Effect of non-linearities in elastomeric material dampers on torsional oscillation control

The effect of quadratic and cubic non-linearities in elastomeric material dampers used to quiet torsional oscillations of internal-combustion engines shafts is investigated. In the present work, a non-linear elastomeric damper or absorber is used to control the torsional vibrations of the crankshaft in internal combustion engines, when subject to external excitation torque. The method of multiple scales is used to derive four first-order differential equations governing the modulation of the amplitudes and phases of the two modes of the crankshaft and the absorber for the fundamental resonance. These equations are used to determine the steady state amplitudes and system stability. A relationship that relates the elastomer properties and other system parameters is found. The effects of damping, detuning, non-linear terms, and magnitude of excitation are analyzed. A stability analysis is performed on the steady state solutions.