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• A novel method is proposed to suppress the torsional vibration of high-damped rotors. • A high-damped rotor is replaced approximately by an equivalent undamped rotor using the WDE. • Two closed-form expressions for a suitable system of springs and viscous dampers are proposed to design an optimal DVA. • The torsional vibration of the high-damped rotor is significantly reduced by attached an optimal DVA. In the rotating systems, the torsional vibration of damped rotors usually appears and induces the imbalance of systems. The dynamic vibration absorber (DVA) is used for reducing the torsional vibration of damped rotors. Recent researches have shown that traditional methods are suitable for reducing the torsional vibration of weak damped rotors. However, the traditional methods will cause significant errors for high-damped rotors. Therefore, a novel method is proposed to suppress the torsional vibration of high-damped rotors using a dynamic vibration absorber based on Weighted Dual Estimation (WDE) of equivalent linearization techniques. The high-damped rotor is replaced approximately by an equivalent undamped rotor based on the WDE of equivalent linearization techniques. Two closed-form expressions for a suitable system of springs and viscous dampers of the optimal DVA are determined to suppress the torsional vibration of high-damped rotors. The numerical analysis results show that the torsional vibration of the high-damped rotor has surprisingly reduced at the resonant frequency region by using the optimal DVA. The proposed expressions for a suitable system of springs and viscous dampers of the optimal DVA are reliable for suppressing the torsional vibration of a highly damped rotor. [ABSTRACT FROM AUTHOR]