Aim of the research. Free axisymmetric fluctuation of a cylindrical orthotropic cover, the infinite length contacting to the infinite elastic medium and filled with liquid is investigated. Methods. At design of the thin-walled shell designs which are widely applied in aviation, the missile and space equipment and various fields of the industry, an important task is dynamic calculation of the intense deformed condition of these designs. At a research of dynamics of covers it is necessary to determine own frequencies and forms of small fluctuations, and frequencies from the lower part of a range are of the greatest interest. It is supposed that the rigidity of material of a cover is a little more than rigidity of material of the environment. The solution of the equations of movements of the environment is considered in two options. Results. The frequency equation is received. The analysis of frequency and a form of fluctuations of a cover is carried out. The schedule of dependence of frequency of own axisymmetric fluctuations of a system on wave formation in the longitudinal direction is constructed. By means of an asymptotic method the frequency equations of the ridge cylindrical covers filled with liquid are constructed, the approximate frequencies of the equation and simple settlement formulas allowing to find values of the minimum own frequencies of fluctuations of the considered system are received, the forced fluctuations of the supported cover filled with liquid are investigated and defined is amplitude frequency characteristics of the considered oscillatory processes.

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В работе с применением приближенно аналитических методов исследуется задача свободного колебания неоднородно ортотропной прямоугольной пластинки, лежащей на вязко упругом основании, причем краевые условия являются однородными. Предполагается, что модули упругости и плотность пластинки являются непрерывными функциями трех пространственных координат и коэффициенты Пуассона принимаются постоянными. При конкретных значениях характерных функций, характеризующих свойства пластинки и основания, проведен численный расчет, и результаты представлены в виде таблиц и графиками зависимостей.