SH波作用下地表覆盖层对浅埋圆夹杂散射的影响
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摘要
本文研究了带有覆盖层的半无限空间中圆形夹杂对SH波的散射问题。利用复变函数法和多极坐标移动技术讨论了带有覆盖层的半空间内浅埋圆形夹杂对稳态任意方向入射平面SH波的散射问题。根据SH波散射的衰减特性,该问题采用大圆弧假定法求解,利用半径很大的圆来拟合地表覆盖层的直边界,将具有地表覆盖层的半空间直边界问题转化为曲面边界问题。借助Helmholtz定理预先写出问题波函数的一般形式解,再利用边界条件并借助复数Fourier-Hankel级数展开把问题化为求解波函数中未知系数的无穷线性代数方程组,截断该无穷代数方程组可求得该问题的数值结果。最后,通过算例来讨论地表覆盖层对浅埋圆形夹杂动应力集中的影响。结果表明,半空间地表覆盖层的存在,即使厚度很薄,对入射SH波的散射也具有很大影响,覆盖层刚度和厚度的变化可显著改变浅埋夹杂周边动应力集中系数的分布。
The scattering of SH-wave by subsurface circular inclusions in a layered elastic half-space is studied in this paper. The problem of the scattering of SH-wave by a subsurface circular inclusion in a layered elastic half-space is investigated based on the complex function method and wave function expansion method for arbitrary incident angle. According to the attenuation characteristics of SH-wave, the solution of scattering of SH-wave was given by a circular inclusion embedded in a layered half-space with an almost flat circular boundary to approximate the straight boundary of surface elastic layer. The general solution of the Biot's wave function is given using the theory of Helmholtz and a system of infinite linear algebraic equations of the present problem can be given by means of the complex series expansion technology and the boundary conditions of the problem. Finally, the dynamic stress concentration factors around the circular inclusion and the ground motion are discussed in numerical examples. The calculation results show that the existence of a surface layer on a half-space, even if it is very thin, has great influence on incident plane SH-wave. The variation of stiffness and thickness of the surface layer can remarkably change the dynamic behavior of circular inclusion.
The scattering of SH-wave by subsurface circular inclusions in a layered elastic half-space is studied in this paper. The problem of the scattering of SH-wave by a subsurface circular inclusion in a layered elastic half-space is investigated based on the complex function method and wave function expansion method for arbitrary incident angle. According to the attenuation characteristics of SH-wave, the solution of scattering of SH-wave was given by a circular inclusion embedded in a layered half-space with an almost flat circular boundary to approximate the straight boundary of surface elastic layer. The general solution of the Biot's wave function is given using the theory of Helmholtz and a system of infinite linear algebraic equations of the present problem can be given by means of the complex series expansion technology and the boundary conditions of the problem. Finally, the dynamic stress concentration factors around the circular inclusion and the ground motion are discussed in numerical examples. The calculation results show that the existence of a surface layer on a half-space, even if it is very thin, has great influence on incident plane SH-wave. The variation of stiffness and thickness of the surface layer can remarkably change the dynamic behavior of circular inclusion.
