二维直角平面内偏心圆形衬砌对稳态入射平面SH波的散射
|
摘要
利用复变函数法、多极坐标变换及傅里叶级数展开技术求解二维直角平面内偏心圆形衬砌对稳态入射平面SH(shearing horizontal)波的散射问题。首先构造出介质内不存在偏心圆形衬砌时的入射波场和反射波场;其次建立介质内存在偏心圆形衬砌时由衬砌外边界产生的能够自动满足直角边应力自由条件的散射波解和衬砌外边界向衬砌介质内的折射波解以及衬砌内边界的散射波解,从而利用叠加原理可写出衬砌介质内外的总波场。利用衬砌外边界处应力位移的连续条件和内边界处应力自由条件以及傅里叶级数展开方法列出求解波解中未知系数的无穷代数方程组,在满足计算精度的前提下通过有限项截断,得到相应有限代数方程组的解,最后通过算例具体讨论衬砌内边界处的动应力集中系数和水平直边界位移幅度比及其相位随无量纲波数、入射波入射角、衬砌位置及其偏心度的不同而变化的情况,结果表明文中算法的有效实用性。
Complex function method and multi-polar coordinate and Fourier series expansion technology are used here to study the scattering of circular eccentric lining in right-angle plane space to steady incident plane SH-wave(shearing horizontal wave). At first, the scattering solution excited by the external boundary of the circular eccentric lining existing in the space, which satisfies the free stress conditions of the two right-angle boundaries and the refraction wave solution excited by the exterior boundary of the lining and the reflection wave solution excited by the interior boundary of the lining are formulated; then the incident wave and the reflection wave in the right-angle plane space which has no circular eccentric lining are constructed; therefore, the total displacement fields inside and outside the lining can be constructed using overlapping principle. An infinite algebraic equations of unknown coefficients existing in the scattering and refraction solution fields can be gained using multi-polar coordinate transformation and Fourier series expansion technology and the conditions of displacement/stress at the boundaries of the circular eccentric lining, it can be solved by using limit items in the infinite series which can give a high computation precision. An example is given to illustrate the variations of DSCF(dynamic stress concentration factor) at the interior boundary of the circular eccentric lining and the variations of displacement ratio and the phase of the displacement on the horizontal boundary of the right-angle plane space vs the variations of dimensionless wave number and the incident angle and the location and the eccentricity of the circular eccentric lining, the results of the example show the effectiveness and efficiency of the method introduced here.
Complex function method and multi-polar coordinate and Fourier series expansion technology are used here to study the scattering of circular eccentric lining in right-angle plane space to steady incident plane SH-wave(shearing horizontal wave). At first, the scattering solution excited by the external boundary of the circular eccentric lining existing in the space, which satisfies the free stress conditions of the two right-angle boundaries and the refraction wave solution excited by the exterior boundary of the lining and the reflection wave solution excited by the interior boundary of the lining are formulated; then the incident wave and the reflection wave in the right-angle plane space which has no circular eccentric lining are constructed; therefore, the total displacement fields inside and outside the lining can be constructed using overlapping principle. An infinite algebraic equations of unknown coefficients existing in the scattering and refraction solution fields can be gained using multi-polar coordinate transformation and Fourier series expansion technology and the conditions of displacement/stress at the boundaries of the circular eccentric lining, it can be solved by using limit items in the infinite series which can give a high computation precision. An example is given to illustrate the variations of DSCF(dynamic stress concentration factor) at the interior boundary of the circular eccentric lining and the variations of displacement ratio and the phase of the displacement on the horizontal boundary of the right-angle plane space vs the variations of dimensionless wave number and the incident angle and the location and the eccentricity of the circular eccentric lining, the results of the example show the effectiveness and efficiency of the method introduced here.
引文
1刘殿魁,盖秉政,淘贵源.论孔附近的动应力集中.力学学报,1981,(特刊):65~77.LIU DianKui,GAI BingZheng,TAO Gui Yuan.On dynamic stress concentration in the neighbour-hood of a cavity.Acta Mechanica Sinica,1981,(T):65~77(In Chinese).
2刘殿魁,田家勇.SH波对界面圆柱性弹性夹杂散射及动应力集中.爆炸与冲击,1991,9(2):115~123.LIU DianKui,TIAN JiaYong.Scattering and dynamic stress concentration of SH-wave by interface cylindrical elastic inclusion.Explosion and Shock Waves,1991,9(2):115~123(In Chinese).
