An asymptotic approach of analysis is used to analyze the antisymmetric anti-plane shear dispersion of an elastic inhomogeneous five-layered plate in the presence of material contrasts. The resultant exact dispersion relation, overall cut-off frequency and the low-frequency range are determined. Two different asymptotic contrasting material setups for layered plates are employed with regards to the optimal shortened polynomial dispersion relation in the context of the structure under consideration. The asymptotic behaviors of the displacements and stresses in the respective layers of the plate are also examined. Finally, we provided some concluding remarks.

中文翻译：

---

弹性五层板抗平面剪切振动的动力学和色散的渐近研究

采用渐近分析的方法来分析存在材料对比的弹性非均质五层板的非对称反平面剪切分散。确定所得的精确色散关系，总截止频率和低频范围。关于所考虑的结构的最佳缩短多项式色散关系，采用了两种不同的层合板渐近对比材料设置。还检查了板各层中位移和应力的渐近行为。最后，我们提供了一些总结性意见。