Vibrations of an elastic disk during complex rotation

Vibrations of Curved and Twisted Blades During Complex Rotation

“…Therefore, we will consider only the inertia of turn of an element about the w-axis, which affects the torsional vibrations of the blade. Then [2], we obtain…”

“…Let the vibrations of the blade under the inertial forces be steady. The condition ω ω >> 0 allows us to study the relative (elastic) vibrations of the blade in two stages [1,2]. At the first stage, the rigid disk simply rotates with angular velocity r ω, centrifugal forces act on the blade, and there are no vibrations.…”

“…Since some elements of the matrix A contain the coefficients ω 2 quickly increasing with ω, system (11) is stiff and has rapidly increasing functions among partial solutions. Therefore, the orthogonalization method [1,2] is additionally used to numerically integrate the system.…”

Interconnection of critical states of parabolic shells in simple and compound rotations with values of their natural precession vibration frequencies

“…One of the most important factors is associated with the proximity of their working velocities to the so-called critical velocities. As this takes place the critical states of a rotor may emerge both at the regimes of their simple spinning (Ziegler, 1968) and in their compound rotations (Gulyayev and Domaretsky, 1996;Gulyayev et al, 2001). In as much as both of these critical state types are determined by action of non-conservative forces, depending on the character of the elastic rotor motion and its elastic displacements, the modes of the rotor behaviours are different in these cases.…”

“…In this event, in response to the superposition and gyroscopic interaction of different types of rotations, elastic precession vibrations are generated, which can acquire resonant character under specific value of angular velocity of its own spinning. In the reference frame related to the carrier, the mentioned precession vibrations manifest themselves in the form of certain stationary deformed states, which are symmetric with respect to the plane containing the vectors of angular velocities of the rotor spinning and the carrier slewing (Barlow, 1976;Gulyayev and Domaretsky, 1996;Sacata et al, 1989).…”