Multiple Periodic Symmetric Limit Cycles of Two Coupled Sommerfeld Rotors

The chapter introduces orthogonal rotor equations of the Cauchy form into rotor dynamics where the integration time is substituted by a rotation angle. This has the advantage that the periodic rotations and vibrations of Sommerfeld rotors are calculable using Fourier expansions, which leads to a new moment speed characteristic of the rotor where the classical result is massively corrected by the unbalanced mass moment of inertia. The chapter extends these investigations to two unbalanced visco-elastically supported rotors. New forms of limit cycles are calculated when the applied driving moments lead to mean values of the rotation speeds with the ratios 1:1 and 1:3, resulting in single and triple periodic limit cycles, respectively. For more general driving moments, the periodicity conditions are violated and the stationary rotor vibrations become pseudo-stochastic.