搜索

x

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

轴对称指向性球面波的界面反射波

段韵达 胡恒山

引用本文:
Citation:

轴对称指向性球面波的界面反射波

段韵达, 胡恒山

Interface reflection wave of axisymmetric directional spherical-wave

Duan Yun-Da, Hu Heng-Shan
PDF
HTML
导出引用
  • 无限大平面刚性障板中圆形活塞源的声辐射场可近似为轴对称指向性球面波, 前人只给出了活塞面与界面平行时轴对称指向性球面波的界面响应表达式, 本文针对活塞面与界面不平行的情况, 推导了轴对称指向性球面波的锥面波展开式, 并进一步导出了其界面反射波的表达式. 在源距远大于声波波长的情况下通过鞍点法将界面反射波的表达式化简为了简化表达式. 简化式不仅计算上简洁, 而且物理含义清楚: 轴对称指向性球面波的界面反射波可视为镜像活塞源激发的轴对称指向性球面波与反射系数的乘积. 计算表明, 当活塞半径小于声波波长时, 反射波对活塞与界面的夹角和接收点的环向方位角不太敏感, 反射波的指向性较弱; 当活塞半径大于声波波长时, 反射波对活塞与界面的夹角和接收点的环向方位角很敏感, 反射波的指向性很强. 增加活塞与界面的夹角, 反射波先增加后减小, 反射波的指向性先增强后减弱; 当活塞与界面的夹角等于活塞中心镜像点与接收点的连线与界面法线的夹角时, 反射波最大, 反射波的指向性最强.
    The sound radiation field of a circular piston source in an infinite plane rigid baffle can be approximated as an axisymmetric directional spherical-wave. The interface response expressions of the axisymmetric directional spherical-wave for the piston parallel with the interface has already been obtained in previous studies. On condition that the distance from the piston center to the interface is much greater than the piston radius, we first derive the conical wave expansion of the axisymmetric directional spherical-wave which is obtained by using the conical wave expansion of the homogeneous spherical-wave and the formula of the axisymmetric directional spherical-wave excited by a circular piston in an rigid infinite plane, and then derive the expression of the interface reflection wave of the axisymmetric directional spherical-wave for the piston non-parallel to the interface. The expression of the interface reflection wave is simplified into a simplified expression by saddle point method on condition that the source distance is much larger than the acoustic wavelength. The simplified expression is not only simple in the calculation, but also clear in the physical meaning. The simplified expression shows that the interface reflection wave of the axisymmetric directional spherical-wave can be regarded as the product of the axisymmetric directional spherical-wave excited by the piston mirror image and the reflection coefficient. The calculations show that when the piston radius is smaller than the acoustic wavelength, the reflected wave is less sensitive to the angle included between the piston and the interface and the azimuth of the receiving point, and the directivity of the reflected wave is weak. When the piston radius is greater than the acoustic wavelength, the reflected wave is very sensitive to the angle included between the piston and the interface and the azimuth of the receiving point, and the directivity of the reflected wave is strong. Increasing the angle included between the piston and the interface, the reflected wave and its directivity both first increase and then decrease. The reflected wave is largest and the directivity of the reflected wave is strongest when the angle included between the piston and the interface is equal to that between the interface normal and the connecting line between the mirror image of the piston center and the receiving point.
      通信作者: 胡恒山, hhs@hit.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11972132, 11734017)资助的课题
      Corresponding author: Hu Heng-Shan, hhs@hit.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11972132, 11734017)
    [1]

    腾舵, 杨虎, 李道江 2016 水声换能器基础 (西安: 西北工业大学出版社) 第1—3页

    Ten D, Yang H, Li D J 2016 Underwater Acoustic Transducer Foundation (Xi’an: Northwestern Polytechnical University Press) pp1–3 (in Chinese)

    [2]

    杨坤德, 段睿, 李辉, 马远良 2019 水下声源定位理论与技术 (北京: 电子工业出版社) 第1—3页

    Yang K D, Duan R, Li H, Ma Y L 2019 Theory and Technology of Underwater Sound Source Location (Beijing: Publishing House of Electronics Industry) pp1–3 (in Chinese)

    [3]

    莫喜平 2012 应用声学 31 171Google Scholar

    Mo X P 2012 Appl. Acoust. 31 171Google Scholar

    [4]

    Hall D E 1987 Basic Acoustics (New York: Harper & Row Publishers) pp161–177

    [5]

    朱中锐 2015 声呐障板下矢量水听器应用引论 (哈尔滨: 哈尔滨工程大学出版社) 第29页

    Zhu Z R 2015 Introduction to the Application of Vector Hydrophone under Sonar Baffle (Harbin: Harbin Engineering University Press) p29 (in Chinese)

