New theoretical results were obtained in definition of the stability longitudinal stress of the stiffened cylindrical shells both with internal and external arrangement of the stiffened stacks. They were obtained due to application of the dynamic approach to the solution of the refined equilibrium equations, introduction of the Qfactor of the structural elements into the system of equations, definition and application of the forces and moments in the calculation, that act in the sections of the joint bending of the shell and elements of stiffening. Expressions are given, which define the process of stability loss, including parameters of wave generation and amplitude of shell oscillation from the moment of application of the axial compressive force P0 up to the moment of snap action. With dynamic approach to the solution of the problem of the shell’s longitudinal stability the achievement of the first zero frequency by one of the higher modes of bending oscillations of the shell will indicate the loss of stability under the impact of the axial compressive force P0. This process is most obvious during testing of the absolutely flexible shells, which permit multiple loading. In the initial step of shell loading with axial compressive force P0, high-frequency bending oscillations with m, n ˃˃ 1 modes and low amplitudes occur. With a rise in force P0 oscillation frequency begins to drop, and amplitude to increase, with oscillatory mode remaining unchanged. There is a snap action when zero frequency is achieved for the first time by one of the oscillatory modes. This fact allowed formulation of the basic principles of nondestructive method for estimation of the critical stability stress of the flight-ready shell, main point of which is in the comparison of the theoretical curve of the frequency drop due to force P0 action on the structure versus the actual curve of the frequency drop of the flight-ready structure under the impact of the same values of P0 in the elastic range.
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