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

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.