平面SV波在饱和土半空间中圆柱形孔洞周边的散射
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摘要
在Biot饱和多孔介质动力学理论的基础上,利用Fourier-Bessel级数展开法,得到SV波在饱和土半空间中圆柱形孔洞周边的散射问题的解析解答。与已有相关问题的解析解答进行对比,验证了此解的正确性,并给出算例,分析了入射频率对柱面上的应力集中因子的影响。
On the basis of Biot dynamic theory,the dynamic response of cylindrical cavities to incident SV waves is investigated.An analytic solution is derived for the cavities embedded within a fluid-saturated porous media half space by using Fourier-Bessel series expansion technique in this paper.The solutions are proofed by comparison with the existing related solutions.Numerical results are given and the effect of the dimensionless frequency of the incident SV wave on the dynamical stress concentration factor on the surface of the cavity are shown.
On the basis of Biot dynamic theory,the dynamic response of cylindrical cavities to incident SV waves is investigated.An analytic solution is derived for the cavities embedded within a fluid-saturated porous media half space by using Fourier-Bessel series expansion technique in this paper.The solutions are proofed by comparison with the existing related solutions.Numerical results are given and the effect of the dimensionless frequency of the incident SV wave on the dynamical stress concentration factor on the surface of the cavity are shown.
引文
[1]徐长节,吴世明,蔡袁强,等.波在饱和土中柱状空穴界面上的反射[J].计算力学学报,1997,14(增刊):291-294.
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[4]Kattis S E,Beskos D E,Cheng AHD.2D dynamic response of unlined and lined tunnels in poro-elastic soil to harmonic body waves[J].Earthquake Engineering and Structure Dynamics,2003,32:97-110.
[5]尤红兵.层状饱和土半空间中凹陷地形和隧洞对弹性波的散射[D].天津:天津大学,2005.
[6]李伟华,赵成刚.饱和土半空间中圆柱形孔洞对平面P的散射[J].岩土力学,2004,25(12):1867-1872.
[7]姜领发,王建华,周香莲.半空间饱和土中的圆形孔洞对稳态剪切波的散射[J].岩土工程学报,2007,29(3):366-371.
[8]Davis C A,Lee VW,Bardet J P.Transverse response of underground cavities and pipes to incident SVwaves[J].Earthquake Engineeringand Structure Dynamics,2001,30:383-410.
[9]李伟华.含饱和土的复杂局部场地波动散射问题的解析解和显式有限元数值模拟[D].北京:北京交通大学,2004.
[10]Biot MA.Theory of propagation of elastic wave in fluid-saturated porous soil[J].The Journal of the Acoustical Society of America,1956,28(2):168-178.
[11]Greetsma J.Some aspects of elastic wave propagation in fluid-saturated porous solids[J].Geophys,1961,26:169-181
[12]Li Weihua,Zhao Chenggang.Scattering of plane SV waves by cylindrical canyons in saturated porous medium[J].Soil Dynamics andEarthquake Engineering,2005,25:981-995.
[13]数学手册编写组.数学手册[M].北京:高等教育出版社,1979.
[2]胡亚元,王立忠,陈云敏,等.饱和土中平面应变波在圆柱体上的散射和折射[J].地震学报,1998,20(3):300-307.
[3]陆建飞,王建华.饱和土中任意形状孔洞对弹性波的散射[J].力学学报,2002,34(6):904-912.
[4]Kattis S E,Beskos D E,Cheng AHD.2D dynamic response of unlined and lined tunnels in poro-elastic soil to harmonic body waves[J].Earthquake Engineering and Structure Dynamics,2003,32:97-110.
[5]尤红兵.层状饱和土半空间中凹陷地形和隧洞对弹性波的散射[D].天津:天津大学,2005.
[6]李伟华,赵成刚.饱和土半空间中圆柱形孔洞对平面P的散射[J].岩土力学,2004,25(12):1867-1872.
[7]姜领发,王建华,周香莲.半空间饱和土中的圆形孔洞对稳态剪切波的散射[J].岩土工程学报,2007,29(3):366-371.
[8]Davis C A,Lee VW,Bardet J P.Transverse response of underground cavities and pipes to incident SVwaves[J].Earthquake Engineeringand Structure Dynamics,2001,30:383-410.
[9]李伟华.含饱和土的复杂局部场地波动散射问题的解析解和显式有限元数值模拟[D].北京:北京交通大学,2004.
[10]Biot MA.Theory of propagation of elastic wave in fluid-saturated porous soil[J].The Journal of the Acoustical Society of America,1956,28(2):168-178.
[11]Greetsma J.Some aspects of elastic wave propagation in fluid-saturated porous solids[J].Geophys,1961,26:169-181
[12]Li Weihua,Zhao Chenggang.Scattering of plane SV waves by cylindrical canyons in saturated porous medium[J].Soil Dynamics andEarthquake Engineering,2005,25:981-995.
[13]数学手册编写组.数学手册[M].北京:高等教育出版社,1979.
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