The edge wave is a kind of infragravity wave. It¡¦s forcing and evolu- ion are different from common progressive waves. It may damage the co- astal area when a wave incident to the shore with an angle is reflected and reflected back by topography. In this thesis,by AWCP deployed near Kao- hsiung and Hualien harbor,the flow and surface elevation of the tsunami generated in PingTung earthquake and typhoon waves are analyzed.By assuming uni-directional progressive waves and HHT, the theoretical solution is used to check if the edge wave exists. The primary results suggest that Stokes edge wave is a significant component of the tsunami in Kaohsiung area and it might be generated when the tsunami arrived the DongGung or SGC.The infragravity wave generated by typhoon waves in typhoon Kaemi, Bopha and Hugupit are also edge waves by the relation between pressure and flow.That means edge waves be generated by typhoon waves outside the Hualien harbor will transport low frequence energy to the the harbor basin and cause the resonance of Hualien harbor.

In the thesis explicit dual parabolic-elliptic models are constructed for the Konenkov flexural edge wave and the Stoneley-type flexural interfacial wave in case of thin linearly elastic plates. These waves do not appear in an explicit form in the original equations of motion within the framework of the classical Kirchhoff plate theory. The thesis is aimed to highlight the contribution of the edge and interfacial waves into the overall displacement field by deriving specialised equations oriented to aforementioned waves only. The proposed models consist of a parabolic equation governing the wave propagation along a plate edge or plate junction along with an elliptic equation over the interior describing decay in depth. In this case the parabolicity of the one-dimensional edge and interfacial equations supports flexural wave dispersion. The methodology presented in the thesis reveals a dual nature of edge and interfacial plate waves contrasting them to bulk-type wave propagating in thin elastic structures. The thesis tackles a number of important examples of the edge and interfacial wave propagation. First, it addresses the propagation of Konenkov flexural wave in an elastic isotropic plate under prescribed edge loading. For the latter, parabolic-elliptic explicit models were constructed and thoroughly investigated. A similar problem for a semi-infinite orthotropic plate resulted in a more general dual parabolic-elliptic model. Finally, an anal- ogous model was derived and analysed for two isotropic semi-infinite Kirchhoff plates under perfect contact conditions.