Loss of stability of thin-walled structural elements of aircraft is the most common type of destruction. In this work, the definition of the critical velocity of a pressure wave moving over the surface of an acclivous, ribbed cylindrical shell, which is the most common design element of all aviation and rocket systems, is considered. The article takes into account the discreteness of the location of stiffeners (stringers), in contrast to other works, where ribbing is taken into account only within the framework of a constructive orthotropic model. In the quasi-static formulation, the problem of the stability of a shallow shell with a discrete arrangement of stringers under the action of a moving radial load has been solved. The range of critical speeds of movement of the load is defined. An example is considered.

The problem of dynamic deformation of a plate with a two-layer composite shell with a heat-shattering coating collapsing in time under the action of a running load is solved approximately. The problem is solved in a dynamic formulation, considering that the deformed state of the shell depends both on the spatial coordinates and on time. The problem is reduced to solving two differential equations of the shell in partial derivatives with respect to deflections and the stress function. These equations contain discontinuous ratios for unknowns, which are associated with the dynamic destruction of the heat-shielding coating. According to the Bubnov method, the problem is also reduced to a system of differential equations, but already in ordinary derivatives. The solution of these equations is obtained in closed form. In addition, the natural vibration frequencies of the structure and the critical velocities of the load are found depending on the degree of damage to the protective layer. Formulas for oscillation frequencies and critical speeds are obtained in closed form.

In the dynamic and quasi-static statements, the issue of non-stationary deformation and stability of the solid propellant rocket engine (SPRE) was approximately solved. It is modeled by a thin, smooth cylindrical shell, inside of which, on a part of its length, there is an elastic base corresponding to a gradually burning powder charge. A pressure wave is moving along the outer surface of the body, simulated by the running load. The deformed state of the shell is considered axisymmetric and is determined on the basis of the moment theory of the shells. For diverse variants of mounting the ends of the shell in a closed form, expressions were obtained for the critical velocity of the load. Examples were considered.

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