倾斜入射快纵波在饱和土中单个圆柱体周围的散射
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摘要
在Biot饱和土波动理论的基础上,采用波函数展开法,研究了饱和土体中单个圆柱体对倾斜入射PI波的散射特性,计算了背向散射谱和总散射截面积。结果表明,饱和土体中PI波倾斜入射时,随着倾斜入射角的增大,总散射截面积在减小,产生的散射波主要以PI波和SV波为主;随着饱和土体渗透系数的减小,PI波、PⅡ波和SV波背向散射谱平均幅值均呈增大趋势,但PI波背向散射谱幅值变化程度较小。
On the basis of Biot's dynamic theory,the scattering of obliquely incident PI-wave around a cylinder in saturated soil was investigated by using wave function expansion technique,and the backscattering spectrum and the total scattering cross section of the cylinder were calculated.The numerical results show that when the obliquely incident wave is PI-wave,the total scattering cross section decreases with the increase of obliquely incident angle,and the scattered waves produced by the cylinder are just PI-wave and SV-wave.The average amplitude of backscattering spectrum for PI-wave,PⅡ-wave and SV-wave increases with the decrease of permeability coefficient of saturated soil,but the change range of the amplitude of backscattering spectrum for PI-wave is small.
On the basis of Biot's dynamic theory,the scattering of obliquely incident PI-wave around a cylinder in saturated soil was investigated by using wave function expansion technique,and the backscattering spectrum and the total scattering cross section of the cylinder were calculated.The numerical results show that when the obliquely incident wave is PI-wave,the total scattering cross section decreases with the increase of obliquely incident angle,and the scattered waves produced by the cylinder are just PI-wave and SV-wave.The average amplitude of backscattering spectrum for PI-wave,PⅡ-wave and SV-wave increases with the decrease of permeability coefficient of saturated soil,but the change range of the amplitude of backscattering spectrum for PI-wave is small.
引文
[1]White R M.Elastic wave scattering at a cylindrical discontinuity in a solid[J].Journal of the Acoustical Society of America,1958,30(8):771-785.
[2]Schuetz L S,Neubauer W G.Acoustic reflection from cylinders-nonabsorbing and absorbing[J].Journal of the Acoustical Society of America,1977,62(3):513-517.
[3]FlaxL,Varadan VK,Varadan VV.Scattering of an obliquely incident acoustic wave by an infinite cylinder[J].Journal of the Acoustical Socie-ty of America,1980,68(6):1832-1835.
[4]Li TB,Ueda M.Sound scattering of a plane wave obliquely incident on a cylinder[J].Journal of the Acoustical Society of America,1989,86(6):2363-2368.
[5]Lon F,Lecroq F,Dcultot D,et al.Scattering of an obliquely incident acoustic wave by an infinite hollowcylindrical shell[J].Journal of theAcoustical Society of America,1992,91(3):1388-1392.
[6]Huang W,Wang Y J,Rokhlin S I.Oblique scattering of an elastic wave from a multilayered cylinder in a solid[J].Journal of the Acoustical So-ciety of America,1996,99(5):2742-2954.
[7]刘胜兴,王耀俊.横向各向同性柱状复合结构对超声波的散射[J].声学学报,2002,27(2):149-156.
[8]Mitri F G,Fellah Z E A,Chapelon J Y.Acoustic backscattering form function of absorbing cylinder targets[J].Journal of the Acoustical Societyof America,2004,115(4):1411-1413.
[9]徐平,夏唐代,韩同春.饱和弹性土体中圆柱壳体对弹性波的散射[J].地震学报,2006,28(2):183-189.
[10]梁建文,刘中宪.柱面波在半空间中洞室周围的散射[J].地震工程与工程振动,2008,28(5):27-37.
[11]李伟华,赵成刚.平面SV波在饱和土半空间中圆柱形孔洞周边的散射[J].地震工程与工程振动,2008,28(6):1-7.
[12]Biot MA.Theory of propagation of elastic waves in a fluid-saturated porous solid[J].Journal of the Acoustical Society of America,1956,28(2):168-191.
[13]Stoll R D,Kan TK.Reflection of acoustic waves at a water-sediment interface[J].Journal of the Acoustical Society of America,1981,70(1):149-156.
[2]Schuetz L S,Neubauer W G.Acoustic reflection from cylinders-nonabsorbing and absorbing[J].Journal of the Acoustical Society of America,1977,62(3):513-517.
[3]FlaxL,Varadan VK,Varadan VV.Scattering of an obliquely incident acoustic wave by an infinite cylinder[J].Journal of the Acoustical Socie-ty of America,1980,68(6):1832-1835.
[4]Li TB,Ueda M.Sound scattering of a plane wave obliquely incident on a cylinder[J].Journal of the Acoustical Society of America,1989,86(6):2363-2368.
[5]Lon F,Lecroq F,Dcultot D,et al.Scattering of an obliquely incident acoustic wave by an infinite hollowcylindrical shell[J].Journal of theAcoustical Society of America,1992,91(3):1388-1392.
[6]Huang W,Wang Y J,Rokhlin S I.Oblique scattering of an elastic wave from a multilayered cylinder in a solid[J].Journal of the Acoustical So-ciety of America,1996,99(5):2742-2954.
[7]刘胜兴,王耀俊.横向各向同性柱状复合结构对超声波的散射[J].声学学报,2002,27(2):149-156.
[8]Mitri F G,Fellah Z E A,Chapelon J Y.Acoustic backscattering form function of absorbing cylinder targets[J].Journal of the Acoustical Societyof America,2004,115(4):1411-1413.
[9]徐平,夏唐代,韩同春.饱和弹性土体中圆柱壳体对弹性波的散射[J].地震学报,2006,28(2):183-189.
[10]梁建文,刘中宪.柱面波在半空间中洞室周围的散射[J].地震工程与工程振动,2008,28(5):27-37.
[11]李伟华,赵成刚.平面SV波在饱和土半空间中圆柱形孔洞周边的散射[J].地震工程与工程振动,2008,28(6):1-7.
[12]Biot MA.Theory of propagation of elastic waves in a fluid-saturated porous solid[J].Journal of the Acoustical Society of America,1956,28(2):168-191.
[13]Stoll R D,Kan TK.Reflection of acoustic waves at a water-sediment interface[J].Journal of the Acoustical Society of America,1981,70(1):149-156.
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