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高盟, 高广运, 王滢, 冯世进. 均布突加荷载作用下圆柱形衬砌振动响应的解析解[J]. 岩土工程学报, 2010, 32(2).
引用本文: 高盟, 高广运, 王滢, 冯世进. 均布突加荷载作用下圆柱形衬砌振动响应的解析解[J]. 岩土工程学报, 2010, 32(2).
Analytical solution on dynamic response of lining subjected to sudden internal uniform loading[J]. Chinese Journal of Geotechnical Engineering, 2010, 32(2).
Citation: Analytical solution on dynamic response of lining subjected to sudden internal uniform loading[J]. Chinese Journal of Geotechnical Engineering, 2010, 32(2).

均布突加荷载作用下圆柱形衬砌振动响应的解析解

Analytical solution on dynamic response of lining subjected to sudden internal uniform loading

  • 摘要: 考虑土与衬砌结构的动力相互作用,研究了圆柱形衬砌结构的瞬态响应问题。将土体和衬砌结构分别视为无限弹性可压缩介质和弹性壳体,通过引入势函数将土体的位移控制方程化为二维轴对称波动方程,根据界面连续条件,建立弹性壳体的振动方程。利用拉普拉斯变换及逆变换,求得了均布突加荷载作用下壳体振动响应完全解析解。在此基础上,分析了均布突加荷载作用下土体泊松比、剪切模量及衬砌剪切模量、衬砌厚度对衬砌动力响应的影响。

     

    Abstract: Considering the dynamic interaction between lining and soil, the transient dynamic response of a cylindrical lining subjected to impact loading is presented. The lining structure and soil are respectively treated as cylindrical elastic shell and infinite elastic and compressible medium. A two-dimensional axisymmetric wave equation is derived from the governing equation of displacement by introducing the potential functions. The motion equation for shells is established based on continuity conditions. The analytical solution for dynamic response of the lining subjected to sudden internal uniform loading is derived using the Laplace transforms and inverse transforms. On this basis, the influences of the Poisson’s ratio of soil, shear modulus of soil, shear modulus of lining and thickness of lining on dynamic response of the lining are analyzed.

     

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