圆弧形沉积谷地对Rayleigh波三维散射解析解
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摘要
采用假定的大圆弧面来模拟半空间,利用波函数展开法和有限项Fourier级数展开技术,在频域内给出圆弧形沉积谷地对Rayleigh波三维散射的一个解析解.以此解答为基础,进一步分析入射波的频率和入射角度以及谷地深度对圆弧形沉积谷地场地反应的影响.数值结果表明,入射频率和入射角度以及沉积谷地深度对沉积谷地地表位移有重要影响.
An analytical solution for the 3D scattering of Rayleigh waves by circular-arc alluvial valleys in frequency do-main was provided in this paper by adopting the circular surface assumption to simulate half-space surface and by using the wave function expansion method and the finite Fourier series expansion technique as well.Based on the solutiont,he effects of the incident frequency and incident angle of Rayleigh waves,and the valley depth on the dynamic response of circular-arc alluvial valleys were discussed.The numerical results show that the surface displacement amplitudes significantly depend on incident angle and the incident frequency of the Rayleigh waves,and the arc depth.
An analytical solution for the 3D scattering of Rayleigh waves by circular-arc alluvial valleys in frequency do-main was provided in this paper by adopting the circular surface assumption to simulate half-space surface and by using the wave function expansion method and the finite Fourier series expansion technique as well.Based on the solutiont,he effects of the incident frequency and incident angle of Rayleigh waves,and the valley depth on the dynamic response of circular-arc alluvial valleys were discussed.The numerical results show that the surface displacement amplitudes significantly depend on incident angle and the incident frequency of the Rayleigh waves,and the arc depth.
引文
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[6]梁建文,严林隽,秦东,等.圆弧形沉积河谷场地在平面SV波入射下的动力响应[J].土木工程学报,2003,36(12):74-82.Liang Jianwen,Yan Linjun,Qin Dong,et al.Dynamic response of circular-arc sedimentary valley site under in-cident plane SV waves[J].China Civil Engineering Journal,2003,36(12):74-82(in Chinese).
[7]Todorovska M I,Lee V W.A note on response of shal-low circular valleys to Rayleigh waves:Analytical ap-proach[J].Earthquake Engineering and Engineering Vibration,1990,3:21-34.
[8]梁建文,张秋红,李方杰.浅圆沉积谷地对瑞雷波的散射——高频解[J].地震学报,2006,28(2):176-182.Liang Jianwen,Zhang Qiuhong,Li Fangjie.Scattering of Rayleigh waves by a shallow circular alluvial valley:High-frequency solution[J].Acta Seismologica Sinica,2006,28(2):176-182(in Chinese).
[9]Lee V W,Sabban M S,Ghosh T.3D surface motion of long semi-circular longitudinal canyonsI:ncident plane P waves[J].European Journal of Earthquake Engi-neering,1996,9(3):12-22.
[10]Knowles J K.A note on elastic surface waves[J]-.Journal of Geophysical Research,1966,71:5480-5481.
[11]Pao Y H,Mow C C.Diffraction of Elastic Waves and Dynamic Stress Concentrations[M].New York:Crane,Russak and Company,1973.
[12]Abramowita M,Stegun I A.Handbook of Mathematical Functions,with Formulas,Graphs,and Mathematical Tables[M].New York:Dover Publication,1972.
[13]Stratton J A.Electromagnetic Theory[M].New York:McGraw-Hill,1941.
[14]Hamming R W.Numerical Methods for Scientists and Engineers[M].New York:McGraw-Hill,1962.
[15]徐果明,周蕙兰.地震学原理[M].北京:科学出版社,1982.Xu Guoming,Zhou Huilan.Principles of Earthquake[M].Beijing:Science Press,1982(in Chinese).
[2]Wong H L,Trifunac M D.Surface motion of a semi-elliptical alluvial valley for incident plane SH waves[J].Bulletin of the Seismological Society of America,1974,64:1389-1408.
[3]Todorovska M I,Lee V W.Surface motion of shallow circular alluvial valleys for incident plane SH waves:Analytical solution[J].Soil Dynamics and Earthquake Engineering,1991,4:192-200.
[4]Yuan Xiaoming,Liao Zhengpeng.Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section[J].Earthquake Engineering and Struc-ture Dynamics,1995,24(10):1303-1313.
[5]梁建文,严林隽,李军伟,等.圆弧形沉积河谷场地在平面P波入射下的响应[J].岩土力学,2001,22(2):138-143.Liang Jianwen,Yan Linjun,Li Junwei,et al.Response of circular-arc alluvial valleys under incident plane P waves[J].Rock and Soil Mechanics,2001,22(2):138-143(in Chinese).
[6]梁建文,严林隽,秦东,等.圆弧形沉积河谷场地在平面SV波入射下的动力响应[J].土木工程学报,2003,36(12):74-82.Liang Jianwen,Yan Linjun,Qin Dong,et al.Dynamic response of circular-arc sedimentary valley site under in-cident plane SV waves[J].China Civil Engineering Journal,2003,36(12):74-82(in Chinese).
[7]Todorovska M I,Lee V W.A note on response of shal-low circular valleys to Rayleigh waves:Analytical ap-proach[J].Earthquake Engineering and Engineering Vibration,1990,3:21-34.
[8]梁建文,张秋红,李方杰.浅圆沉积谷地对瑞雷波的散射——高频解[J].地震学报,2006,28(2):176-182.Liang Jianwen,Zhang Qiuhong,Li Fangjie.Scattering of Rayleigh waves by a shallow circular alluvial valley:High-frequency solution[J].Acta Seismologica Sinica,2006,28(2):176-182(in Chinese).
[9]Lee V W,Sabban M S,Ghosh T.3D surface motion of long semi-circular longitudinal canyonsI:ncident plane P waves[J].European Journal of Earthquake Engi-neering,1996,9(3):12-22.
[10]Knowles J K.A note on elastic surface waves[J]-.Journal of Geophysical Research,1966,71:5480-5481.
[11]Pao Y H,Mow C C.Diffraction of Elastic Waves and Dynamic Stress Concentrations[M].New York:Crane,Russak and Company,1973.
[12]Abramowita M,Stegun I A.Handbook of Mathematical Functions,with Formulas,Graphs,and Mathematical Tables[M].New York:Dover Publication,1972.
[13]Stratton J A.Electromagnetic Theory[M].New York:McGraw-Hill,1941.
[14]Hamming R W.Numerical Methods for Scientists and Engineers[M].New York:McGraw-Hill,1962.
[15]徐果明,周蕙兰.地震学原理[M].北京:科学出版社,1982.Xu Guoming,Zhou Huilan.Principles of Earthquake[M].Beijing:Science Press,1982(in Chinese).
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