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On wave propagation and uniqueness in one-dimensional elastic bodies

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Abstract

A notion referred to as the Wave Propagation Property is analyzed in the context of the nonlinear theory of one-dimensional elastic bodies. Roughly speaking, a body possesses this property if mechanical disturbances propagate with bounded speed. A uniqueness theorem is proven with the aid of the results on wave propagation.

Zusammenfassung

Ein Begriff, bezeichnet als Wellenfortpflanzungseigenschaft, wird in Zusammenhang mit der nicht-linearen Theorie des eindimensionalen elastischen Körpers untersucht. Ein Körper besitzt, gross gesprochen, diese Eigenschaft, wenn sich mechanische Störungen mit beschränkter Geschwindigkeit fortpflanzen. Mit Hilfe des Ergebnisses für Wellenfortpflanzung wird ein Eindeutigkeitsatz bewiesen.

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References

  1. Wheeler, Lewis T. and Eli, Sternberg, Some Theorems in Classical Elastodynamics, Arch. Rat. Mech. Anal., 31, (1968) 51.

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  2. Wheeler, Lewis T., Some Results in the Linear Dynamical Theory of Anisotropic Elastic Solids, Quart. Appl. Math., 28, (1970) 91.

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  3. Wheeler, Lewis T. and R. Ray Nachlinger, On the Propagation of Waves and Uniqueness, Department of Mechanical Engineering, University of Houston, TR 1902.

  4. Barberan, Jose and Ismael, Herrera, Uniqueness Theorems and the Speed of Propagation of Signals in Viscoelastic Matherials, Arch. Rat. Mech. Anal. 23, (1966) 173.

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Authors and Affiliations

  1. University of Houston, 77004, Houston, Texas

    R. Ray Nachlinger & Lewis T. Wheeler

Authors
  1. R. Ray Nachlinger
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  2. Lewis T. Wheeler
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Nachlinger, R.R., Wheeler, L.T. On wave propagation and uniqueness in one-dimensional elastic bodies. J Elasticity 3, 141–146 (1973). https://doi.org/10.1007/BF00045820

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  • DOI: https://doi.org/10.1007/BF00045820

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