Slender rotating structures are used in many mechanical systems. These structures can suffer from undesired vibrations that can affect the components and safety of a system. Furthermore, since some these structures can operate in a harsh environment, installation and operation of sensors that are needed for closed-loop and collocated control schemes may not be feasible. Hence, the need for an open-loop non-collocated scheme for control of the dynamics of these structures. In this work, the effects of drive speed modulation on the dynamics of slender rotating structures are studied.

Slender rotating structures are a type of mechanical rotating structures, whose length to diameter ratio is large. For these structures, the torsion mode natural frequencies can be low. In particular, for isotropic structures, the first few torsion mode frequencies can be of the same order as the first few bending mode frequencies. These situations can be conducive for energy transfer amongst bending and torsion modes. Scenarios with torsional vibrations experienced by rotating structures with continuous rotor-stator contact occur in many rotating mechanical systems. Drill strings used in the oil and gas industry are an example of rotating structures whose torsional vibrations can be deleterious to the components of the drilling system. As a novel approach to mitigate undesired vibrations, the effects of adding a sinusoidal excitation to the rotation speed of a drill string are studied. A portion of the drill string located within a borewell is considered and this rotating structure has been modeled as an extended Jeffcott rotor and a sinusoidal excitation has been added to the drive speed of the rotor. After constructing a three-degree-of-freedom model to capture lateral and torsional motions, the equations of motions are reduced to a single differential equation governing torsional vibrations during continuous stator contact. An approximate solution has been obtained by making use of the Method of Direct Partition of Motions with the governing torsional equation of motion. The results showed that for a rotor undergoing forward or backward whirling, the addition of sinusoidal excitation to the drive speed can cause an increase in the equivalent torsional stiffness, smooth the discontinuous friction force at contact, and reduce the regions of negative slope in the friction coefficient variation with respect to speed. Experiments with a scaled drill string apparatus have also been conducted and the experimental results show good agreement with the numerical results obtained from the developed models. These findings suggest that the extended Jeffcott rotordynamics model can be useful for studies of rotor dynamics in situations with continuous rotor-stator contact. Furthermore, the results obtained suggest that the drive speed modulation scheme can have value for attenuating drill-string vibrations.