Summary
In this paper some special types of finite amplitude wave motions are considered, for which kinematical non-linearities do not arise in the equations of motion of an elastic solid. Consequently, only constitutive non-linearities occur and, for special classes of materials, solutions may be read off from corresponding solutions in the linear theory. These include SH-waves1 and Love waves in layered or inhomogeneous media. Finite amplitude transverse circularly-polarized harmonic progressive waves are shown to propagate in any compressible or incompressible isotropic elastic material. Some effects of homogeneous pre-stress are also investigated.
Zusammenfassung
Es werden Spezialfälle von Wellenbewegungen mit endlicher Amplitude betrachtet, für die keine kinematischen Nichtlinearitäten in den Bewegungsgleichungen des elastischen Festkörpers auftreten. Es kommen also nur Material-Nichtlinearitäten vor. Für gewisse Klassen von Materialien können die Lösungen aus den entsprechenden der linearen Theorie gewonnen werden. Hierher gehören horizontal polarisierte Scherwellen und Lovesche Wellen in geschichteten oder inhomogenen Medien. Es wird gezeigt, daß sich harmonische, zirkularpolarisierte Transversalwellen in jedem kompressiblen oder inkompressiblen elastischen Material fortpflanzen. Einige Effekte homogener Vorspannung werden ebenfalls untersucht.
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Carroll, M.M. Some results on finite amplitude elastic waves. Acta Mechanica 3, 167–181 (1967). https://doi.org/10.1007/BF01453713
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DOI: https://doi.org/10.1007/BF01453713