PRECESSION VIBRATION OF CONIC SHELLS IN COMPLEX ROTATION

Vibrations of thin rotating shells were studied in [1-6]. The vibration of thin shells performing a complex rotation is accompanied by additional dynamic effects characteristic of the deformable systems, the elements of which are involved simultaneously in several motions. The gyroscopic interaction of these motions leads to the loss of common phase of vibrations in the system. As a result, precession vibrations, in which the mode of motion has the form of a traveling wave, are excited in the system. The investigation of the dynamics of such systems by the method of spectral analysis faces considerable difficulties due to the fact that as these systems rotate, the spectrum of natural modes and frequencies splits and evolves with the change of the angular velocity. For this reason, it is more convenient to investigate such systems by direct mathematical modeling of these processes using the numerical analysis techniques. The present paper deals with the problem of vibrations of a rotating elastic conic shell, the axis of rotation of which performs a plane turn. A similar problem in the quasistatic case was analyzed in [6]. In the present paper, this problem is solved taking into account the gyroscopic interaction between the rotational rigid motion of the system and relative elastic vibrations of the elements of the shell. As a result of solving this problem, it is found that the complex rotation of the system leads to the excitation of the precession vibrations. Under certain conditions, these vibrations are resonant. The complex rotation generates the elastic moment acting upon the shell and transmitted to the supporting contour of the shell. It is established that this moment may substantially exceed the gyroscopic torque due to complex rotation of the equivalent rigid rotor. These effects can occur in rotors of aircraft engines during reorientation maneuvers.