引文
[1]Pao Y. H., and Mow C. C. Diffraction of Elastic Waves and Dynamic Stress Concentrations. Crane and Russak, New York,1973:114-304p
[2]鲍亦兴,毛昭宙著.刘殿魁,苏先樾译.弹性波的衍射与动应力集中.北京：科学出版社,1993：72-202页
[3]黎在良,刘殿魁著.固体中的波.北京：科学出版社,1995：286-319页,377-431页
[4]钟伟芳,聂国华著.弹性波的散射理论.武汉：华中理工大学出版社1997：137-189页
[5]王铎,马兴瑞,刘殿魁.弹性动力学最新进展.北京：科学出版社,1995：13-15页
[6]Pao Y H. Elastic Waves in Solids. ASME Journal of Applied Mechanics. 1983(4):1152-1164P
[7]王铎,汪越胜.界面动力学研究近况.上海力学.1993(4)：1-15页
[8]林皋.地下结构抗震分析综述(上).世界地震工程.Vo1.5.1990(2)：1-10页
[9]Pao. Yih-hsing, Applied mechanics in science and engineering, Applied Mechanics Review,1998 51(2):141-153P
[10]洪善桃.关于弹性波近代发展的概述.上海力学.1986(3)：66-77页
[11]林宏,刘殿魁.半无限空间中圆形孔洞周围SH波的散射.地震工程与工程振动.2002,22(2)：9-16页
[12]王国庆,刘殿魁.SH波对浅埋相邻多个圆孔作用的动力分析.哈尔滨工程大学学报.2003(1)：108-113页
[13]乐胜辉.地下浅埋圆形结构对SH波的散射.哈尔滨工程大学硕士学位论文.2007：1-77页
[14]林宏,史文谱,刘殿魁.SH波入射时浅埋结构的动力分析.哈尔滨工程大学学报.2001,22(6)：83-87页
[15]平面SH波在浅埋椭圆柱形孔洞上的散射与动应力集中.暨南大学学报.2005,26(3)：324-330页
[16]杨宇.楔形地形对入射波散射解析研究进展.低温建筑技 术.2005,108(6)：50-51页
[17]Sezawa K. Scattering of Elastic Waves and Some Allied Problems. Bull Earthquake Res Inst Tokyo Imperial Univ.1927,3:19P
[18]Wolf A. Motion of a Rigid Sphere in an Acoustic Wave Field. Geophysics. 1945,10:91P
[19]Nagase M. Diffraction of Elastic Wave by a Spherical Surface. J. Phys. Soc. Japan.1957,11(3):279P
[20]Knopoff L. Scattering of Compressional Waves by Spherical Obstacles. Geophysics.1959,24(1):30P
[21]Nishimura G. Jimbo Y A. Dynamic Problem of Stress Concentration Stresses in the Vicinity of a Spherical Matter Included in an Elastic Solid Under Dynamical Force. J Faculty of Engineering, Univ of Tokyo.1955,24: 101P
[22]White R M. Elastic Wave Scattering at a Cylindrical Discontinuity in a Solid. J Acoust Soc Am,1958,30(8):771P
[23]Kato K. Reflections of Sound Wave due to a Hollow Cylinder in an Elastic Body. Mem Inst Sci Indus Res. Vol.9 Osaka University, Japan,1952:65P
[24]Pao Y H, Mow C C. Dynamic Stress Concentration in an Elastic Plate with Rigid Circular Inclusion. Proc 4th National Cong of Appl Mech.1962: 235P
[25]Mow C C, Mente L J. Dynamic Stresses and Displacements Around Cylindrical Discontinuities due to Plane Harmonic Shear Waves. J Appl Mech.1963,39(4):598P
[26]Baron M L, Mattews A T. Diffraction of a Pressure Wave by a Cylindrical Cavity in an Elastic Medium. ASME J Appl Mech.1961,28:347P
[27]Baron M L, Parnes R. Displacements and Velocities Produced by the Diffraction of a Pressure Wave by a Cylindrical Cavity in an Elastic Medium. ASME J Appl Mech,1962,29:385P
[28]Jain D L, Kanwal R P. Scattering of Elastic Waves by Circular Cylindrical Flaws and Inclusions. J Appl Phys,1979,59(6):4067-4108P
