Investigation of gyroscopic effects in vibrating fluid-filled cylinders subjected to axial rotation

Abstract

Vibrating patterns of distributed oscillating structures, subjected to rotation, also turn in the direction of inertial revolution but with different angular rates, which depend on the geometry of the structures, the number of modes, etc. This effect, found by G. Bryan in 1890, has numerous applications in navigational instruments such as cylindrical rotational sensors. This effect is also important in astrophysics and seismology. In the present paper the authors consider the main principles of the theory of gyroscopic effects in distributed structures. The model of a thick vibrating cylinder filled with a fluid and subjected to inertial rotation is analyzed. The dynamics of the cylinder is considered in terms of linear elasticity and the fluid is supposed to be ideal and inviscid, but fully involved in the rotation. It is presumed that the angular rate of inertial rotation is constant and has axial orientation. It is also assumed that the angular rate is much smaller than the lowest eigenvalue of the system and hence the centrifugal effects, proportional to square of the angular rate, are neglected. The influence of the following on Bryan's factor are investigated: the non-axisymmetric modes of the system, the eigenvalues for a fixed mode, the mass density of the fluid, the modulus of elasticity, the bulk modulus, Poisson ratio, the thickness and inner radius of the cylinder. It is shown that the difference between rotational angular rates of the system and its vibrating patterns is substantial for lower eigenvalues and circumferential wave numbers