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2015 | OriginalPaper | Chapter

7. Miscellaneous Green’s Functions

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Abstract

This last chapter presents five Green’s functions and one application technique of the complex integral. The first and second sections consider the 2D static Green’s dyadic for an orthotropic elastic solid, and for an inhomogeneous elastic solid. The third section discusses the Green’s function for torsional waves in an anisotropic solid. The fourth section discusses wave reflection at a moving boundary. The fifth section is concerned with wave scattering by a rigid inclusion.Both are for SH-wave and their Green's functions are obtained in the exact closed form. The last section shows an excellent application technique of the complex integral. It reduces a semi-infinite integral, which includes the product of two Bessel functions, to a finite integral that is very suitable for numerical evaluation. 

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Literature
go back to reference Erdélyi A (ed) (1954) Tables of integral transforms, vols I and II. McGraw-Hill, New York Erdélyi A (ed) (1954) Tables of integral transforms, vols I and II. McGraw-Hill, New York
go back to reference Friedlander FG (1958) Sound pulses. Cambridge University Press, Cambridge Friedlander FG (1958) Sound pulses. Cambridge University Press, Cambridge
go back to reference Mal AK (1970) Interaction of elastic waves with a Griffith crack. Int J Eng Sci 8:763–776CrossRefMATH Mal AK (1970) Interaction of elastic waves with a Griffith crack. Int J Eng Sci 8:763–776CrossRefMATH
go back to reference Pao Y-H, Mow C-C (1973) Diffraction of elastic waves and dynamic stress concentrations. Crane Russak, New York Pao Y-H, Mow C-C (1973) Diffraction of elastic waves and dynamic stress concentrations. Crane Russak, New York
go back to reference Watanabe K (1982) Scattering of SH-wave by a cylindrical discontinuity in an inhomogeneous elastic medium. Bull JSME 25(205):1055–1060CrossRef Watanabe K (1982) Scattering of SH-wave by a cylindrical discontinuity in an inhomogeneous elastic medium. Bull JSME 25(205):1055–1060CrossRef
go back to reference Watson GN (1966) A treatise on the theory of Bessel functions, vol 2. Cambridge University Press, CambridgeMATH Watson GN (1966) A treatise on the theory of Bessel functions, vol 2. Cambridge University Press, CambridgeMATH
Metadata
Title
Miscellaneous Green’s Functions
Author
Kazumi Watanabe
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-17455-6_7

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