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

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Ahmetolan S., Demirci A., Peker A., Özdemir N.

Zeitschrift fur Angewandte Mathematik und Physik, cilt.75, sa.2, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 75 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s00033-024-02213-y
  • Dergi Adı: Zeitschrift fur Angewandte Mathematik und Physik
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: 35C20, 74E05, 74J35, 74K20, Nonlinear elasticity, Shear waves, Solitary waves, Weak inhomogeneity
  • Marmara Üniversitesi Adresli: Hayır

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.