Abstract
The scattering problem of a time-harmonic dependent plane elastic wave by a multi-layered thermoelastic body in an isotropic and homogeneous elastic medium is considered. The direct scattering problem is formulated. Integral representations for the total exterior elastic field and the total interior thermoelastic fields as well as expressions for the far-field patterns are obtained containing the physical parameters of the interior thermoelastic layers. A reciprocity type theorem, a general type scattering theorem and an optical type theorem for plane wave incidence are presented and proved.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
C. Athanasiadis, V. Sevroglou, I.G. Stratis, 3-D elastic scattering theorems for point sources: acoustic and electromagnetic waves. J. Math. Phys. 43, 5683–5697 (2002)
C. Athanasiadis, V. Sevroglou, I.G. Stratis, Scattering relations for point-generated dyadic fields in two-dimensional linear elasticity. Q. Appl. Math. LXIV, 695–710 (2006)
C. Athanasiadis, P.A. Martin, A. Spyropoulos, I.G. Stratis, Scattering relations for point generated dyadic fields. Math. Methods Appl. Sci. 31, 987–1003 (2008).
E. Athanasiadou, V. Sevroglou, S. Zoi, Scattering theorems of elastic waves for a thermoelastic body. Math. Methods Appl. Sci. 41(3), 998–1004 (2016). https://doi.org/10.1002/mma.4051
F. Cakoni, Boundary integral methods for thermoelastic screen scattering problem in \(\mathbb {R}^3\). Math. Methods Appl. Sci. 23, 441–466 (2000)
F. Cakoni, G. Dassios, The coated thermoelastic body within a low frequency elastodynamic field. Int. J. Eng. Sci. 36, 1815–1838 (1998)
G. Dassios, K. Kiriaki, The low-frequency theory of elastic wave scattering. Q. Appl. Math. 42, 225–248 (1984)
G. Dassios, K. Kiriaki, D. Polyzos, On the scattering amplitudes of elastic waves. ZAMP 38, 856–873 (1987)
G. Dassios, K. Kiriaki, D. Polyzos, Scattering theorems for complete dyadic fields. Eng. Sci. 33, 269–277 (1995)
G, Dassios, R. Kleinman, Low Frequency Scattering (Clarendon Press, Oxford, 2000)
G. Dassios, V. Kostopoulos, The scattering amplitudes and cross sections in the theory of thermoelasticity. SIAM J. Appl. Math. 48, 79–98 (1988)
G. Dassios, V. Kostopoulos, On Rayleigh expansions in thermoelastic scattering. SIAM J. Appl. Math. 50, 1300–1324 (1990)
G. Dassios, V. Kostopoulos, Scattering of elastic waves by a small thermoelastic body. Eng. Sci. 32, 1593–1603 (1994)
R. Duduchava, D. Natroshvili, E. Shargorodsky, Basic boundary value problems of thermoelasticity for anisotropic bodies with cuts I and II. Georgian Math. J. 2, 123–140 and 3, 259–276 (1995)
V.D. Kupradze, T.G. Gegelia, M.O. Basheleishvili, T.V. Burchuladze, Three Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity. North Holland Series in Applied Mathematics and Mechanics (North-Holland, Amsterdam, 1979)
W. Nowacki, Thermoelasticity, 2nd edn. (Revised and Enlarged PWN-Polish Scientific Publishers, Warsaw and Pergamon Press, Oxford, New York, 1986)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Athanasiadou, E.S., Sevroglou, V., Zoi, S. (2020). Scattering Relations of Elastic Waves by a Multi-Layered Thermoelastic Body. In: Daras, N., Rassias, T. (eds) Computational Mathematics and Variational Analysis. Springer Optimization and Its Applications, vol 159. Springer, Cham. https://doi.org/10.1007/978-3-030-44625-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-030-44625-3_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-44624-6
Online ISBN: 978-3-030-44625-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)