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Methods of the Classical Theory of Elastodynamics pp 43–136Cite as

The Method of Functionally Invariant Solutions (the Smirnov-Sobolev Method)

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Abstract

The method of functionally invariant solutions was developed in the 1930s by Smirnov and Sobolev who called it “the method of complex solutions”. It was designed for solving two- and three-dimensional nonstationary problems of isotropic elasticity and was closely related to the refined body of mathematics of theoretical seismology. The most detailed description of the method was presented by Smirnov and Sobolev in [3.1,2]. The method was further developed and applied to solving elastodynamic problems mosdy in the Soviet Union. In the 1930–50s it was used for analyzing and solving a number of problems of nonstationary oscillations of a half-space [3.3,4], elastic wave propagation within a layer [3.5], reflection and refraction of elastic waves, the general theory of Rayleigh waves [3.6–11], and diffraction of plane acoustic waves by a wedge [3.12]. The method was also employed for solving two- [3.13–15] and three-dimensional [3.16] problems of diffraction of plane elastic waves at cuts and welded half-planes.

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  1. Institute of Mechanics, Moscow State University, 1, Michurinsky Prospect, 117192, Moscow, Russia

    Professor Dr. Vladimir B. Poruchikov

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  1. Professor Dr. Vladimir B. Poruchikov
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© 1993 Springer-Verlag Berlin Heidelberg

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Poruchikov, V.B. (1993). The Method of Functionally Invariant Solutions (the Smirnov-Sobolev Method). In: Methods of the Classical Theory of Elastodynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77099-9_3

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  • DOI: https://doi.org/10.1007/978-3-642-77099-9_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-77101-9

  • Online ISBN: 978-3-642-77099-9

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