Gaussian Wave Packets in Linear and Nonlinear Anisotropic Elastic Solids

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Gaussian wave packets are high frequency, asymptotic solutions to the equations of elastodynamics. They can be used, for example, to model pulse propagation in complex materials with smoothly varying properties and sharp surfaces of material discontinuity. The fundamental departure from the usual geometrical optics development is that the phase function is assumed to be complex valued. This has important consequences for the behaviour of the solution in the neighbourhood of the unique central ray. For example, if the initial disturbance is in the shape of a gaussian envelope, the propagated pulse remains gaussian. Nonlinear effects are taken into account by assuming the strains remain small, so that weakly nonlinear wave theory can be used. A nonlinear phase modulation equation is derived; and solved for an initial disturbance corresponding to an acceleration wave. This example illustrates that one can obtain a much richer theory through the use of complex phase.

Original languageEnglish (US)
Title of host publicationNorth-Holland Series in Applied Mathematics and Mechanics
Pages491-504
Number of pages14
EditionC
DOIs
StatePublished - Jan 1 1989

Publication series

NameNorth-Holland Series in Applied Mathematics and Mechanics
NumberC
Volume35

Fingerprint

Wave packets
Wave Packet
Geometrical optics
Phase modulation
Disturbance
Modulation Equations
Geometrical Optics
Phase Modulation
Elastodynamics
Asymptotic Solution
Nonlinear Waves
Nonlinear Effects
Envelope
Half line
Discontinuity
Propagation
Model

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Computational Mechanics

Cite this

Norris, A. (1989). Gaussian Wave Packets in Linear and Nonlinear Anisotropic Elastic Solids. In North-Holland Series in Applied Mathematics and Mechanics (C ed., pp. 491-504). (North-Holland Series in Applied Mathematics and Mechanics; Vol. 35, No. C). https://doi.org/10.1016/B978-0-444-87272-2.50079-8
Norris, Andrew. / Gaussian Wave Packets in Linear and Nonlinear Anisotropic Elastic Solids. North-Holland Series in Applied Mathematics and Mechanics. C. ed. 1989. pp. 491-504 (North-Holland Series in Applied Mathematics and Mechanics; C).
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Norris, A 1989, Gaussian Wave Packets in Linear and Nonlinear Anisotropic Elastic Solids. in North-Holland Series in Applied Mathematics and Mechanics. C edn, North-Holland Series in Applied Mathematics and Mechanics, no. C, vol. 35, pp. 491-504. https://doi.org/10.1016/B978-0-444-87272-2.50079-8

Gaussian Wave Packets in Linear and Nonlinear Anisotropic Elastic Solids. / Norris, Andrew.

North-Holland Series in Applied Mathematics and Mechanics. C. ed. 1989. p. 491-504 (North-Holland Series in Applied Mathematics and Mechanics; Vol. 35, No. C).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Norris A. Gaussian Wave Packets in Linear and Nonlinear Anisotropic Elastic Solids. In North-Holland Series in Applied Mathematics and Mechanics. C ed. 1989. p. 491-504. (North-Holland Series in Applied Mathematics and Mechanics; C). https://doi.org/10.1016/B978-0-444-87272-2.50079-8