3许贻燕,韩峰.平面SH波在相邻多个半圆形凹陷地形上的散射.地震工程与工程震动,1992,12(2):12~17.XUYi Yan,HAN Feng.Scattering of several half-circular canyon to SH-wave.Earthquake Engineering and Engineering Vibration,1992,12(2):12~17(In Chinese).
4王铎,汪越胜.界面动力学研究近况.上海力学,1993,14(4):1~15.WANG Duo,WANG YueSheng.Recent developments in interface dynamics.Shanghai Mechanics,1993,14(4):1~15(In Chinese).
5汪越胜,王铎.SH波对有部分脱胶衬砌的圆形孔洞的散射.力学学报,1994,26(4):462~469.WANGYueSheng,WANG Duo.Diffraction of SH-waves by a circular cavity with a partially debonded liner.Acta Mechanica Sinica,1994,26(4):462~469(In Chinese).
6房营光.相邻多个浅圆弧凹陷地形对平面SH波散射的级数解.应用数学和力学,1995,16(7):615~624.FANGYingGuang.Series solution for scattering of plane SH-waves by multiple shallow circular-arc canyons.Applied Mathematics and Mechanics,1995,16(7):615~624(In Chinese).
7史守峡,韩峰,王振清,等.各向异性介质中有衬砌的非圆形结构与SH波的相互作用.应用数学和力学,1996,17(9):809~820.SHI ShouXia,HANFeng,WANGZhenQing,et al.The interaction of plane SH-waves and non-circular cavity surfaced with lining in anisotropic media.Applied Mathematics and Mechanics,1996,17(9):809~820(In Chinese).
8袁晓铭.地表下圆弧形加塞区平面散射对地面运动的影响.地球物理学报,1996,39(3):373~381.YUANXiaoMing.Effect of a circular undergroundinclusion on surface motion under incident plane SHwaves.Acta Geophysica Sinica,1996,39(3):373~381(In Chinese).
9韩峰,刘殿魁.各向异性介质中SH波对有衬砌的任意形半凹陷地形的散射.应用数学和力学,1997,18(8):753~761.HANFeng,LIUDianKui.Scatteringof plane SH-waves onsemi-canyon topography of arbitrary shape withliningin anisotropic media.Applied Mathematics and Mechanics,1997,18(8):753~761(In Chinese).
10刘殿魁,刘宏伟.SH波散射与界面圆孔附近的动应力集中.力学学报,1998,30(5):597~604.LIUDianKi,LIUHongWei.Scatteringand dynamic stress concentration of SH-wave by interface circular hole.Mechanics Transaction,1998,30(5):597~604(In Chinese).
11史守峡.SH波对结构表面上含有多个半圆形介质夹杂的散射.航空学报,2001,22(1):19~23.SHI ShouXia.Scattering of SH-wave by the structure surface with multiple semi-cylindrical medium inclusion.Acta Aeronautical et Astronautica Sinica,2001,22(1):19~23(In Chinese).
12王志伟,齐辉,刘殿魁.具有刚性覆盖层的界面圆环形衬砌对SH波的散射.哈尔滨工程大学学报,2002,23(4):81~85.WANG Zhi Wei,QI Hui,LIU DianKui.Scattering of SH-wave by interface circular lining with rigid surfacing layer.Journal of Harbin Engineering University,2002,23(4):81~85(In Chinese).
13杨班权,刘又文,薛孟君,等.纤维增强复合材料的刚性圆柱夹杂双周期分布模型的平面问题.机械强度,2004,26(3):332~336.YANG BanQuan,LIU YouWen,XUE MengJun,et al.Study on problems of the fiber-reinforced composites with double periodical circular rigidinclusions.Journal of Mechanical Strength,2004,26(3):332~336(In Chinese).
14Emets F,Kunets Ya I,Matus VV.Scatteringof SHwaves by an elastic thin-walled rigidly supportedinclusion.Archive of Applied Mechanics,2004,73(11-12):769~780.
15LUJ-F,Hanyga A.Scattering of SH-wave by a crackterminating at the interface of a bi material.Computational Mechanics,2004,34(1):74~85.
