多层沉积凹陷地形对平面SH波散射问题的解析解
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摘要
利用波函数展开法给出了含多个沉积层凹陷地形对平面SH波散射二维问题的一个解析解,并以一具有3个沉积层的凹陷地形为例,分析了凹陷地形中沉积层排列次序对SH波散射的影响。结果表明,凹陷地形中沉积层排列次序将显著改变凹陷地形的卓越频率,沉积层的某个(些)排列次序有可能对入射波产生巨大的放大作用;此外,沉积层的刚度、厚度以及凹陷地形的深宽比等均对凹陷地形的放大效应也有一定的影响。
By wave function expansion method,an analytical solution for two-dimensional scattering of plane SH waves around a canyon with multi-layered alluvia was given;and effect of the sequence of the alluvial layers on the scattering of SH waves was studied by an example of a canyon with three alluvial layers.It was demonstrated that,the sequence of alluvial layers in a canyon changes predominant frequencies of the canyon significantly;and large amplification to the incident wave may be caused for certain sequence of the alluvial layers;stiffness and thickness of the alluvial layers,and depth-to-width ratio of the canyon,etc.have influences on the amplification.
By wave function expansion method,an analytical solution for two-dimensional scattering of plane SH waves around a canyon with multi-layered alluvia was given;and effect of the sequence of the alluvial layers on the scattering of SH waves was studied by an example of a canyon with three alluvial layers.It was demonstrated that,the sequence of alluvial layers in a canyon changes predominant frequencies of the canyon significantly;and large amplification to the incident wave may be caused for certain sequence of the alluvial layers;stiffness and thickness of the alluvial layers,and depth-to-width ratio of the canyon,etc.have influences on the amplification.
引文
[1]Trifunac M D.Scattering of plane SH waves by a semi-cylindrical canyon[J].Earthquake Engineering and Structural Dynamics,1973,1:267-281.
[2]Wong H L,Trifunac M D.Scattering of plane SH-waves by a semi-elliptical canyon[J].Earthquake Engineering and Structural Dynamics,1974,3:157-169.
[3]Cao H,Lee V W.Scattering of plane SH waves by circular cylindrical canyons with variable depth-to-width ratio[J].Euro J of Earthq Eng,1989,3(2):29-37.
[4]Yuan X,Liao Z.Scattering of plane SH waves by cylindrical canyons of circular-arc cross-section[J].Soil Dynam Earthq Eng,1994,13:407-412.
[5]Cao H,Lee V W.Scattering and diffraction of plane P waves by circular cylindrical canyons with variable depth-to-width ratio[J].Soil Dynam Earthq Eng,1989,9:141-150.
[6]Lee V W,Cao H.Diffraction of SV waves by circular cylindrical canyons of various depths[J].J Eng Mech,ASCE,1989,115:2 035-2 056.
[7]梁建文,张郁山,Lee V W.圆弧形层状凹陷地形对平面SH波的散射[J].振动工程学报,2003,16(2):158-165.LIANG Jian-wen,ZHANG Yu-shan,Lee V W.Scattering of plane SH waves by a circular-arc layered canyon[J].Journal of Vibration Engineering,2003,16(2):158-165.
[8]梁建文,严林隽,Lee V W.圆弧形凹陷地形表面覆盖层对入射平面P波的影响[J].固体力学学报,2002,23(4):397-411.LIANG Jian-wen,YAN Lin-jun,Lee V W.Scattering of incident plane P waves by a circular-arc canyon with a covering layer[J].Acta Mechnica Solida Sivica.2002,23(4):397-411.
[9]梁建文,严林隽,Lee V W.圆弧形凹陷地形表面覆盖层对入射平面SV波的影响[J].地震学报,2001,23(6):622-636.LIANG Jian-wen,YAN Lin-jun,Lee V W.Effects of a covering layer in a circular-arc canyon on incident plane SV waves[J].Acta Seismologica Sinica.2001,23(6):622-636.
[10]Abramowita M,Stegun I A.Handbook of mathematical functions,with formulas,graphs and mathematical tables[M].New York:Dover Publisher,1972.
[2]Wong H L,Trifunac M D.Scattering of plane SH-waves by a semi-elliptical canyon[J].Earthquake Engineering and Structural Dynamics,1974,3:157-169.
[3]Cao H,Lee V W.Scattering of plane SH waves by circular cylindrical canyons with variable depth-to-width ratio[J].Euro J of Earthq Eng,1989,3(2):29-37.
[4]Yuan X,Liao Z.Scattering of plane SH waves by cylindrical canyons of circular-arc cross-section[J].Soil Dynam Earthq Eng,1994,13:407-412.
[5]Cao H,Lee V W.Scattering and diffraction of plane P waves by circular cylindrical canyons with variable depth-to-width ratio[J].Soil Dynam Earthq Eng,1989,9:141-150.
[6]Lee V W,Cao H.Diffraction of SV waves by circular cylindrical canyons of various depths[J].J Eng Mech,ASCE,1989,115:2 035-2 056.
[7]梁建文,张郁山,Lee V W.圆弧形层状凹陷地形对平面SH波的散射[J].振动工程学报,2003,16(2):158-165.LIANG Jian-wen,ZHANG Yu-shan,Lee V W.Scattering of plane SH waves by a circular-arc layered canyon[J].Journal of Vibration Engineering,2003,16(2):158-165.
[8]梁建文,严林隽,Lee V W.圆弧形凹陷地形表面覆盖层对入射平面P波的影响[J].固体力学学报,2002,23(4):397-411.LIANG Jian-wen,YAN Lin-jun,Lee V W.Scattering of incident plane P waves by a circular-arc canyon with a covering layer[J].Acta Mechnica Solida Sivica.2002,23(4):397-411.
[9]梁建文,严林隽,Lee V W.圆弧形凹陷地形表面覆盖层对入射平面SV波的影响[J].地震学报,2001,23(6):622-636.LIANG Jian-wen,YAN Lin-jun,Lee V W.Effects of a covering layer in a circular-arc canyon on incident plane SV waves[J].Acta Seismologica Sinica.2001,23(6):622-636.
[10]Abramowita M,Stegun I A.Handbook of mathematical functions,with formulas,graphs and mathematical tables[M].New York:Dover Publisher,1972.
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