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Linear and Nonlinear Wave Propagation in Coated or Uncoated Elastic Half-spaces

  • Chapter
Waves in Nonlinear Pre-Stressed Materials

Part of the book series: CISM Courses and Lectures ((CISM,volume 495))

Abstract

In these lectures, we discuss three closely related topics. We first discuss derivation of the nonlinear evolution equation for surface acoustic waves and show that all known methods of derivation should and do give the same evolution equation. We then study linear wave propagation in a coated elastic half-space and show how the dispersion relation can be expressed elegantly in terms of the surface-impedance matrices associated with the layer and half-space. We derive a two-term expression for the wave speed in the long-wavelength limit. Finally, we look at periodic and solitary waves in a coated elastic half-space. We derive the nonlinear evolution equation for small-amplitude long-wavelength travelling waves propagating in a coated elastic half-space where the thin coating induces weak dispersion. We explain a simple method that can be used to compute periodic or solitary travelling-wave solutions.

The author thanks Professor V.E. Gusev for reading an earlier version of these notes and for drawing his attention to the work of Professor V.P. Reutov.

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Authors and Affiliations

  1. Department of Mathematics, Keele University, Keele, UK

    Yibin Fu

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  1. Yibin Fu
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Editors and Affiliations

  1. CNRS Paris, France

    Michel Destrade

  2. University of Lecce, Italy

    Giuseppe Saccomandi

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Fu, Y. (2007). Linear and Nonlinear Wave Propagation in Coated or Uncoated Elastic Half-spaces. In: Destrade, M., Saccomandi, G. (eds) Waves in Nonlinear Pre-Stressed Materials. CISM Courses and Lectures, vol 495. Springer, Vienna. https://doi.org/10.1007/978-3-211-73572-5_4

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  • DOI: https://doi.org/10.1007/978-3-211-73572-5_4

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-73571-8

  • Online ISBN: 978-3-211-73572-5

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