Non-linear waves in slightly anisotropic elastic media

Riemann waves in an elastic medium with small cubic anisotropy

“…This will be taken into consideration in the series expansion of ~. For quasi-transverse non-linear waves in an isotropic medium, the essential terms of the expansion of q5 turn out to be It was shown in [2] that quasi-transverse waves in a medium with small anisotropy (which is always the case in practice) acquire new qualitative properties. For the effects of non-linearity and anisotropy to app,ear in their interactions, the terms in the expansion of @ that account for anisotropy must be of the same order as the non-linear terms, i.e.…”

“…This term appears even naturally in an isotropic medium when there is constant prestrain in the plane of the wave front. Non-linear waves in such a medium have been studied in numerous publications, including [2]; Riemann waves were already described in [3].…”

“…Since the strains are small, the function • may be represented by a series in powers of ui, retaining as many powers of ui as necessary for the effects of the non-linearity of the medium to appear. It is well known [1,2] that to that end it is sufficient to retain fourth powers of ui. Because of the non-linearity, purely longitudinal and purely transverse elastic waves become quasilongitudinal and quasi-transverse.…”

Transverse corrugation solitons in a three-layered non-linearly elastic medium

“…When this does not give rise to any misunderstandings, we shall only talk about the plate. We represent the energy of the non-linearly elastic plate in the form [2][3][4] where ~) is the energy referred to unit volume of the plate prior to deformation. The expression ~,<~pq> = ~ denotes that the term for which k + 2p + 3q = n(n >_ 2) are summed, and integration is carried out over the volume V0 of the plate prior to deformation.…”

“…In the theory of finite deformations [2][3][4], the elastic energy of a medium is described in the form of an expansion in the invariants of the Lagrange strain tensor…”