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## 留言板 引用本文: 赵密, 龙彭振, 王丕光, 张超, 杜修力. 多个椭圆柱波浪力的一种解析解. 力学学报, 待出版 Zhao Mi, Long Pengzhen, Wang Piguang, Zhang Chao, Du Xiuli. An analytical solution for wave pressure on arrays of elliptical bodies. Chinese Journal of Theoretical and Applied Mechanics, in press doi: 10.6052/0459-1879-21-318
 Citation: Zhao Mi, Long Pengzhen, Wang Piguang, Zhang Chao, Du Xiuli. An analytical solution for wave pressure on arrays of elliptical bodies. Chinese Journal of Theoretical and Applied Mechanics, in press ## 多个椭圆柱波浪力的一种解析解

##### doi: 10.6052/0459-1879-21-318

###### 作者简介:王丕光, 教授, 主要研究方向: 近海工程结构抗震及防灾减灾. E-mail: wangpiguang1985@126.com
• 中图分类号: TU311.3

## AN ANALYTICAL SOLUTION FOR WAVE PRESSURE ON ARRAYS OF ELLIPTICAL BODIES

• 摘要: 波浪在大尺寸结构表面会产生不可忽略的散射波, 该散射波会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, 随后考虑将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.

• 图  1  柱体布置和坐标系统

Figure  1.  Arrangement of bodies and coordinates systems

图  2  四柱体阵列图

Figure  2.  Sketch of four bodies arranged in a square form.

图  3  截断误差对本文解计算结果的影响

Figure  3.  Impacts of truncation error on the present method

图  4  不同入射角($\alpha {\text{ = }}{{\text{0}}^{ \circ }}$ $\alpha {\text{ = 9}}{{\text{0}}^{ \circ }}$ )下数值解与本文解的对比

Figure  4.  The wave pressures on bodies ${P_i}$ versus $\theta$ with N = 4 and ka = 1 obtained present method by and the FEM (Wang et al, 2019).

图  5  不同入射角($\alpha {\text{ = }}{{\text{0}}^{ \circ }}$ $\alpha {\text{ = 9}}{{\text{0}}^{ \circ }}$ )下数值解与本文解的对比

Figure  5.  The wave forces on bodies ${F_i}$ versus ka with N = 4 obtained by the present method and FEM (Wang et al, 2019).

图  6  入射角$\alpha {\text{ = }}{{\text{0}}^{ \circ }}$ 时数值解与本文解云图

Figure  6.  The wave fields with N = 4, $\alpha {\text{ = }}{{\text{0}}^{ \circ }}$ and ka = 1 obtained by the FEM (Wang et al, 2019) and present method.

图  7  入射角$\alpha {\text{ = }}{{\text{0}}^{ \circ }}$ 时数值解与本文解的相对误差

Figure  7.  The relative error of the wave pressure between the present method and the FEM with N = 4, $\alpha {\text{ = }}{{\text{0}}^{ \circ }}$ and ka = 1.

图  8  双柱体阵列图

Figure  8.  Sketch of arrangement of twin bodies standing side by side.

图  9  不同入射角($\alpha {\text{ = }}{{\text{0}}^{ \circ }}$ $\alpha {\text{ = 9}}{{\text{0}}^{ \circ }}$ )下两种阵列的本文解与单柱解的对比

Figure  9.  The wave forces on bodies ${F_i}$ versus ka with N = 2 and 4 compared with that of an isolated body.

图  10  双柱阵列中各柱体总受力比值

Figure  10.  Scaling values of total wave force $F_i^{q = 15}/F_i^{q = 2}$ on bodies versus ka as twin bodies standing side by side.

图  11  双柱阵列中各柱体总受力比值

Figure  11.  Scaling values of total wave force $F_i^{q = 15}/F_i^{q = 2}$ on bodies versus Dr as twin bodies standing side by side.

图  12  四柱阵列中各柱体总受力比值

Figure  12.  Scaling values of total wave force $F_i^{q = 15}/F_i^{q = 2}$ on bodies versus ka as four bodies arranged in a square form.

图  13  四柱阵列中各柱体总受力比值

Figure  13.  Scaling values of total wave force $F_i^{q = 15}/F_i^{q = 2}$ on bodies versus Dr as four bodies arranged in a square form.

图  14  两种阵列中C1柱体总受力比值

Figure  14.  Scaling values $F_1^{q = 15}/F_1^{q = 2}$ of C1 versus ka in two arrangements

15  两种阵列中C1柱体总受力比值

15.  Scaling values $F_1^{q = 15}/F_1^{q = 2}$ of C1 versus Dr in two arrangements

图  15  两种阵列中C1柱体总受力比值(续)

Figure  15.  Scaling values $F_1^{q = 15}/F_1^{q = 2}$ of C1 versus Dr in two arrangements (continued)

表  1  计算波浪力的效率(秒)

Table  1.   The numerical costs for calculating the total wave forces (seconds)

 N Method Dr = 0.5 Dr = 1.0 2 Analytical 9.51 8.87 FEM 2.94 10.54 4 Analytical 52.95 48.61 FEM 9.69 94.18
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##### 出版历程
• 网络出版日期:  2021-10-08

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