竖向激励下弹性半空间单一覆盖层的表面位移
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摘要
利用传递矩阵法和Laplace-Hankel联合变换技术,推导出层间完全接触的弹性半空间单一覆盖层模型表面作用脉冲荷载时覆盖层表面竖向位移场解析解.通过退化为弹性半空间问题,与经典解对比,验证了该计算方法的准确性.
The analytical solution of vertical displacement field on the surface of the model from pulse loading on the surface is derived by means of transfer matrix and Laplace-Hankel combined transform.In the derivation all layers contact with each other completely.By degenerating the model into elastic half-space,the numerical result obtained is compared with that of the classical solution and the reliability of the calculation in this dissertation is validated.
The analytical solution of vertical displacement field on the surface of the model from pulse loading on the surface is derived by means of transfer matrix and Laplace-Hankel combined transform.In the derivation all layers contact with each other completely.By degenerating the model into elastic half-space,the numerical result obtained is compared with that of the classical solution and the reliability of the calculation in this dissertation is validated.
引文
[1]FRANSSENS G R.Calculation of the elasto-dynamic Green’s functions inlayered media by means of a modifiedpropagator matrix method[J].Geophys J R Astron Soc,1983,75(3):669-691.
[2]APSEL RJ,LUCOJ E.On the Green’s function for a layered half-space:PartⅠ[J].Bull Seismol Soc Am,1983,73(4):909-929.
[3]LUCOJ E,APSEL RJ.On the Green’s function for a layered half-space:PartⅡ[J].Bull Seismol Soc Am,1983,73(4):931-951.
[4]KAUSEL E,PEEK R.Dynamic loads in the interior of a layered stratum:an explicit solution[J].Bull SeismolSoc Am,1982,72(5):1459-1481.
[5]孟凡顺,郭海燕,叶天麒.用传递矩阵法求解多层层状弹性半空间轴对称动力问题的奇异解[J].地震工程与工程振动,1995,15(2):44-51.
[6]黄菊花,何成宏,杨国泰.任意激励下层状粘弹性地基表面振动的解析解[J].塑性工程学报,1999,6(1):74-80.
[7]SAN Ping-zeng.Elastic dynamic solutions for multi-layer systems and analysis techniques for drilled shafts stabi-lized slopes[D].Akron:Univ of Akron,2002.
[8]YU H Y.Forced torsional oscillations of multilayered solids[J].Int J Engin Sci,2008,46(3):250-259.
[9]王元汉,谢诗伟,谢洪阳.计算层状地基板的半解析数值方法[J].岩石力学与工程学报,2002,21(增2):2447-2450.
[10]杨桂通,张善元.弹性动力学[M].北京:中国铁道出版社,1988:203-218.
[11]刘凯欣,刘广裕.垂直点源的一个精确解[J].科学通报,2004,49(5):419-423.
[2]APSEL RJ,LUCOJ E.On the Green’s function for a layered half-space:PartⅠ[J].Bull Seismol Soc Am,1983,73(4):909-929.
[3]LUCOJ E,APSEL RJ.On the Green’s function for a layered half-space:PartⅡ[J].Bull Seismol Soc Am,1983,73(4):931-951.
[4]KAUSEL E,PEEK R.Dynamic loads in the interior of a layered stratum:an explicit solution[J].Bull SeismolSoc Am,1982,72(5):1459-1481.
[5]孟凡顺,郭海燕,叶天麒.用传递矩阵法求解多层层状弹性半空间轴对称动力问题的奇异解[J].地震工程与工程振动,1995,15(2):44-51.
[6]黄菊花,何成宏,杨国泰.任意激励下层状粘弹性地基表面振动的解析解[J].塑性工程学报,1999,6(1):74-80.
[7]SAN Ping-zeng.Elastic dynamic solutions for multi-layer systems and analysis techniques for drilled shafts stabi-lized slopes[D].Akron:Univ of Akron,2002.
[8]YU H Y.Forced torsional oscillations of multilayered solids[J].Int J Engin Sci,2008,46(3):250-259.
[9]王元汉,谢诗伟,谢洪阳.计算层状地基板的半解析数值方法[J].岩石力学与工程学报,2002,21(增2):2447-2450.
[10]杨桂通,张善元.弹性动力学[M].北京:中国铁道出版社,1988:203-218.
[11]刘凯欣,刘广裕.垂直点源的一个精确解[J].科学通报,2004,49(5):419-423.
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