[29]Jain D L, Kanwal R P. Scattering of Elastic Waves by an Elastic Sphere. Int J Eng Sci.1980,18:829-839P
[30]S. K. Datta. Scattering of Elastic Waves, Mechanics Today. S. Nemat-Nasser. ed. Vol.4. Pergamon Press, New York,1978:149-208P
[31]Kriegsmann G A, Norris A N, Reiss E L. Scattering by Penetrable Acoustic Targets. Wave Motion,1984,6:501-516P
[32]Liu D.K., Gai B.Z. and Tao G. Y. Applications of the Method of Complex Functions to Dynamic Stress Concentrations. Wave Motion.1982,4: 293-304P
[33]韩峰.复变函数方法在弹性波散射及动应力集中问题研究中的应用.哈尔滨建筑大学博士学位论文.1991：1-42页
[34]王竹溪,郭敦仁.特殊函数概论.北京：北京大学出版社,2000
[35]Gubernatis J. E., Domany, E., Krumhansl J. A. and Huberman M. The Born Approximation in the Theory of the Scattering of Elastic Waves by Flaws. J. Appl. Physics.1977,48:2812-2819P
[36]Mal A.K.and Knopoff L. Elastic Wave Velocities in Tow-Component Systems. J.of Inxtitute of Appl. Math 1976,3:376-387P
[37]Waterman P. Matrix Theory of Elastic Wave Scattering. J. Acou. Soc. America.1976,60:567-580P
[38]Pao Y. H. Betti's Identity and Transition Matrix for Elastic Waves, I. Theory. J. Acou. Soc. America.1976,60:556-556P
[39]S.K.Datta, Scattering of Elastic Waves, Mechanics Today, Nemat-Nasser, Vol.4, Pergamon Press, New York,1978:149-208P
[40]Achenbach J. D., Gautesen A. K. and McMaken H. Ray Method for Waves in Elastic Solids with Application to Scattering by Cracks. Pitman Advanced Publishing Progran, Boston.1982:86-119P
[41]刘殿魁,盖秉政,陶贵源.论孔附近的动应力集中.力学学报特刊1981：65-77页
[42]Liu D.K. and Han F. Scattering of Plane SH-waves by Cylindrical Canyon of Arbitrary Shapes in Anisotropic Media. Acta Mechanica Sinica.1990, 6(3):256-266P
[43]Liu D.K. and Han F. Scattering of plane SH-wave by Cylindrical Canyon of Arbitrary Shapes. Int. H. Soil. Dyn. and Ear. Eng.1991,10(5):249-255P
[44]Han F., Wei Y. and Liu D. K. The Interaction of Plane SH-wave and Circular Cavity Surfaced with Lining in Anisotropic Media. Applied Mathematics and Mechanics.1995,16(2):1067-1078P
[45]Shi S. X. Han F. Wang Z. Q., and Liu. D. K. The Interaction of Plane SH-wave and Non-circular Cavity Surfaced with Lining in Anisotropic Media, Applied Mathematics and Mechanics.1996,17(9):809-820P
[46]胡超,刘殿魁.无限大板开孔弹性波的散射及动应力集中.力学学报.特刊.1995：125-134页
[47]Liu D. K. and Hu C. Scattering of Flexural Wave and Dynamic Stress Concentration in Mindlin's Thick Plates With a Cutout. Acta Mechanica Sinica.1996,12(2):169-185P
[48]H.CAO and V.W.LEE. Scattering and diffraction of plane P-waves by circular cylindrical canyons with variable depth-to-width ratio. Soil Dynamics and Earthquake engineering,1990,9 (3):141-150P
[49]梁建文,严林隽,Vincent W lee.圆弧形层状沉积谷地对入射平面P波的散射解析解.地震学报.2001,23(2)：167-184页
[50]梁建文,严林隽.圆弧形层状沉积谷地对入射平面SV波的散射解析解.固体力学学报.2003,24(2)：235-243页
