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Degenerated Hyperbolic Approximations of the Wave Theory of Elastic Plates

  • Igor Selezov
Part of the Operator Theory: Advances and Applications book series (OT, volume 117)

Abstract

A 3-D problem of elastodynamics is formulated for a layer as an initial boundary value (IBV) problem for hyperbolic equations. The problem is investigated to reduce this 3-D problem to a degenerated 2-D problem, i.e. to construct hyperbolically degenerated model with respect to a spatial coordinate so that the corresponding approximate problem would be also of a hyperbolic type. This is a problem of hyperbolic degeneration and it is solved here by means of the power series method and introduction of the rule to truncate the infinite systems. Several hyperbolic models as mathematical approximations for wave motion in elastic plates are obtained without any physical assumptions ordinarily used in the theory of elastic plates.

Classification number

MSI N 35L30 

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Copyright information

© Springer Basel AG 2000

Authors and Affiliations

  • Igor Selezov
    • 1
  1. 1.Department of Wave ProcessesInst. of Hydromechanics NAS of UkraineKievUkraine

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