Multi-scale stick-slip dry friction at contact interface plays a significant role in the nonlinear system dynamics. Classic coulomb friction model cannot reflect the complex dry friction phenomenon accurately. In this paper, a dry friction system with multi-scale stick-slip characteristics was studied. A displacement-based Iwan hysteretic constitutive model was used to model interface friction. After the equation of motion was established, numerical solution of the system under harmonic excitation was obtained with the central difference method. The steady state dynamic response was obtained under 1:1 and 1:2 resonance condition. It is showed that, in the case of 1:1 resonance, the dynamic behavior is extremely sensitive with transversal heteroclinic point, and double-periodic motion and chaos happen at characteristic parameters. In the case of 1:2 resonance, there are infinitely homoclinic points, and chaotic motion may emerge under small perturbations.