[51]梁建文,严林隽,李军伟,Vincent W lee圆弧形沉积河谷场地在平面P波入射下的响应.岩土力学.2001,22(2)：138-143页
[52]王建华,姜领发,周香莲.稳态P波对半无限饱和土中的圆形孔洞的散射[J].南昌工程学院学报.2005,24(1)：8-19页
[53]史文谱,刘殿魁等.半无限空间中稳态P波在衬砌周围的散射.地震工程与工程振动.2002,23(3)：19-26页
[54]张彦帅.半圆弧凸起地形对平面P波的散射解析解.天津大学硕士学
位论文.2004：1-57页
[55]温立平.饱和土层状沉积谷地对平面P波散射的解析解.天津大学硕士学位论文.2004：1-51页
[56]陈涛,胡超,黄文虎.P波入射时含圆柱形空腔板弹性波散射与动应力集中.地震工程与工程振动.2006,26(4)：32-36页
[57]杨宇.含圆弧形沉积的楔形地形对平面SH波和P波的散射.天津大学硕士学位论文.2005：1-68页
[58]钟伟芳,聂国华.弹性波的散射理论.华中理工大学出版社,1997
[59]刘殿魁,田家勇.SH波对界面圆柱形弹性夹杂散射及动应力集中.爆炸与冲击.1999,19(2)：115-123页
[60]史守峡,杨庆山,刘殿魁,齐辉.SH波对圆形夹杂与裂纹的散射及其动应力集中.复合材料学报.2000,17(3)：107-112页
[61]刘殿魁,杨在林, 刘建百.界面可移动圆柱形刚性夹杂对SH波散射及动应力集中.哈尔滨建筑大学学报.2001,34(6)：2-7页
[62]李宏亮,刘殿魁. SH波作用下裂纹对圆夹杂散射动应力集中问题的影响.哈尔滨工程大学学报.2005,26(3)：359-363页
[63]刘殿魁,吕晓棠. 浅埋圆柱形弹性夹杂附近的半圆形凸起对SH波的散射.哈尔滨工程大学学报.2006,27(2)：189-194页
[64]刘刚,刘殿魁,杜永军,陈海涛.浅埋圆柱形弹性夹杂附近等腰三角形凸起地形引起的SH波的散射.地震工程与工程振动.2006,26(4)：1-8页
[65]史文谱,张春萍,褚京莲,李禄昌,胡爱芹.直角平面边界固定半圆形夹杂对稳态入射平面SH波的散射.振动与冲击.2007,126(1)：121-124页
[66]王慧文,孙晓娟,刘殿魁.浅埋圆形夹杂附近半圆形沉积层对SH波的散射与地表位移.黑龙江工程学院学报.2006,20(2)：1-5页
[67]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页
[68]刘殿魁,刘宏伟.孔边裂纹对SH波散射及动应力强度因子.力学学报.1999,31(3)：292-299页
[69]刘宏伟,刘殿魁.界面圆孔对SH波的散射远场解.固体力学学报. 1999,20(4)：349-355页
[70]史守峡,刘殿魁.SH波与界面多圆孔的散射及动应力集中.力学学报.2001(1)：60-70页
[71]林宏,刘殿魁.半无限空间中圆形孔洞周围SH波的散射.地震工程与工程振动.2002,22(2)：9-16页
[72]廖振鹏.工程波动理论导引.北京：科学出版社,1996
[73]杨在林,孙柏涛,刘殿魁.SH波在浅埋可移动圆柱形刚性夹杂处的散射与地震动.2008,28(4)：1-5页
[2]鲍亦兴,毛昭宙著.刘殿魁,苏先樾译.弹性波的衍射与动应力集中.北京：科学出版社,1993：72-202页
[3]黎在良,刘殿魁著.固体中的波.北京：科学出版社,1995：286-319页,377-431页
[4]钟伟芳,聂国华著.弹性波的散射理论.武汉：华中理工大学出版社1997：137-189页
[5]王铎,马兴瑞,刘殿魁.弹性动力学最新进展.北京：科学出版社,1995：13-15页
[6]Pao Y H. Elastic Waves in Solids. ASME Journal of Applied Mechanics. 1983(4):1152-1164P
[7]王铎,汪越胜.界面动力学研究近况.上海力学.1993(4)：1-15页
[8]林皋.地下结构抗震分析综述(上).世界地震工程.Vo1.5.1990(2)：1-10页
[9]Pao. Yih-hsing, Applied mechanics in science and engineering, Applied Mechanics Review,1998 51(2):141-153P
[10]洪善桃.关于弹性波近代发展的概述.上海力学.1986(3)：66-77页
[11]林宏,刘殿魁.半无限空间中圆形孔洞周围SH波的散射.地震工程与工程振动.2002,22(2)：9-16页
[12]王国庆,刘殿魁.SH波对浅埋相邻多个圆孔作用的动力分析.哈尔滨工程大学学报.2003(1)：108-113页
[13]乐胜辉.地下浅埋圆形结构对SH波的散射.哈尔滨工程大学硕士学位论文.2007：1-77页
[14]林宏,史文谱,刘殿魁.SH波入射时浅埋结构的动力分析.哈尔滨工程大学学报.2001,22(6)：83-87页
[15]平面SH波在浅埋椭圆柱形孔洞上的散射与动应力集中.暨南大学学报.2005,26(3)：324-330页
[16]杨宇.楔形地形对入射波散射解析研究进展.低温建筑技 术.2005,108(6)：50-51页
[17]Sezawa K. Scattering of Elastic Waves and Some Allied Problems. Bull Earthquake Res Inst Tokyo Imperial Univ.1927,3:19P
[18]Wolf A. Motion of a Rigid Sphere in an Acoustic Wave Field. Geophysics. 1945,10:91P
[19]Nagase M. Diffraction of Elastic Wave by a Spherical Surface. J. Phys. Soc. Japan.1957,11(3):279P
[20]Knopoff L. Scattering of Compressional Waves by Spherical Obstacles. Geophysics.1959,24(1):30P
