Analysis of the dynamics of thin isotropic cylindrical shell in asymptotic approach

•Vibration of a thin cylindrical shell problem is formulated.•Formulation is done by asymptotic approach under cylindrical symmetry.•Analytical solutions are obtained with clarity.•Obtained solutions are numerically discussed.

In this paper, a dynamic behavior of an isotropic cylindrical shell under cylindrical symmetry is presented by asymptotic approach. Here some special assumptions are set to make the problem simple. An attempt is taken to give an analytic expression of radial vibration of a semi-infinite cylinder. In this problem it is assumed that the thickness of the shell is so small that variants of the vibrations exhibit infinite power series expansion across the thickness. As a result of this assumption it is shown that all modes of variants remain uncoupled and satisfy the same equations of motion approximately.