Parametric instability of cylindrical shells filled with a fluid

A theoretical study is carried out on the problem of parametric instability of cylindrical shells carrying an incompressible fluid with a free surface and subjected to the action of longitudinal inertial forces due to the motion of the shell basis according to a periodic law. The Bubnov-Galerkin method is used to derive a system of linear differential equations with periodic coefficients for describing the behavior of the shell-fluid system. The major regions of dynamic instability of the system are determined. The results obtained are compared with graphical data.