The present paper studies the anti-plane shear motion of an inhomogeneous elastic five-layered plate amidst the four contrasting material setups. The asymptotic analysis method in regard to the various material parameters is adopted for the study. The respective displacements, stresses and the Rayleigh-Lamb dispersion relation corresponding to the antisymmetric anti-plane motion with perfect interlayer and traction-free (on the outer faces) boundary conditions are determined. Furthermore, in order to analyze the said dispersion relation in the presence of these contrasts, a unification of parameters was proposed. The overall cutoff frequencies and the low-frequency estimates are determined for both the generalized and unified settings. A comparative analysis between the unified Rayleigh-Lamb dispersion relation and the optimal shortened polynomial dispersion relation is carried for each contrast. We also established some asymptotic formulae for the related unified displacements and stresses.

中文翻译：

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弹性五层结构反特性下反平面剪切分散的渐近分析

本文研究了在四种对比材料设置中非均匀弹性五层板的反平面剪切运动。本研究采用关于各种材料参数的渐近分析方法。确定了与具有完美夹层和无牵引力（在外面）边界条件的反对称反平面运动相对应的各个位移，应力和瑞利-兰姆散射关系。此外，为了在存在这些对比的情况下分析所述色散关系，提出了参数的统一。确定通用设置和统一设置的总截止频率和低频估计值。对每种对比度进行了统一的瑞利-兰姆色散关系与最优缩短多项式色散关系之间的比较分析。我们还为相关的统一位移和应力建立了一些渐近公式。