    [6]

    莫喜平, 于婧涵 2019 声学学报 44 751

    Mo X P, Yu J H 2019 Acta Acustica 44 751

    [7]

    何正耀 2020 水声换能器及基阵建模与设计 (北京: 科学出版社) 第2页

    Hei Z Y 2020 Modeling and Design of Underwater Acoustic Transducer and Array (Beijing: Science Press) p2 (in Chinese)

    [8]

    New R, Becker R I, Wilhelmij P 1981 J. Acoust. Soc. Am. 70 1518Google Scholar

    [9]

    Mast T D, Yu F 2005 J. Acoust. Soc. Am. 118 3457Google Scholar

    [10]

    Mellow T 2006 J. Acoust. Soc. Am. 120 90Google Scholar

    [11]

    莫喜平 2018 应用声学 37 671Google Scholar

    Mo X P 2018 J. Appl. Acoust. 37 671Google Scholar

    [12]

    纪伟, 刘忠乐 2017 水雷战与舰船防护 25 7

    Ji W, Liu Z L 2017 Mine Warf. Ship Def. 25 7

    [13]

    梅元贵, 许建林, 耿烽, 周朝晖, 李刚 2006 铁道学报 28 74Google Scholar

    Mei Y G, Xu J L, Geng F, Zhou C H, Li G 2006 J. China Rail. Soc. 28 74Google Scholar

    [14]

    李禹志, 李昕珈, 王青东, 郭各朴, 马青玉 2019 声学技术 38 327

    Li Y Z, Li X J, Wang Q D, Guo G P, Ma Q Y 2019 Tech. Acoust. 38 327

    [15]

    Amédin C K, Berry A, Champoux Y, Allard J F 1995 J. Acoust. Soc. Am. 98 1757Google Scholar

    [16]

    Wang C N, Cho H M 2005 Appl. Acoust. 66 866Google Scholar

    [17]

    Schakel M D, Smeulders D, Slob E C, Heller H K 2011 J. Appl. Phys. 109 15678

    [18]

    Schakel M D, Smeulders D, Slob E C, Heller H K 2011 Geophysics 76 N29Google Scholar

    [19]

    Schakel M D, Smeulders D, Slob E C, Heller H K 2012 Transport Porous Med. 93 1Google Scholar

    [20]

    Pride S R 1994 Phys. Rev. B 50 15678Google Scholar

    [21]

    Pride S R, Haartsen M W 1996 J. Acoust. Soc. Am. 100 1301Google Scholar

    [22]

    王鑫 2020 化学工程与装备 285 115

    Wang X 2020 Chem. Eng. Eq. 285 115

    [23]

    Aki K, Richards P G 2002 Quantitative Seismology (California: University Science Books) pp194–207

    [24]

    Morse P M, Feshbach H 1953 Methods of Theoretical Physics (Part II) (NewYork: McGraw-Hill) pp1323, 1457

    [25]

    裴彦良, 王揆洋, 李官保, 李西双, 刘晨光 2007 石油仪器 21 20

    Pei Y L, Wang K Y, Li G B, Li X S, Liu C G 2007 Petrol. Instrum. 21 20

    [26]

    谈国君 2010 江苏水利 000 28Google Scholar

    Tang G J 2010 Jiangsu Water Resour. 000 28Google Scholar

    [27]

    张虹斌, 周忠海, 刘军礼, 程广欣 2012 中国水运 12 211

    Zhang H B, Zhou Z H, Liu J L, Cheng G X 2012 China Water Transport 12 211

    [28]

    奚定平 1998 贝塞尔函数 (北京: 高等教育出版社) 第13—16页

    Xi D P 1998 Bessel Function (Beijing: Higher Education Press) pp13–16 (in Chinese)

  • 图 1  无限大平面刚性障板中的圆形活塞与界面的示意图

    Fig. 1.  Schematic diagram of a piston in an infinite plane rigid baffle and an interface.

    图 2  ${p_{\text{f}}}\left( M \right)$, ${p_{\text{f}}}\left( O \right)$$ {p_{{\text{f0}}}} $的时域波形 (a) $a = 0.1\;\text{m}$; (b) $a = 1\;\text{m}$

    Fig. 2.  Time-domain waveforms of ${p_{\text{f}}}\left( M \right)$, ${p_{\text{f}}}\left( O \right)$ and $ {p_{{\text{f0}}}} $: (a) $a = 0.1\;\text{m}$; (b) $a = 1\;\text{m}$.

