ◽  
Time History ◽  
Natural Generalization ◽  
Elastic Half Space ◽  
Form Solution ◽  
Elementary Functions ◽  
Heaviside Step Function ◽  
Lamb’S Problem

SUMMARY In this paper, we derive the exact closed-form solution for the displacement in the interior of an elastic half-space due to a buried point force with Heaviside step function time history. It is referred to as the tensor Green’s function for the elastic wave equation in a uniform half-space, also a natural generalization of the classical 3-D Lamb’s problem, for which previous solutions have been restricted to the cases of either the source or the receiver or both are located on the free surface. Starting from the complex integral solutions of Johnson, we follow the similar procedures presented by Feng and Zhang to obtain the closed-form expressions in terms of elementary functions as well as elliptic integrals. Numerical results obtained from our closed-form expressions agree perfectly with those of Johnson, which validates our explicit formulae conclusively.

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