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Оscillations of closed conical shells with complex rotation

The paper consider a system of two closed conical shells connected by a central rigid insert rotating in opposite directions in a central force field with a constant angular velocity around the axis of symmetry of the system. The shell element is subjected to a load consisting of gravitational and inertial forces, but at large values of the angular velocity of the system, the gravitational loads can be neglected. The gyroscopic interaction between the rotational portable motion of the system and the relative elastic oscillations of the elements is a source of excitation of precession oscillations, which may be resonant or unstable. Occurring when changing the axis of orientation of the system gyroscopic moment causes the appearance of alternating stresses, which significantly affect the strength and reliability of the shells. Such problems arise in construction engineering, mechanical engineering, aircraft construction, space engineering and other sectors of the economy. The main load acting on the elements of such systems are significant centrifugal forces of inertia, which significantly affect the strength characteristics of structures. Taking into account the periodicity of the right-hand side and the coefficients of the system of resolving equations, with the help of the projection method it is possible to reduce the resolving equations to the system of ordinary differential equations, which approximately replaces the original one. The solution of the obtained system of equations makes it possible to determine the forms of oscillations and forces in a composite conical shell at various parameters of the shell and the ratios of the velocities of the shell's own rotation and the rotation of its center of mass.