Optimal Tuning of Amplitude Proportional Coulomb Friction Damper for Maximum Cable Damping

This paper investigates numerically the optimal tuning of Coulomb friction dampers on cables, where the optimality criterion is maximum additional damping in the first vibration mode. The expression for the optimal friction force level of Coulomb friction dampers follows from the linear viscous damper via harmonic averaging. It turns out that the friction force level has to be adjusted in proportion to cable amplitude at damper position which is realized by amplitude feedback in real time. The performance of this adaptive damper is assessed by simulated free decay curves from which the damping is estimated. It is found that the damping efficiency agrees well with the expected value at the theoretical optimum. However, maximum damping is larger and achieved at a force to amplitude ratio of 1.4 times the analytical value. Investigations show that the increased damping results from energy spillover to higher modes evoked by the amplitude proportional Coulomb friction damper which clamps the cable at its upper and lower positions. The resulting nonsinusoidal cable motion clearly violates the assumption of pure harmonic motion and explains why such dampers have to be tuned differently from optimal linear viscous dampers.