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Zeynep Kalaycıoğlu | Tem 03, 2024
The study titled “SH Waves in a weakly inhomogenous half space with a nonlinear thin layer coating” was published in Zeitschrift Für Angewandte Mathematik Und Physik (ZAMP) by ITU Mathematics Engineering faculty members Prof. Dr. Semra Ahmetolan, Assoc. Prof. Dr. Ali Demirci, Assoc. Prof. Dr. Ayse Peker-Dobie, and Dr. Neşe Özdemir.
In this study, the self-modulation of Love waves propagating in a nonlinear half-space covered by a nonlinear layer was investigated. It was assumed 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. 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.
https://doi.org/10.1007/s00033-024-02213-y