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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。
Considering the dynamic interaction between soil and lining structure, the transient response of cylindrical lining structure is studied. The soil and lining structures are regarded as infinitely elastic compressible media and elastic shell respectively. By introducing the potential function, the displacement control equation of soil mass is transformed into two-dimensional axisymmetric wave equation. According to the continuous interface conditions, the vibration of elastic shell equation. Using Laplace transform and inverse transform, the complete analytic solution of the shell vibration response under uniform uniform sudden load is obtained. On this basis, the influence of soil bulk Poisson’s ratio, shear modulus, lining shear modulus and lining thickness on the lining dynamic response are analyzed.