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Ray Expansion Theory

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Encyclopedia of Continuum Mechanics

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Synonyms

Ray series application for the description of transient wave propagation

Definitions

Ray series are power series, the coefficients of which are the discontinuities in arbitrary order partial time derivatives of the desired functions, while the time of arrival of the wave front is the independent variable; in so doing the order of the partial time derivative coincides with the power exponent of the independent variable.

Preliminary Remarks

In solving problems of the propagation and attenuation of transient waves carrying the jumps in the field parameters on the wave front, the methods utilizing ray expansions are most efficient. A zeroth term of a ray series exactly describes the changes in the field parameter discontinuity along the ray, but the rest of the terms within the radius of the series convergence reveal the changes in the field behind the wave front.

The questions of the ray series application to transient wave problems have been considered by many investigators, and...

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References

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Author information

Authors and Affiliations

  1. Voronezh State Technical University, Voronezh, Russia

    Yury A. Rossikhin

  2. Research Center on Dynamics of Solids and Structures, Voronezh State Technical University, Voronezh, Russia

    Marina V. Shitikova

Authors
  1. Yury A. Rossikhin
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  2. Marina V. Shitikova
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Corresponding author

Correspondence to Marina V. Shitikova .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Institut für Mechanik, Magdeburg, Germany

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, QLD, Australia

    Andreas Öchsner

Section Editor information

  1. Research Center on Dynamics of Solids and Structures, Voronezh State Technical University, Voronezh, Russia

    Marina V. Shitikova

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Rossikhin, Y.A., Shitikova, M.V. (2019). Ray Expansion Theory. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_97-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_97-1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

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