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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2005, Volume 46, Issue 1, Pages 160–172
(Mi pmtf2236)
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This article is cited in 4 scientific papers (total in 4 papers)
Purely transverse waves in elastic anisotropic media
N. I. Ostrosablin Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, 630090, Novosibirsk
Abstract:
Formulas are obtained for decompositions of the third- and fourth-rank tensors symmetric in the last two and three indices, respectively, into irreducible parts invariant relative to the orthogonal group of coordinate transformation. The corresponding parts of the decompositions are orthogonal to each other. These decompositions are used to obtain a general representation of the displacement vectors of plane transverse waves in elastic isotropic and anisotropic solids. It is shown that the displacement vectors of transverse waves are second-, third-, and fourth-degree homogeneous polynomials of the wave normal. Special orthotropic materials are found that transmit purely transverse waves for any direction of the wave normal. The eigenmoduli, eigenstates, and engineering constants (bulk moduli, Young’s moduli, Poisson’s ratios, shear moduli, and Lamé constants of the closest isotropic materials) are determined for these materials.
Keywords:
irreducible invariant decomposition, longitudinal and transverse waves, anisotropy, elastic moduli, eigenmoduli, eigenstate.
Received: 27.04.2004
Citation:
N. I. Ostrosablin, “Purely transverse waves in elastic anisotropic media”, Prikl. Mekh. Tekh. Fiz., 46:1 (2005), 160–172; J. Appl. Mech. Tech. Phys., 46:1 (2005), 129–140
Linking options:
https://www.mathnet.ru/eng/pmtf2236 https://www.mathnet.ru/eng/pmtf/v46/i1/p160
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