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Formulation of Elastodynamic Problems. Some General Results

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Methods of the Classical Theory of Elastodynamics

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Abstract

In this chapter transient dynamic problems are formulated within the linear theory of elasticity. In particular, limitations on the solution in the neighborhood of singular curves and points are considered. The notions of solutions containing weak and strong discontinuities are introduced, and the uniqueness theorem for dynamic problems with strong discontinuities is proven. The Green—Volterra formula and various representations of solutions to the equations of motion of homogeneous isotropic continuous media are presented. These are needed for solving elastodynamic problems. The relationship between the solutions to transient problems and the ones to static, steady-state, and stationary dynamic problems is discussed.

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Authors and Affiliations

  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). Formulation of Elastodynamic Problems. Some General Results. In: Methods of the Classical Theory of Elastodynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77099-9_2

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  • DOI: https://doi.org/10.1007/978-3-642-77099-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-77101-9

  • Online ISBN: 978-3-642-77099-9

  • eBook Packages: Springer Book Archive

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