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General Laws of Propagation of Elastic Waves in Crystals

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Theory of Elastic Waves in Crystals

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Abstract

The laws of propagation of elastic waves in crystals follow from the general equations of motion derived in section 3 for an elastically deformed medium . Here the force of gravity may be neglected, so we may use (3.10)

EquationSource% MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyWdiNaam % i-amaaBaaaleaacaWGPbaabeaakiabg2da9maalaaabaGaeyOaIyRa % eq4Wdm3aaSbaaSqaaiaadMgacaWGRbaabeaaaOqaaiabgkGi2kaadI % hadaWgaaWcbaGaam4AaaqabaaaaOGaaiOlaaaa!44E5! \[\rho {\"u _i} = \frac{{\partial {\sigma _{ik}}}} {{\partial {x_k}}}.\] $$
((15.1))

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References

  • A relation is covariant if both parts are in a form from which it is obvious that they change identically in response to coordinate transformation.

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  • Musgrave [13] has used the form of (19.28) to construct a general theory of elastic waves in crystals, but this is inapplicable even to a crystal as important as quartz.

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  • Of course, (19.22) and (19.25) are now not obeyed, since the coordinate axes have been chosen in another way.

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Authors and Affiliations

  1. Laboratory of Theoretical Physics, Physics Institute of the Academy of Sciences of the Belorussian SSR, Belarus

    Academician Fedor I. Fedorov (Director, Chairman)

  2. Department of Theoretical Physics, Belorussian State University, Minsk, Belarus

    Academician Fedor I. Fedorov (Director, Chairman)

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  1. Academician Fedor I. Fedorov
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© 1968 Springer Science+Business Media New York

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Fedorov, F.I. (1968). General Laws of Propagation of Elastic Waves in Crystals. In: Theory of Elastic Waves in Crystals. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1275-9_3

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  • DOI: https://doi.org/10.1007/978-1-4757-1275-9_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-1277-3

  • Online ISBN: 978-1-4757-1275-9

  • eBook Packages: Springer Book Archive

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