Pochtman, Yu. M.; Titov, S. O. The stability of cylindrical shells under with time fast growing loadings. (Russian) Zbl 0664.73024 Dokl. Akad. Nauk Ukr. SSR, Ser. A 1987, No. 6, 32-36 (1987). The problem of dynamic stability of reinforced cylindrical shells under with-time fast growing loadings, is investigated by formulating the analytical stability criteria which take into account the influence of axial, tangential and normal inertial components and allow to obtain the solution for stationary waves. A cylindrical shell reinforced by the grid of longitudinal and transversal elements (stringers and frames), subjected to an axial compressive load (or external pressure), varying with time after an exponential low, is considered. The expressions of potential and kinetic energy in terms of the middle surface displacements are given and the solution satisfying the hinged edge supporting conditions, is presented. Having substituted such a solution in expressions of potential and kinetic energy, two systems of differential equations, describing the character of the possible movement of the shell, are obtained. After some intermediary substitutions and transformations, these equations may be rewritten as an eigenvalue system, depending on time, from whose minimized eigenfunctions the final equation describing the character of possible movement of the shell is obtained and the criteria to determine the critical time and the critical load for fast growing displacements in the case of exponential growing load, are formulated. Reviewer: G.V.Vasiliev MSC: 74H55 Stability of dynamical problems in solid mechanics 74K15 Membranes 74E30 Composite and mixture properties Keywords:Lagrange’s equation of second order; reinforced cylindrical shells; analytical stability criteria; solution for stationary waves; stringers; frames; axial compressive load; external pressure; potential; kinetic energy; hinged edge supporting conditions; two systems of differential equations; eigenvalue system; critical time; critical load; fast growing displacements; exponential growing load PDFBibTeX XMLCite \textit{Yu. M. Pochtman} and \textit{S. O. Titov}, Dokl. Akad. Nauk Ukr. SSR, Ser. A 1987, No. 6, 32--36 (1987; Zbl 0664.73024)