    图 3  活塞面关于界面的镜像

    Fig. 3.  Mirror image of the piston surface with respect to the interface.

    图 4  $ {P_{{\text{ref}}}} $$ {P_{{\rm{ref\_jian}}}} $的比较 (a)$ a = 0.1\;\text{m} $且快速地层; (b)$ a = 0.1\;\text{m} $且慢速地层; (c)$ a = 1\;\text{m} $且快速地层; (d)$ a = 1\;\text{m} $且慢速地层

    Fig. 4.  Comparison of $ {P_{{\text{ref}}}} $ and $ {P_{{\rm{ref\_jian}}}} $: (a)$ a = 0.1\;\text{m} $ and fast formation; (b)$ a = 0.1\;\text{m} $ and slow formation; (c)$ a = 1\;\text{m} $ and fast formation; (d)$ a = 1\;\text{m} $ and slow formation.

    图 5  不同夹角α下在M$( {20\sqrt 3 , \;0, \; - 10} )$处的反射波 (a)$a = 0.1\;\text{m}$; (b)$a = 1\;\text{m}$

    Fig. 5.  Reflected wave under different included angle α for point M at $( {20\sqrt 3 , \;0, \; - 10} )$: (a)$a = 0.1\;\text{m}$; (b)$a = 1\;\text{m}$.

    图 6  不同夹角α下在M$( {20\sqrt 3 , \;45, \; - 10} )$处的反射波 (a) $a = 0.1\;\text{m}$; (b)$a = 1\;\text{m}$

    Fig. 6.  Reflected wave under different included angle α for point M at $( {20\sqrt 3 , \;45, \; - 10} )$: (a) $a = 0.1\;\text{m}$; (b) $a = 1\;\text{m}$.

    图 7  不同夹角α下在M$( {20\sqrt 3 , \;90, \; - 10})$处的反射波 (a)$a = 0.1\;\text{m}$; (b)$a = 1\;\text{m}$

    Fig. 7.  Reflected wave under different included angle α for point M at $( {20\sqrt 3 , \;90, \; - 10} )$: (a)$a = 0.1\;\text{m}$; (b)$a = 1\;\text{m}$.

    图 8  $\alpha = {45^{\circ}}$时不同${\varphi _M}$下的反射波和其指向图 (a)$a = 0.1\;\text{m}$时的反射波; (b)$a = 0.1\;\text{m}$时的指向图; (c)$a = 1\;\text{m}$时的反射波; (d)$a = 1\;\text{m}$时的指向图

    Fig. 8.  Reflected waves and directional diagrams at different azimuths ${\varphi _M}$ for $\alpha = {45^{\circ}}$: (a) Reflected waves for $ a = 0.1\;\text{m} $; (b) directional diagram for $ a = 0.1\;\text{m} $; (c) reflected waves for $ a = 1\;\text{m} $; (d) directional diagram for $ a = 1\;\text{m} $.

    图 9  不同夹角α下的反射波的指向图 (a)$a = 0.1\;\text{m}$; (b)$a = 1\;\text{m}$

    Fig. 9.  Directional diagrams under different angle α: (a)$a = 0.1\;\text{m}$; (b)$a = 1\;\text{m}$.

    图 10  $a = 1\;\text{m}$时不同夹角α下的指向图 (a)$ {\beta _{M{E_{1}}}} = {20^{\circ}} $; (b)$ {\beta _{M{E_{1}}}} = {40^{\circ}} $

    Fig. 10.  Directional diagrams under different angle α for $a = 1\;\text{m}$: (a)$ {\beta _{M{E_{1}}}} = {20^{\circ}} $; (b)$ {\beta _{M{E_{1}}}} = {40^{\circ}} $.

    图 11  $\left| B \right|$$ {\beta _{M{E_{1}}}} $的变化曲线

    Fig. 11.  Variation curve of $\left| B \right|$ with $ {\beta _{M{E_{1}}}} $.

    表 1  流体和固体参数

    Table 1.  Parameters of fluid and solid.

