EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

多个椭圆柱波浪力的一种解析解

赵密 龙彭振 王丕光 张超 杜修力

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 doi: 10.6052/0459-1879-21-318
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 doi: 10.6052/0459-1879-21-318
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 doi: 10.6052/0459-1879-21-318

多个椭圆柱波浪力的一种解析解

doi: 10.6052/0459-1879-21-318
基金项目: 国家自然科学基金(52078010, 51421005)资助项目
详细信息
    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)

    NMethodDr = 0.5Dr = 1.0
    2Analytical9.518.87
    FEM2.9410.54
    4Analytical52.9548.61
    FEM9.6994.18
    下载: 导出CSV
  • [1] Morison J R, Johnson J W, Schaaf S A. The force exerted by surface waves on piles. Journal of Petroleum Technology, 1950, 2(05): 149-154 doi: 10.2118/950149-G
    [2] 中国交通运输部. 海港水文规范. 北京: 人民交通出版社, 2013

    Ministry of Transport of the People's Republic of China. Code of hydrology for sea harbour. Beijing: China Communications Press, 2013 (in Chinese)
    [3] 刘嘉斌. 基于势流理论的大型桥墩结构波浪作用研究[博士论文]. 哈尔滨: 哈尔滨工业大学, 2019

    Liu Jiabin. Research of wave action on large-scale bridge foundation based on potential theory. [PhD Thesis]. Harbin: Harbin Institute of Technology, 2019 (in Chinese)
    [4] MacCamy R C, Fuchs R A. Wave forces on piles: a diffraction theory. U. S. Army Corps of Eng. : Technical Memo. 1954
    [5] 陶建华, 丁旭. 大尺度结构物的二阶波浪荷载. 力学学报, 1988, 05: 385-392

    Tao Jianhua, Ding Xu. Second order wave loads on large structures, Acta Mechanica Sinica, 1988, 05: 385-392 (in Chinese)
    [6] Newman J N. The second-order wave force on a vertical cylinder. Journal of Fluid Mechanics. 1996, 320: 417-443
    [7] Tao L, Song H, Chakrabarti S. Scaled boundary FEM solution of short-crested wave diffraction by a vertical cylinder. Computer methods in applied mechanics and engineering, 2007, 197(1-4): 232-242 doi: 10.1016/j.cma.2007.07.025
    [8] Song H, Tao L, Chakrabarti S. Modelling of water wave interaction with multiple cylinders of arbitrary shape. Journal of Computational Physics, 2010, 229(5): 1498-1513 doi: 10.1016/j.jcp.2009.10.041
    [9] Wang P, Wang X, Zhao M, et al. A numerical model for earthquake-induced hydrodynamic forces and wave forces on inclined circular cylinder. Ocean Engineering, 2020, 207: 107382 doi: 10.1016/j.oceaneng.2020.107382
    [10] Linton C M, Evans D V. The interaction of waves with arrays of vertical circular cylinders. Journal of Fluid Mechanics. 1990, 215: 549-569
    [11] Kagemoto H, Yue D. Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method. J. Fluid Mech. 1986, 166(-1): 189-209
    [12] Chen J T, Lee Y T, Lin Y J. Interaction of water waves with vertical cylinders using null-field integral equations. Applied Ocean Research, 2009, 31(2): 101-110 doi: 10.1016/j.apor.2009.06.004
    [13] 缪国平, 余志兴, 缪泉明等. 流体动力干扰对单排圆柱桩列波浪力的影响. 力学学报. 1998, 05: 2-9

    Miao Guoping, Yu Zhixing, Miao Quanming, et al. On the effects of hydrodynamic interaction upon the wave force on vertical pile array of single row, Acta Mechanica Sinica, 1998, 05: 2-9 (in Chinese)
    [14] Wang P, Zhao M, Du X, et al. A finite element solution of earthquake-induced hydrodynamic forces and wave forces on multiple circular cylinders. Ocean Engineering. 2019, 189: 106336
    [15] Chen H S, Mei C C. Wave forces on a stationary platform of elliptical shape. Journal of Ship Research. 1973, 17(02): 61-71
    [16] Williams A N. Wave forces on an elliptic cylinder. Journal of Waterway, Port, Coastal, and Ocean Engineering. 1985, 111(2): 433-449
    [17] Liu J, Guo A, Li H. Analytical solution for the linear wave diffraction by a uniform vertical cylinder with an arbitrary smooth cross-section. Ocean Engineering, 2016, 126(nov.1): 163-175
    [18] Liu J, Guo A, Fang Q, et al. Investigation of linear wave action around a truncated cylinder with non-circular cross section. Journal of Marine Science and Technology, 2018, 23(4): 866-876 doi: 10.1007/s00773-017-0516-0
    [19] Zhang S., Williams A. N Water scattering by submerged elliptical disk. Journal of Waterway, Port, Coastal and Ocean, 1996, 122: 38-45 doi: 10.1061/(ASCE)0733-950X(1996)122:1(38)
    [20] Bhatta D D. Wave diffraction by circular and elliptical cylinders in finite depth water. International Journal of Pure and Applied Mathematics, 2005, 19(1): 67-85
    [21] Wang P, Zhao M, Du X, et al. Analytical solution for the short-crested wave diffraction by an elliptical cylinder. European Journal of Mechanics - B/Fluids. 2019, 74: 399-409
    [22] 王丕光, 黄义铭, 赵密等. 椭圆形柱体地震动水压力的简化分析方法. 震灾防御技术, 2019, 14(1): 24-34 (Wang Piguang, Huang Ying, Zhao Mi, et al. The simplified method for the earthquake induced hydrodynamic pressure on elliptical cylinder. Technology for Earthquake Disaster Prevention, 2019, 14(1): 24-34 (in Chinese) doi: 10.11899/zzfy20190103
    [23] Chatjigeorgiou I K. The hydrodynamics of arrays of truncated elliptical cylinders. European Journal of Mechanics - B/Fluids. 2013, 37: 153-164
    [24] Chatjigeorgiou I K. Three dimensional wave scattering by arrays of elliptical and circular cylinders. Ocean Engineering. 2011, 38(13): 1480-1494
    [25] Chatjigeorgiou I K, Mavrakos S A. An analytical approach for the solution of the hydrodynamic diffraction by arrays of elliptical cylinders. Applied Ocean Research. 2010, 32(2): 242-251
    [26] Lee W. Acoustic scattering by multiple elliptical cylinders using collocation multipole method. Journal of Computational Physics. 2012, 231(14): 4597-4612
    [27] Liu J, Guo A, Fang Q, et al. Wave action by arrays of vertical cylinders with arbitrary smooth cross-section. Journal of Hydrodynamics. 2020, 32(1): 70-81
    [28] Abramowitz M, Stegun I. Handbook of mathematical functions with formulas, graphs, and mathematical tables. New York: Dover, 1964.
    [29] Særmark K. A note on addition theorems for Mathieu functions. Zeitschrift für angewandte Mathematik und Physik. 1959, 10(4): 426-428
    [30] Meixner J, Schäfke F W. Mathieusche Funktionen und Sphäroidfunktionen. Berlin: Springer, 1954
  • 加载中
图(16) / 表(1)
计量
  • 文章访问数:  22
  • HTML全文浏览量:  5
  • PDF下载量:  3
  • 被引次数: 0
出版历程
  • 网络出版日期:  2021-10-08

目录

    /

    返回文章
    返回