Abstract: Systems and methods for damping torsional oscillations of downhole systems are described. The systems include a downhole drilling system disposed at an end of the downhole system in operative connection with a drill bit. A damping system is installed on the downhole drilling system, the damping system having at least one damper element configured to dampen at least one HFTO mode. At least one mode-shape tuning element is arranged on the drilling system. The at least one mode-shape tuning element is configured and positioned on the drilling system to modify at least one of a shape of the HFTO mode, a frequency of the HFTO mode, an excitability of the HFTO mode, and a damping efficiency of the at least one damper element.

Abstract: A method for reducing vibrations in a drill tubular coupled to a drill bit configured to drill a borehole in a formation includes: constructing a model of a system having the drill tubular, the model having a mass distribution, a stiffness, and/or a damping of the drill tubular; and calculating a plurality of modes using the model. The method also includes increasing an effective damping of the drill tubular for the plurality of modes by modifying at least one of the mass distribution, the stiffness, and the damping of the drill tubular using a predefined damping criterion, wherein the predefined damping criterion includes a ratio, the ratio having a deflection at the drill bit of at least one mode in the plurality and an eigenfrequency of the at least one mode in the plurality, wherein the deflection at the drill bit is raised to a power other than one.

Abstract: Systems and methods for damping torsional oscillations of downhole systems are described. The systems include a downhole drilling system disposed at an end of the downhole system in operative connection with a drill bit. A damping system is installed on the downhole drilling system, the damping system having at least one damper element configured to dampen at least one HFTO mode. At least one mode-shape tuning element is arranged on the drilling system. The at least one mode-shape tuning element is configured and positioned on the drilling system to modify at least one of a shape of the HFTO mode, a frequency of the HFTO mode, an excitability of the HFTO mode, and a damping efficiency of the at least one damper element.

Abstract: A method for reducing vibrations in a drill tubular coupled to a drill bit configured to drill a borehole in a formation includes: constructing a model of a system having the drill tubular, the model having a mass distribution, a stiffness, and/or a damping of the drill tubular; and calculating a plurality of modes using the model. The method also includes increasing an effective damping of the drill tubular for the plurality of modes by modifying at least one of the mass distribution, the stiffness, and the damping of the drill tubular using a predefined damping criterion, wherein the predefined damping criterion includes a ratio, the ratio having a deflection at the drill bit of at least one mode in the plurality and an eigenfrequency of the at least one mode in the plurality, wherein the deflection at the drill bit is raised to a power other than one.

Abstract: A method for reducing drill tubular vibrations includes: constructing a mathematical model the drill tubular having mass distribution, material stiffness and material damping; constructing an equation of motion of the drill tubular in one of a time domain and frequency domain; transforming the equation of motion into a modal domain equation of motion to provide a mode shape of the drill tubular at an eigenfrequency, the mode shape providing an amplitude at a position along the drill tubular; comparing the amplitude at the position along the drill tubular to a threshold amplitude value; modifying at least one of the mass distribution, material stiffness and material damping if the amplitude exceeds the threshold value; and iterating the above step until at least one of the amplitude of the latest mode shape at the position is less than or equal to the threshold amplitude value and a predetermined constraint limits the modifying.

Abstract: A method for reducing drill tubular vibrations includes: constructing a mathematical model the drill tubular having mass distribution, material stiffness and material damping; constructing an equation of motion of the drill tubular in one of a time domain and frequency domain; transforming the equation of motion into a modal domain equation of motion to provide a mode shape of the drill tubular at an eigenfrequency, the mode shape providing an amplitude at a position along the drill tubular; comparing the amplitude at the position along the drill tubular to a threshold amplitude value; modifying at least one of the mass distribution, material stiffness and material damping if the amplitude exceeds the threshold value; and iterating the above step until at least one of the amplitude of the latest mode shape at the position is less than or equal to the threshold amplitude value and a predetermined constraint limits the modifying.