The paper considers thin-walled cylindrical shells in turbulent liquid or gas flows under the axisymmetric external or internal spatio-temporal random pressure field. For such shells, the paper determines random fields of the normal displacements, stresses and curvature alterations. The main objective is to identify probabilities of the events that the shell parameters (displacements, stresses and curvature) would never exceed their standard values over the entire length, and the given time interval of the system operation. The paper uses the basic concepts and statistical dynamics methods of the mechanical systems, including impedance, transfer function, Green's function, correlation function, energy spectrum of the random fields and processes, etc. Relatively simple solutions are obtained by the Green's function method for the inertialess shells loaded with a random stationary pressure field distributed along its length and presented in a quasi-harmonic form with the random amplitudes and frequencies. Efficient solutions to the stated dynamic problems are also obtained by expanding them in terms of the proper axisymmetric modes of the shell oscillation, as well as for the case, where the pressure field could be represented by the spatio-temporal two-dimensional white noise. The paper shows a fundamental possibility of obtaining an exact solution to the stated problems for the general case of loading, when pressure on the shell could be represented as a generalized two-dimensional Fourier transform in coordinates and time.

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