2刘殿魁,田家勇.SH波对界面圆柱性弹性夹杂散射及动应力集中.爆炸与冲击,1991,9(2):115~123.LIU DianKui,TIAN JiaYong.Scattering and dynamic stress concentration of SH-wave by interface cylindrical elastic inclusion.Explosion and Shock Waves,1991,9(2):115~123(In Chinese).
3许贻燕,韩峰.平面SH波在相邻多个半圆形凹陷地形上的散射.地震工程与工程震动,1992,12(2):12~17.XUYi Yan,HAN Feng.Scattering of several half-circular canyon to SH-wave.Earthquake Engineering and Engineering Vibration,1992,12(2):12~17(In Chinese).
4王铎,汪越胜.界面动力学研究近况.上海力学,1993,14(4):1~15.WANG Duo,WANG YueSheng.Recent developments in interface dynamics.Shanghai Mechanics,1993,14(4):1~15(In Chinese).
5汪越胜,王铎.SH波对有部分脱胶衬砌的圆形孔洞的散射.力学学报,1994,26(4):462~469.WANGYueSheng,WANG Duo.Diffraction of SH-waves by a circular cavity with a partially debonded liner.Acta Mechanica Sinica,1994,26(4):462~469(In Chinese).
6房营光.相邻多个浅圆弧凹陷地形对平面SH波散射的级数解.应用数学和力学,1995,16(7):615~624.FANGYingGuang.Series solution for scattering of plane SH-waves by multiple shallow circular-arc canyons.Applied Mathematics and Mechanics,1995,16(7):615~624(In Chinese).
7史守峡,韩峰,王振清,等.各向异性介质中有衬砌的非圆形结构与SH波的相互作用.应用数学和力学,1996,17(9):809~820.SHI ShouXia,HANFeng,WANGZhenQing,et al.The interaction of plane SH-waves and non-circular cavity surfaced with lining in anisotropic media.Applied Mathematics and Mechanics,1996,17(9):809~820(In Chinese).
8袁晓铭.地表下圆弧形加塞区平面散射对地面运动的影响.地球物理学报,1996,39(3):373~381.YUANXiaoMing.Effect of a circular undergroundinclusion on surface motion under incident plane SHwaves.Acta Geophysica Sinica,1996,39(3):373~381(In Chinese).
9韩峰,刘殿魁.各向异性介质中SH波对有衬砌的任意形半凹陷地形的散射.应用数学和力学,1997,18(8):753~761.HANFeng,LIUDianKui.Scatteringof plane SH-waves onsemi-canyon topography of arbitrary shape withliningin anisotropic media.Applied Mathematics and Mechanics,1997,18(8):753~761(In Chinese).
10刘殿魁,刘宏伟.SH波散射与界面圆孔附近的动应力集中.力学学报,1998,30(5):597~604.LIUDianKi,LIUHongWei.Scatteringand dynamic stress concentration of SH-wave by interface circular hole.Mechanics Transaction,1998,30(5):597~604(In Chinese).
11史守峡.SH波对结构表面上含有多个半圆形介质夹杂的散射.航空学报,2001,22(1):19~23.SHI ShouXia.Scattering of SH-wave by the structure surface with multiple semi-cylindrical medium inclusion.Acta Aeronautical et Astronautica Sinica,2001,22(1):19~23(In Chinese).
12王志伟,齐辉,刘殿魁.具有刚性覆盖层的界面圆环形衬砌对SH波的散射.哈尔滨工程大学学报,2002,23(4):81~85.WANG Zhi Wei,QI Hui,LIU DianKui.Scattering of SH-wave by interface circular lining with rigid surfacing layer.Journal of Harbin Engineering University,2002,23(4):81~85(In Chinese).
13杨班权,刘又文,薛孟君,等.纤维增强复合材料的刚性圆柱夹杂双周期分布模型的平面问题.机械强度,2004,26(3):332~336.YANG BanQuan,LIU YouWen,XUE MengJun,et al.Study on problems of the fiber-reinforced composites with double periodical circular rigidinclusions.Journal of Mechanical Strength,2004,26(3):332~336(In Chinese).
14Emets F,Kunets Ya I,Matus VV.Scatteringof SHwaves by an elastic thin-walled rigidly supportedinclusion.Archive of Applied Mechanics,2004,73(11-12):769~780.
15LUJ-F,Hanyga A.Scattering of SH-wave by a crackterminating at the interface of a bi material.Computational Mechanics,2004,34(1):74~85.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心