多个椭圆柱波浪力的一种解析解

AN ANALYTICAL SOLUTION FOR WAVE PRESSURE ON ARRAYS OF ELLIPTICAL BODIES

波浪在大尺寸结构表面产生不可忽略的散射波,该散射波在多柱体体系中继续传播,并在同体系中的其他柱体上产生高次散射波.本文基于椭圆坐标系和绕射波理论首先推导了波浪作用下椭圆单柱体产生的散射波压力公式,随后考虑该散射波在多柱体系中的传播,将其视为第二次入射波,推导出柱体上第二次散射波压力公式,同理可以推导出高次散射波压力公式,最后得到椭圆多柱体波浪力解析解,并用数值解验证了本文解析方法的正确性.本文以双柱体和四柱体体系为例,分析了不同参数(波数、净距、波浪入射角度等)下,高次散射波对柱体上波浪作用的影响.结果表明:波数较大的情况下,高次散射波引起柱体上的波浪力不能忽略;结构间距较大的情况下,虽然高次波的作用有减小的趋势但仍然明显;高次散射波来自多个柱体对入射波的散射,柱体数目的增加后,高次波的影响会增加,结构所受的高次波作用因参数变化而起的波动会变剧烈;高次波对上游柱体波浪力的贡献较对下游柱体的贡献大.

In an array of elliptical cylinders, upon impinging on large structure, linear incident waves are scattered by bodies;the scattered waves due to linear incident waves subsequently impinge other bodies;the higher-order scattered waves are generated in the same manner as the multiple scattering problem exists. Based on the diffraction theory and elliptic cylindrical coordinates, the analytical solution for the incident and the scattered waves, say the first-order scattered wave, on an isolated elliptical body is formulated firstly;then, with the first-order scattered wave from other bodies as the excitation source, the analytical solution for second-order scattered waves is developed;Analogously, the analytical solution for higher-order scattered waves is obtained;finally, the total wave pressure on a body in an array is obtained in a form of a sum of the incident wave pressure, the first-order scattered wave pressure due to the linear incident wave and the scattered wave pressure considering multiple scattering waves. The present method is validated by a FEM and is applied to two cases in which multiple scattering problem on bodies with different parameters(wave number, separation, wave propagation direction, etc.) is discussed. It can be seen from the results that the effect of highorder scattered wave matters as the wave number is large;multiple scattering problem is reducing but still exists as the distance between bodies increasing;As the quantity of bodies growing, the multiple scattering problem is increasing and its impact is drastically undulant;the effect of high-order scattered wave on the leading structures is larger than that on the one in the downstream.