[21]Nishimura G. Jimbo Y A. Dynamic Problem of Stress Concentration Stresses in the Vicinity of a Spherical Matter Included in an Elastic Solid Under Dynamical Force. J Faculty of Engineering, Univ of Tokyo.1955,24: 101P
[22]White R M. Elastic Wave Scattering at a Cylindrical Discontinuity in a Solid. J Acoust Soc Am,1958,30(8):771P
[23]Kato K. Reflections of Sound Wave due to a Hollow Cylinder in an Elastic Body. Mem Inst Sci Indus Res. Vol.9 Osaka University, Japan,1952:65P
[24]Pao Y H, Mow C C. Dynamic Stress Concentration in an Elastic Plate with Rigid Circular Inclusion. Proc 4th National Cong of Appl Mech.1962: 235P
[25]Mow C C, Mente L J. Dynamic Stresses and Displacements Around Cylindrical Discontinuities due to Plane Harmonic Shear Waves. J Appl Mech.1963,39(4):598P
[26]Baron M L, Mattews A T. Diffraction of a Pressure Wave by a Cylindrical Cavity in an Elastic Medium. ASME J Appl Mech.1961,28:347P
[27]Baron M L, Parnes R. Displacements and Velocities Produced by the Diffraction of a Pressure Wave by a Cylindrical Cavity in an Elastic Medium. ASME J Appl Mech,1962,29:385P
[28]Jain D L, Kanwal R P. Scattering of Elastic Waves by Circular Cylindrical Flaws and Inclusions. J Appl Phys,1979,59(6):4067-4108P
[29]Jain D L, Kanwal R P. Scattering of Elastic Waves by an Elastic Sphere. Int J Eng Sci.1980,18:829-839P
[30]S. K. Datta. Scattering of Elastic Waves, Mechanics Today. S. Nemat-Nasser. ed. Vol.4. Pergamon Press, New York,1978:149-208P
[31]Kriegsmann G A, Norris A N, Reiss E L. Scattering by Penetrable Acoustic Targets. Wave Motion,1984,6:501-516P
[32]Liu D.K., Gai B.Z. and Tao G. Y. Applications of the Method of Complex Functions to Dynamic Stress Concentrations. Wave Motion.1982,4: 293-304P
[33]韩峰.复变函数方法在弹性波散射及动应力集中问题研究中的应用.哈尔滨建筑大学博士学位论文.1991：1-42页
[34]王竹溪,郭敦仁.特殊函数概论.北京：北京大学出版社,2000
[35]Gubernatis J. E., Domany, E., Krumhansl J. A. and Huberman M. The Born Approximation in the Theory of the Scattering of Elastic Waves by Flaws. J. Appl. Physics.1977,48:2812-2819P
[36]Mal A.K.and Knopoff L. Elastic Wave Velocities in Tow-Component Systems. J.of Inxtitute of Appl. Math 1976,3:376-387P
[37]Waterman P. Matrix Theory of Elastic Wave Scattering. J. Acou. Soc. America.1976,60:567-580P
[38]Pao Y. H. Betti's Identity and Transition Matrix for Elastic Waves, I. Theory. J. Acou. Soc. America.1976,60:556-556P
[39]S.K.Datta, Scattering of Elastic Waves, Mechanics Today, Nemat-Nasser, Vol.4, Pergamon Press, New York,1978:149-208P
[40]Achenbach J. D., Gautesen A. K. and McMaken H. Ray Method for Waves in Elastic Solids with Application to Scattering by Cracks. Pitman Advanced Publishing Progran, Boston.1982:86-119P
