過去的研究顯示雙層均質等向性材料界面間，反平面界面波是不存在的。本文探討雙層非均質材料界面間，反平面界面波存在的可能性。文中首先針對雙層功能性梯度材料的結合，導出雙層材料一些搭配下，反平面界面波存在的條件，並列出對應的允許波數範圍。另由分析某些參數對界面波波速的影響，發現界面波有非頻散性的可能。本文最後針對均質材料與梯度材料的結合進行了探討，結果顯示界面波也可以存在，且若兩層材料的橫向波速不等時，會有兩個截止頻率出現。

It is known that the interfacial waves for anti-plane problems do not exist in layered homogeneous isotropic media. In this thesis, we demonstrate that interfacial waves can exist in the interface of functionally graded materials. We first analyze the media composed by two functionally graded materials where the conditions of existence of interfacial waves are derived and the corresponding interval of wave number is listed. We also examine the effects of some material’s parameters on the interfacial wave speed and wave number. It is found that in some cases interfacial waves are non-dispersive. We also analyze the existence of interfacial waves for the problem of homogeneous isotropic material perfectly bonded to functionally graded materials. For this case, two cut-off frequencies are found when the shear wave velocities for each of two media are not equal.

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