【作者】 浦俊； 卢东强；

【Author】 PU Jun;LU Dong-qiang;Shanghai Institute of Applied Mathematics and Mechanics,School of Mechanics and Engineering Science,Shanghai University;Shanghai Key Laboratory of Mechanics in Energy Engineering;

【机构】 上海大学力学与工程科学学院上海市应用数学和力学研究所； 上海市能源工程力学重点实验室；

【摘要】 在线性势流理论的框架内推导了浸没于两层流体多孔弹性板波动的色散关系.假设流体无黏且不可压缩,流体运动无旋.在两层流体模型中,具有不同密度的上层和下层流体被稳定的界面分开.假设入射波是简谐的且频率给定,将速度势中的时间变量分离.将控制方程通解以及表面和界面的空间位移,分别代入表面、界面以及底部的边界条件,得到了色散关系.浸没板的存在使得表面波模态对应的频率随波数变化的曲线变陡,浸没板行波模态在较低波数下与开阔水域的界面波模态曲线重合,但在较大波数下与开阔水域表面波模态曲线重合了.表面波模态出现了最小群速度和相速度,而界面波出现了最大群速度和相速度。讨论了抗弯刚度、密度比以及界面位置对色散关系、群速度以及相速度的影响.更多还原

【Abstract】 With the framework of the linear flow theory,the dispersion relationship of the two-layer fluid with a submerged porous elastic plate is derived.It is assumed that the fluid is inviscid and incompressible,and the fluid motion is irrotational.In the two-layer fluid model,the upper and lower fluids with different densities separated bya sharp and stable interface.Assuming that the incident wave is harmonic with a given frequency,the time factor of the velocity potential can be separated.The general solution of the governing equation and the spatial displacement of the surface and the interface are substituted into the boundary conditions of the surface,the interface and the bottom respectively,and the dispersion relationship is obtained.The submerged plate makes the curve of dispersion relationship of the surface wave become steeper.The wave mode of the submerged plate coincides with the curve of interface mode inthe open water region at a lower wave number,but it coincides with the curve of surface mode inthe open water region under a larger wave number.The group and phase velocities of the surface wave mode have the minimum values,while those of the interface wave mode have the maximum values.The influence of flexural stiffness,density ratio and interface position on the dispersion relationship,group velocity and phase velocity are discussed.更多还原