Resonant vibrations and acoustic radiation of rotating spherical structures.

Abstract

The generating equations of the problem are considered in terms of a system of three dimensional equations of linear elasticity considered in the spherical coordinates. It is known that in this case the exact solution of the problem could be obtained in the spherical Bessel, associate Legendre and trigonometric functions. The spherical coordinates are introduced so that a constant vector of the inertial angular rate passes through the pole of the coordinates. It is supposed that the angular rate of the inertial rotation is much smaller than a minimal circular frequency of elastic vibrations of the structure and hence, it is possible to neglect the centrifugal forces. It is shown that the elastic waves of the structure are partially involved into rotation (precession) with respect to the inertial space with scale factors depending on nature of elastic modes and their numbers. Corresponding scales factors or Bryan’s factors of the vibrating mode’s precession are calculated depending on nature of the modes, spheroidal or torsional and their numbers. Bryan’s factors of radiated spherical body are calculated and compared with corresponding factors of a free body.