    密度/
    (${\rm{ kg}} \cdot {{\rm{m}}^{ - 3} }$)
    纵波速度/
    (${\text{m}} \cdot {{\text{s}}^{ - 1}}$)
    横波速度/
    (${\text{m}} \cdot {{\text{s}}^{ - 1}}$)
    流体10001500
    快速地层260040002300
    慢速地层200022001200
    下载: 导出CSV
  • [1]

    腾舵, 杨虎, 李道江 2016 水声换能器基础 (西安: 西北工业大学出版社) 第1—3页

    Ten D, Yang H, Li D J 2016 Underwater Acoustic Transducer Foundation (Xi’an: Northwestern Polytechnical University Press) pp1–3 (in Chinese)

    [2]

    杨坤德, 段睿, 李辉, 马远良 2019 水下声源定位理论与技术 (北京: 电子工业出版社) 第1—3页

    Yang K D, Duan R, Li H, Ma Y L 2019 Theory and Technology of Underwater Sound Source Location (Beijing: Publishing House of Electronics Industry) pp1–3 (in Chinese)

    [3]

    莫喜平 2012 应用声学 31 171Google Scholar

    Mo X P 2012 Appl. Acoust. 31 171Google Scholar

    [4]

    Hall D E 1987 Basic Acoustics (New York: Harper & Row Publishers) pp161–177

    [5]

    朱中锐 2015 声呐障板下矢量水听器应用引论 (哈尔滨: 哈尔滨工程大学出版社) 第29页

    Zhu Z R 2015 Introduction to the Application of Vector Hydrophone under Sonar Baffle (Harbin: Harbin Engineering University Press) p29 (in Chinese)

    [6]

    莫喜平, 于婧涵 2019 声学学报 44 751

    Mo X P, Yu J H 2019 Acta Acustica 44 751

    [7]

    何正耀 2020 水声换能器及基阵建模与设计 (北京: 科学出版社) 第2页

    Hei Z Y 2020 Modeling and Design of Underwater Acoustic Transducer and Array (Beijing: Science Press) p2 (in Chinese)

    [8]

    New R, Becker R I, Wilhelmij P 1981 J. Acoust. Soc. Am. 70 1518Google Scholar

    [9]

    Mast T D, Yu F 2005 J. Acoust. Soc. Am. 118 3457Google Scholar

    [10]

    Mellow T 2006 J. Acoust. Soc. Am. 120 90Google Scholar

    [11]

    莫喜平 2018 应用声学 37 671Google Scholar

    Mo X P 2018 J. Appl. Acoust. 37 671Google Scholar

    [12]

    纪伟, 刘忠乐 2017 水雷战与舰船防护 25 7

    Ji W, Liu Z L 2017 Mine Warf. Ship Def. 25 7

    [13]

    梅元贵, 许建林, 耿烽, 周朝晖, 李刚 2006 铁道学报 28 74Google Scholar

    Mei Y G, Xu J L, Geng F, Zhou C H, Li G 2006 J. China Rail. Soc. 28 74Google Scholar

    [14]

    李禹志, 李昕珈, 王青东, 郭各朴, 马青玉 2019 声学技术 38 327

    Li Y Z, Li X J, Wang Q D, Guo G P, Ma Q Y 2019 Tech. Acoust. 38 327

    [15]

    Amédin C K, Berry A, Champoux Y, Allard J F 1995 J. Acoust. Soc. Am. 98 1757Google Scholar

    [16]

    Wang C N, Cho H M 2005 Appl. Acoust. 66 866Google Scholar

    [17]

    Schakel M D, Smeulders D, Slob E C, Heller H K 2011 J. Appl. Phys. 109 15678

    [18]

    Schakel M D, Smeulders D, Slob E C, Heller H K 2011 Geophysics 76 N29Google Scholar

    [19]

    Schakel M D, Smeulders D, Slob E C, Heller H K 2012 Transport Porous Med. 93 1Google Scholar

    [20]

    Pride S R 1994 Phys. Rev. B 50 15678Google Scholar

    [21]

    Pride S R, Haartsen M W 1996 J. Acoust. Soc. Am. 100 1301Google Scholar

    [22]

    王鑫 2020 化学工程与装备 285 115

    Wang X 2020 Chem. Eng. Eq. 285 115

    [23]

    Aki K, Richards P G 2002 Quantitative Seismology (California: University Science Books) pp194–207

    [24]

    Morse P M, Feshbach H 1953 Methods of Theoretical Physics (Part II) (NewYork: McGraw-Hill) pp1323, 1457

    [25]

    裴彦良, 王揆洋, 李官保, 李西双, 刘晨光 2007 石油仪器 21 20

    Pei Y L, Wang K Y, Li G B, Li X S, Liu C G 2007 Petrol. Instrum. 21 20

    [26]

    谈国君 2010 江苏水利 000 28Google Scholar

    Tang G J 2010 Jiangsu Water Resour. 000 28Google Scholar

    [27]

    张虹斌, 周忠海, 刘军礼, 程广欣 2012 中国水运 12 211

    Zhang H B, Zhou Z H, Liu J L, Cheng G X 2012 China Water Transport 12 211

    [28]

    奚定平 1998 贝塞尔函数 (北京: 高等教育出版社) 第13—16页

    Xi D P 1998 Bessel Function (Beijing: Higher Education Press) pp13–16 (in Chinese)

