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Non-linear anti-symmetric shear motion: a comparative study of non-homogeneous and homogeneous plates

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Abstract

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 Schrödinger (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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Acknowledgements

We are grateful to Dear Distinguished Editor Prof. David J. Steigmann as a good advisor for good handling the paper and the respected referee as a good mentor for improving the quality of this paper.

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  1. Department of Mathematics, Faculty of Arts and Sciences, Beykent University, 34520, Istanbul, Turkey

    Dilek Demirkuş

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Demirkuş, D. Non-linear anti-symmetric shear motion: a comparative study of non-homogeneous and homogeneous plates. Z. Angew. Math. Phys. 71, 193 (2020). https://doi.org/10.1007/s00033-020-01417-2

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