SH waves in a weakly inhomogeneous half space with a nonlinear thin layer coating

Semra Ahmetolan, Ali Demirci*, Ayse Peker-Dobie, Nese Ozdemir

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Özet

We investigate the self-modulation of Love waves propagating in a nonlinear half-space covered by a nonlinear layer. We assume that the constituent material of the layer is nonlinear, homogeneous, isotropic, compressible, and hyperelastic, whereas for the half-space, it is nonlinear, heterogeneous, compressible and a different hyperelastic material. By employing the nonlinear thin layer approximation, the problem of wave propagation in a layered half-space is reduced to the one for a nonlinear heterogeneous half-space with a modified nonlinear homogeneous boundary condition on the top surface. This new problem is analyzed by a relevant perturbation method, and a nonlinear Schrödinger (NLS) equation defining the self-modulation of waves asymptotically is obtained. The dispersion relation is derived for different heterogeneous properties of the half-space and the thin layer. Then the results of the thin layer approximation are compared with the ones for the finite layer obtained in Teymur et al. (Int J Eng Sci 85:150–162, 2014). The solitary solutions of the derived NLS equation are obtained for selected real material models. It has been discussed how these solutions are influenced by the heterogeneity of the semi-infinite space.

Orijinal dilİngilizce
Makale numarası68
DergiZeitschrift fur Angewandte Mathematik und Physik
Hacim75
Basın numarası2
DOI'lar
Yayın durumuYayınlandı - Nis 2024

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© The Author(s) 2024.

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