Dynamic Stability of Conical Shells in a Nonlinear Approach.

The paper presents a solution of the nonlinear, dynamic problem of stability of a shell in the form of a truncated cone. The entire shell is loaded by an external pressure increasing rapidly in time. The simply supported shell is thin-walled and its initial deflections are of the order of thickness. The governing equations consist of the equations of motion (including the inertia component in the normal direction) and the quasi-static compatibility equations. Solution of the compatibility conditions yields the function of forces (the functions of deflection and initial deflections being assumed) and is followed by the solution of the equilibrium equation. The Bubnov-Galerkin method is applied to the latter solution. As a result a nonlinear differential equation of second order with respect to time is obtained. External pressure is assumed to vary in a linear manner. A numerical solution and graphs conclude the paper.