Flexible coupler for reducing torsional oscillations

A method of performing mode shape modification of torsional oscillation in a borehole string in a subterranean operation, the method comprising:

• deploying a borehole string in a borehole, the borehole string including a downhole component, a coupling device and a damping device, the coupling device disposed at a coupling device location in the borehole string, the damping device located at a damping device location in the borehole string, the coupling device including an elongated coupler body having a longitudinal axis and a circumference, the coupler body having a torsional stiffness sufficient to transmit rotational motion to the downhole component, the coupling device including a plurality of recesses formed in a wall of the coupler body at different positions along the longitudinal axis of the coupler body, the plurality of recesses extending along a circumference of the coupler body in a direction forming an angle of greater than or equal to 80 degrees with the longitudinal axis, the plurality of recesses imparting a bending stiffness that is less than or equal to a reference bending stiffness;
• performing the subterranean operation, the performing including rotating the borehole string, the rotating including exciting a torsional oscillation;
• selecting the torsional stiffness or the coupling device location to modify a mode shape of the torsional oscillation to maximize a torsional oscillation amplitude at the damping device location in the borehole string;
• modifying the mode shape by the coupling device having the selected stiffness or the selected coupling device location in the borehole string;
• and
• damping the torsional oscillation with the damping device at the damping device location.