Numerical analysis of the flutter of a shallow shell

The stability of vibrations of a shallow shell that is rectangular in plant in a gas flow is studied for an arbitrary vector of flow velocity. Mathematically, the problem is shown to reduce to an ill-conditioned computational problem. To solve this problem, we propose a numerical saturation-free algorithm that allows one to obtain a sufficiently accurate solution for a grid containing 169 (13 $\times$ 13) nodes. In calculations for cylindrical and spherical shallow shells, new mechanical effects concerning the vibration modes and the dependence of the critical flutter velocity on the direction of the flow-velocity vector were found.