Frequency domain solution of 2-DOF torsional dry friction system

The forced vibration response of a two degree of freedom (DOF) torsional system with Coulomb friction was studied, with a full consideration of the pure-slip and stick-slip contact motions. First, the 2-DOF lumped parameter model of such nonlinear system was presented and derived into a non-dimensional form. Second, the harmonic balance approach was used to establish a general frame of solving the response under different contact motion. Accordingly, the critical condition as well as the harmonic expands of friction force of the pure-slip and stick-slip contact motions were presented. Finally, the procedure of dealing with frequency domain solution was proposed. Based on this method, a group of results were obtained under different normal pressures, and were validated by the numerical integration method with a very good agreement. The proposed semi-analytical method provides more clear insights of the torsional dry friction system and therefore has advantage in computational cost.