In this manuscript, the anti-plane shear motion of an asymmetric three-layered inhomogeneous elastic plate is examined. An asymptotic approach is employed for the present investigation. Both thgeneralized and unified dispersion relations within the long-wave low-frequency range have been successfully determined. The obtained unified dispersion relation is investigated taking into account the recently analyzed material contrast for layered plates with mixed stiff-soft layers of different material properties. The asymptotic formulae for the respective fields in addition to the determination of approximate equations of motions have also been presented. A comparative study with the symmetric plate is made; being a special case of the asymmetric plate under consideration. In the end, we provide some deductions and concluding remarks.

中文翻译：

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非对称三层复合板反平面动力学问题的渐近法

在这份手稿中，研究了非对称三层非均匀弹性板的反平面剪切运动。本研究采用渐近方法。已经成功地确定了长波低频范围内的广义和统一色散关系。考虑到最近分析的具有不同材料特性的硬-软混合层的分层板的材料对比，研究了获得的统一色散关系。除了确定运动的近似方程外，还提出了各个场的渐近公式。与对称板进行了对比研究；是所考虑的非对称板的一个特例。最后，我们提供一些推论和结束语。