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Determination of a general solution of three-dimensional Lamé equations of elasticity theory

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Nonlinear Oscillations

Abstract

We integrate the Lamé equation and find new solutions in the case of three-dimensional elasticity theory, which are expressed in terms of harmonic functions. We prove that the solution obtained involves only three independent functions. In a curvilinear orthogonal coordinate system, a general solution of the Lamé equation is expressed in terms of three harmonic functions.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv

    V. P. Revenko

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  1. V. P. Revenko
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__________

Translated from Neliniini Kolyvannya, Vol. 9, No. 1, pp. 109–116, January–March, 2006.

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Revenko, V.P. Determination of a general solution of three-dimensional Lamé equations of elasticity theory. Nonlinear Oscill 9, 107–114 (2006). https://doi.org/10.1007/s11072-006-0029-y

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  • DOI: https://doi.org/10.1007/s11072-006-0029-y

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