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.