Энергетический анализ осесимметричных колебаний цилиндрической оболочки, нагруженной периодическими сосредоточенными массами

Cylindrical periodic shells are widely used in modeling various building structures, pipelines, offshore drilling rig supports, wind farms and other structures. Increasing their wear resistance and preventing the occurrence of risk-bearing operating modes is an urgent problem. In this paper, we investigate one of the potentially dangerous modes caused by axisymmetric vibrations of a circular cylindrical shell of Kirchhoff–Love type with additional inertia in the form of periodic "mass belts" of zero width. The shell is assumed to be infinite and its free harmonic vibrations are analyzed using a Floquet-type exact analytical solution. The dependence of pass bands and stop bands on the mass of the concentrated loads is investigated. At a certain combination of parameters, the points of intersection and quasi-intersection of the boundaries of these bands can coincide. The neighborhood of such a special point is considered in view of the fact that the boundaries of the pass and stop bands of an infinite periodic shell can be obtained and investigated by considering free vibrations of its separated symmetric segment of periodicity. This makes it possible to essentially reduce the volume of calculations, to simplify the determination of the coordinates of this special point, as well as to facilitate the analysis of the vibration field, the integral energy flux and its components. In such a way, the consideration of energy flows and its components not only significantly complements the picture of vibration fields, but also allows us to assess more adequately the nature of vibrations. It is shown that in the vicinity of a singular point there is a sharp change in the character of vibrations, which can lead to dangerous modes of operation of real structures.