Conditions of Stability of Vertical Cylindrical Soft Shell

Abstract

The paper is devoted to the description of stability conditions of a vertical cylindrical flexible inextensible shell. The air is forced upward with the fan inside the shell. On the upper edge of the shell there is a tapering outlet (exhaust), which allows to adjust the height of the shell under the condition of its stability in the vertical position. The analytical dependence of the height of the flexible inextensible shell depending on the relative cross-sectional area of the exhaust has been achieved taking into account the friction forces of the air flow against the shell sides. The purpose of the paper is to develop the method for determining the stability of a flexible, inextensible vertical cylindrical shell in which the air flow is pumped depending on its height. The objectives of research are the following: 1) to formulate the conditions of the air flow movement inside the cylinder; 2) to determine the magnitude of a force holding a cylindrical shell in a vertical position; 3) to get the analytic expression of the critical height of the flexible vertical cylindrical shell, in which it still retains a stable vertical position. Most often, the mathematical model in the theory of shells is based on the classical equilibrium equations of the theory of elastic shells. The scientific novelty of this research is to develop the method of analytical description of the lift force holding the shell in a vertical position when the turbulent air flow is pumped into it on the basis of the Bernoulli equation and technical characteristics of the supercharger.