  • [1] 安秉文, 陈家熠, 李斐然, 李子琪, 吴先梅. π相移光纤光栅水听器的超声波传感指向特性. 物理学报, 2023, 72(6): 064303. doi: 10.7498/aps.72.20222154
    [2] 王明军, 王婉柔, 李勇俊. 利用平面声场对非均匀大气介质光波传输相位的调控. 物理学报, 2022, 71(16): 164302. doi: 10.7498/aps.71.20220484
    [3] 周彦玲, 范军, 王斌, 李兵. 水下环形凹槽圆柱体散射声场空间指向性调控. 物理学报, 2021, 70(17): 174301. doi: 10.7498/aps.70.20210111
    [4] 刘胜兴, 李整林. 海面冰层对声波的反射和散射特性. 物理学报, 2017, 66(23): 234301. doi: 10.7498/aps.66.234301
    [5] 孙宏祥, 方欣, 葛勇, 任旭东, 袁寿其. 基于蜷曲空间结构的近零折射率声聚焦透镜. 物理学报, 2017, 66(24): 244301. doi: 10.7498/aps.66.244301
    [6] 周志刚, 宗谨, 王文广, 厚美瑛. 颗粒样品形变对声波传播影响的实验探究. 物理学报, 2017, 66(15): 154502. doi: 10.7498/aps.66.154502
    [7] 郭俊媛, 杨士莪, 朴胜春, 莫亚枭. 基于超指向性多极子矢量阵的水下低频声源方位估计方法研究. 物理学报, 2016, 65(13): 134303. doi: 10.7498/aps.65.134303
    [8] 宁方立, 董梁, 张文治, 王康. 谐振管内非线性驻波的有限体积数值算法. 物理学报, 2012, 61(19): 190203. doi: 10.7498/aps.61.190203
    [9] 吕君, 赵正予, 周晨, 张援农. 有限振幅声波间的非线性相互作用对声源远场指向性的影响. 物理学报, 2011, 60(8): 084301. doi: 10.7498/aps.60.084301
    [10] 刘启能. 研究一维掺杂声子晶体缺陷模的解析方法. 物理学报, 2011, 60(4): 044302. doi: 10.7498/aps.60.044302
    [11] 王文刚, 刘正猷, 赵德刚, 柯满竹. 声波在一维声子晶体中共振隧穿的研究. 物理学报, 2006, 55(9): 4744-4747. doi: 10.7498/aps.55.4744
    [12] 顾永玉, 张永康, 张兴权, 史建国. 约束层对激光驱动冲击波压力影响机理的理论研究. 物理学报, 2006, 55(11): 5885-5891. doi: 10.7498/aps.55.5885
    [13] 韩汝取, 史庆藩, 孙 刚. 声波在一维易膨胀介质中传播的计算机模拟. 物理学报, 2005, 54(5): 2188-2193. doi: 10.7498/aps.54.2188
    [14] 曹 禹, 杨孔庆. 对声波和弹性波传播模拟的Hamilton系统方法. 物理学报, 2003, 52(8): 1984-1992. doi: 10.7498/aps.52.1984
    [15] 段文山, 洪学仁. 弱相对论等离子体横向扰动下的离子声孤波. 物理学报, 2003, 52(6): 1337-1339. doi: 10.7498/aps.52.1337
    [16] 吴福根, 刘有延. 二维周期性复合介质中声波带隙结构及其缺陷态. 物理学报, 2002, 51(7): 1434-1434. doi: 10.7498/aps.51.1434
    [17] 郑晓瑜, 钱祖文. 有限振幅声波在平面界面上的反射和折射. 物理学报, 1990, 39(1): 89-93. doi: 10.7498/aps.39.89
    [18] 钱祖文, 施修祥, 赵春生, 吕凤玲, 王晓霞. 圆形活塞声源的有限振幅反射波. 物理学报, 1983, 32(9): 1109-1117. doi: 10.7498/aps.32.1109
    [19] 张仁和, 朱柏贤. 指向性辐射器的简正波声场. 物理学报, 1983, 32(4): 490-496. doi: 10.7498/aps.32.490
    [20] 严仁博. 超声楔形换能器的体波和瑞利表面波指向性图案. 物理学报, 1974, 23(6): 41-50. doi: 10.7498/aps.23.41
计量
  • 文章访问数:  2574
  • PDF下载量:  41
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-09-15
  • 修回日期:  2021-11-22
  • 上网日期:  2022-01-26
  • 刊出日期:  2022-04-05

/

返回文章
返回