Stretched-deformed state of closed conical shells with complex rotation

Abstract

In construction machinery, engineering, aircraft engineering, space technology and other branches of the national economy there are problems of studying the stress-strain state of plates, membranes and rotating membranes. The main load on the elements of such systems is the significant centrifugal forces of inertia, which significantly affect the strength characteristics of structures. In many cases, the axis of rotation of mechanical systems can make a turn, which leads to the emergence of not only portable and relative, but also coriolis forces of inertia, which change periodically over time. The gyroscopic interaction between the rotational motion of the system and the relative elastic oscillations of the elements is a source of excitation of precessional oscillations that can be resonant or unstable. As a result of changing the orientation axis of the system, the gyroscopic moment causes the appearance of alternating stresses, which significantly affect the strength and reliability of the structural elements. In the works [1, 3-10] the stress-strain state and oscillations of membranes, plates and shells carrying complex motion in the central force field are investigated. In this paper, the relations that determine the stress-deformed state of the system of two closed conical shells connected by a central rigid insert, which rotates with a constant angular velocity around the axis of symmetry of the system, whose center of mass moves in the central force field are given.