[41]刘殿魁,盖秉政,陶贵源.论孔附近的动应力集中.力学学报特刊1981：65-77页
[42]Liu D.K. and Han F. Scattering of Plane SH-waves by Cylindrical Canyon of Arbitrary Shapes in Anisotropic Media. Acta Mechanica Sinica.1990, 6(3):256-266P
[43]Liu D.K. and Han F. Scattering of plane SH-wave by Cylindrical Canyon of Arbitrary Shapes. Int. H. Soil. Dyn. and Ear. Eng.1991,10(5):249-255P
[44]Han F., Wei Y. and Liu D. K. The Interaction of Plane SH-wave and Circular Cavity Surfaced with Lining in Anisotropic Media. Applied Mathematics and Mechanics.1995,16(2):1067-1078P
[45]Shi S. X. Han F. Wang Z. Q., and Liu. D. K. The Interaction of Plane SH-wave and Non-circular Cavity Surfaced with Lining in Anisotropic Media, Applied Mathematics and Mechanics.1996,17(9):809-820P
[46]胡超,刘殿魁.无限大板开孔弹性波的散射及动应力集中.力学学报.特刊.1995：125-134页
[47]Liu D. K. and Hu C. Scattering of Flexural Wave and Dynamic Stress Concentration in Mindlin's Thick Plates With a Cutout. Acta Mechanica Sinica.1996,12(2):169-185P
[48]H.CAO and V.W.LEE. Scattering and diffraction of plane P-waves by circular cylindrical canyons with variable depth-to-width ratio. Soil Dynamics and Earthquake engineering,1990,9 (3):141-150P
[49]梁建文,严林隽,Vincent W lee.圆弧形层状沉积谷地对入射平面P波的散射解析解.地震学报.2001,23(2)：167-184页
[50]梁建文,严林隽.圆弧形层状沉积谷地对入射平面SV波的散射解析解.固体力学学报.2003,24(2)：235-243页
[51]梁建文,严林隽,李军伟,Vincent W lee圆弧形沉积河谷场地在平面P波入射下的响应.岩土力学.2001,22(2)：138-143页
[52]王建华,姜领发,周香莲.稳态P波对半无限饱和土中的圆形孔洞的散射[J].南昌工程学院学报.2005,24(1)：8-19页
[53]史文谱,刘殿魁等.半无限空间中稳态P波在衬砌周围的散射.地震工程与工程振动.2002,23(3)：19-26页
[54]张彦帅.半圆弧凸起地形对平面P波的散射解析解.天津大学硕士学
位论文.2004：1-57页
[55]温立平.饱和土层状沉积谷地对平面P波散射的解析解.天津大学硕士学位论文.2004：1-51页
[56]陈涛,胡超,黄文虎.P波入射时含圆柱形空腔板弹性波散射与动应力集中.地震工程与工程振动.2006,26(4)：32-36页
[57]杨宇.含圆弧形沉积的楔形地形对平面SH波和P波的散射.天津大学硕士学位论文.2005：1-68页
[58]钟伟芳,聂国华.弹性波的散射理论.华中理工大学出版社,1997
[59]刘殿魁,田家勇.SH波对界面圆柱形弹性夹杂散射及动应力集中.爆炸与冲击.1999,19(2)：115-123页
[60]史守峡,杨庆山,刘殿魁,齐辉.SH波对圆形夹杂与裂纹的散射及其动应力集中.复合材料学报.2000,17(3)：107-112页
[61]刘殿魁,杨在林, 刘建百.界面可移动圆柱形刚性夹杂对SH波散射及动应力集中.哈尔滨建筑大学学报.2001,34(6)：2-7页
[62]李宏亮,刘殿魁. SH波作用下裂纹对圆夹杂散射动应力集中问题的影响.哈尔滨工程大学学报.2005,26(3)：359-363页
[63]刘殿魁,吕晓棠. 浅埋圆柱形弹性夹杂附近的半圆形凸起对SH波的散射.哈尔滨工程大学学报.2006,27(2)：189-194页
[64]刘刚,刘殿魁,杜永军,陈海涛.浅埋圆柱形弹性夹杂附近等腰三角形凸起地形引起的SH波的散射.地震工程与工程振动.2006,26(4)：1-8页
[65]史文谱,张春萍,褚京莲,李禄昌,胡爱芹.直角平面边界固定半圆形夹杂对稳态入射平面SH波的散射.振动与冲击.2007,126(1)：121-124页
[66]王慧文,孙晓娟,刘殿魁.浅埋圆形夹杂附近半圆形沉积层对SH波的散射与地表位移.黑龙江工程学院学报.2006,20(2)：1-5页
[67]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页
[68]刘殿魁,刘宏伟.孔边裂纹对SH波散射及动应力强度因子.力学学报.1999,31(3)：292-299页
[69]刘宏伟,刘殿魁.界面圆孔对SH波的散射远场解.固体力学学报. 1999,20(4)：349-355页
[70]史守峡,刘殿魁.SH波与界面多圆孔的散射及动应力集中.力学学报.2001(1)：60-70页
[71]林宏,刘殿魁.半无限空间中圆形孔洞周围SH波的散射.地震工程与工程振动.2002,22(2)：9-16页
[72]廖振鹏.工程波动理论导引.北京：科学出版社,1996
[73]杨在林,孙柏涛,刘殿魁.SH波在浅埋可移动圆柱形刚性夹杂处的散射与地震动.2008,28(4)：1-5页