Yazar "Demirkus, Dilek" seçeneğine göre listele

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    Antisymmetric bright solitary SH waves in a nonlinear heterogeneous plate
    (Springer International Publishing Ag, 2018) Demirkus, Dilek
    The propagation of nonlinear shear horizontal (SH) waves in an incompressible hyper-elastic plate of uniform thickness is investigated. It is assumed that the plate is made of heterogeneous, isotropic, and generalized neo-Hookean materials. By applying the method of multiple scales, a nonlinear Schrodinger (NLS) equation is derived describing the nonlinear self modulation of the waves. As a result of known solutions of an NLS equation, it is found that the antisymmetric bright solitary SH waves will exist and propagate in this plate. Moreover, not only the effect of the heterogeneity but also the effect of the nonlinearity on the deformation field is discussed for these waves.
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    Antisymmetric dark solitary SH waves in a nonlinear heterogeneous plate
    (Springer International Publishing Ag, 2019) Demirkus, Dilek
    In the present work, we investigate the propagation of the nonlinear shear horizontal (SH) waves in a plate, which is composed of isotropic, hyperelastic, heterogeneous, and generalized neo-Hookean materials. Using the method of multiple scales, we strike a balance between the nonlinearity and the dispersion, and by then, we see that the nonlinear modulation of these waves can express in terms of a nonlinear Schrodinger equation. We know that this equation has been derived from many areas of physics and has some solitary wave solutions. Therefore, we claim that the antisymmetric dark solitary SH waves exist and propagate in this plate, in addition to considering both the heterogeneous effect and the nonlinear effect on the deformation field for these waves.
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    Non-linear anti-symmetric shear motion: a comparative study of non-homogeneous and homogeneous plates
    (Springer International Publishing Ag, 2020) Demirkus, Dilek
    In this article, the non-linear anti-symmetric shear motion for some comparative studies between the non-homogeneous and homogeneous plates, having two free surfaces with stress-free, is considered. Assuming that one plate contains hyper-elastic, non-homogeneous, isotropic, and generalized neo-Hookean materials and the other one consists of hyper-elastic, homogeneous, isotropic, and generalized neo-Hookean materials. Using the method of multiple scales, the self-modulation of the non-linear anti-symmetric shear motion in these plates, as the non-linear Schrodinger (NLS) equations, can be given. Using the known solitary wave solutions, called bright and dark solitary wave solutions, to NLS equations, these comparative studies in terms of the non-homogeneous and non-linear effects are made. All numerical results, based on the asymptotic analyses, are graphically presented for the lowest anti-symmetric branches of both dispersion relations, including the deformation fields of plates.
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    Some comparisons between heterogeneous and homogeneous layers for nonlinear SH waves in terms of heterogeneous and nonlinear effects
    (Sage Publications Ltd, 2021) Demirkus, Dilek
    This paper aims to make some comparative studies between heterogeneous and homogeneous layers for nonlinear shear horizontal (SH) waves in terms of the heterogeneous and nonlinear effects. Therefore, with this aim, two layers are defined as follows: on the one hand, one layer consists of hyperelastic, isotropic, heterogeneous, and generalized neo-Hookean materials; on the other hand, another layer is made up of hyperelastic, isotropic, homogeneous, and generalized neo-Hookean materials. Moreover, it is assumed that upper boundaries are stress-free and lower boundaries are rigidly fixed. The method of multiple scales is used in both analyses, in addition to using the known solutions of the nonlinear Schrodinger (NLS) equation, called bright and dark solitary wave solutions; these comparisons are made, numerically, and then all results are given for the lowest branch of both dispersion relations, graphically. Moreover, these comparisons are observed both on a large scale and on a small scale, not only in terms of the bright and dark solitary wave solutions but also in terms of the heterogeneous and nonlinear effects.
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    Some comparisons between heterogeneous and homogeneous plates for nonlinear symmetric SH waves in terms of heterogeneous and nonlinear effects
    (Springer Int Publ Ag, 2021) Demirkus, Dilek
    In this article, the propagation of nonlinear shear horizontal waves for some comparisons between the heterogeneous and homogeneous plates is considered. It is assumed that one plate is made of up hyper-elastic, heterogeneous, isotropic, and generalized neo-Hookean materials, and the other consists of hyper-elastic, homogeneous, isotropic, and generalized neo-Hookean materials. Using the known solitary wave solutions, called bright and dark solitary wave solutions, to the nonlinear Schrodinger equation, these comparisons are made in terms of the heterogeneous and nonlinear effects. All numerical results, based on the asymptotic analyses in which the method of multiple scales is used, are graphically presented for the lowest dispersive symmetric branch of both dispersion relations.
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    Symmetric bright solitary SH waves in a nonlinear heterogeneous plate
    (Springer International Publishing Ag, 2019) Demirkus, Dilek
    In this work, we investigate the propagation of shear horizontal (SH) waves in a nonlinear hyperelastic plate. We assume that the plate is made of heterogeneous, isotropic, and generalized neo-Hookean materials. The problem is examined with a perturbation method that balances the nonlinearity and dispersion in the analysis. Then, a nonlinear Schrodinger (NLS) equation is derived describing the nonlinear self-modulation of the waves. Using known solutions of an NLS equation, we found that the symmetric bright solitary SH waves will exist and propagate in this plate. Moreover, not only the effect of the heterogeneity, but also the effect of the nonlinearity on the deformation field is also considered for these waves.
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    Symmetric dark solitary SH waves in a nonlinear heterogeneous plate
    (Springer International Publishing Ag, 2019) Demirkus, Dilek
    In the present work, we search for the propagation of nonlinear shear horizontal waves (SH) in a finite thickness plate which consists of heterogeneous, isotropic, and generalized neo-Hookean materials. In the analysis, we apply the method of multiple scales and strike a balance between the nonlinearity and the dispersion. Then, the self-modulation of nonlinear SH waves can be given by a nonlinear Schrodinger equation which has the well-known dark solitary solution. Consequently, we show that the dark solitary SH waves can propagate in this plate. Moreover, we take the effects of heterogeneity and the nonlinearity into account for these waves.