On the synchronization of circularly symmetrical mechanical systems

The article deals with synchronization of an autonomous mechanical system with circular symmetry loaded by aerodynamical forces and subjected to weak linear constraints. The examples of a rigid rotor with elastic objects idealized as inextensible prismatic rods, and of a homogeneous annular array of aerodynamically loaded rods are used. In-phase and out-of-phase synchronous oscillations and different modes of coupling are considered. The effect of the degrees of freedom of the mechanical system on its synchronized response is examined. Systems of difference equations with periodic coefficients are used in the numerical treatment. The results are applicable to the behavior of fans, oscillations of a thick cascade of turbomachinery rotor blading (cascade flutter), helicopter rotors, rotors in hammer mills, and similar problems involving complex external disturbances and circular symmetry.