Theoretical solution of cylindrical shells for axisymmetric plain strain elastodynamic problems

A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special function was introduced to transform the inhomogeneous boundary conditions into the homogeneous ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function was expanded as the multiplication series of Bessel functions and time functions. Then by virtue of the orthogonal properties of Bessel functions, the equation with respect to the time variable was derived, of which the solution is easily obtained. The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic cylindrical shell that is fixed at the internal surface.