三层流体中斜入射波作用下半无限板的水弹性响应

解析地研究了在三层流体中斜入射波浪与半无限弹性板的相互作用引起的波散射和板的水弹性响应. 三层流体在界面处的密度发生阶跃, 各层为一常数. 假设流体不可压缩、无黏、流体运动无旋. 在线性势流理论框架下, 使用本征函数展开法和内积式给出波板相互作用的半解析解. 根据色散关系分析, 得到了表面波模态和界面波模态入射时的临界入射角. 随着物理参数的变化, 临界角将随之发生变化. 临界角决定了当由开阔水域向板覆盖水域传播的表面波或界面波的存在性: (1)板覆盖水域入射界面上, 透射波能否存在; (2)入射界面之上界面中, 板覆盖水域中的透射波以及开阔水域中的反射波能否存在. 当下界面波入射时并且入射角足够大时, 开阔水域中的下界面波模态是整个流体域中唯一存在的模态. 

HYDROELASTIC RESPONSE OF A SEMI-INFINITE PLATE DUE TO OBLIQUELY INCIDENT WAVES IN A THREE-LAYER FLUID1)

Wave scattering and hydroelastic response of semi-infinite elastic plates due to obliquely incident waves in a three-layer fluid are studied analytically. The densities of the three layers of fluid are different with sharp interfaces, but are constant at each layer. The fluid is assumed to be inviscid and incompressible and the motion to be irrotational. Within the frame of the linear potential flow, semi-analytical solutions for wave-plate interaction are derived with the aid of the methods of matched eigenfunction expansions and the inner product of eigenfunction. The critical angles for the incident waves of the surface mode and the interfacial wave mode are deduced in terms of the dispersion relation. As the physical parameters change, the critical angle varies accordingly. The critical angle are closely related with the existence of the surface or interfacial wave modes that propagate from the open water region to the plate-covered one, by which two problems can be answered: (1) Is there a transmitted wave on the incident interface in the plate-covered region; (2) Is there, on the interfaces above the incident surface, a transmitted wave on the plate-covered region and a reflected wave in the open water region. When the low interfacial wave is incident and the incident angle is large enough, the low interfacial wave mode in the open-water region becomes the solo wave mode in the entire fluid domain.