Abstract: In this paper, the response characteristics of a two-degree-of-freedom non-autonomous piecewise smooth nonlinear system, which consists of linear and nonlinear subsystem, are investigated. The piecewise smooth system can be used to determine the most important responses of a rotor/stator rubbing systems, and possesses some following peculiar features: (1) the switching surface is defined by the two displacement coordinates of the system and is a magnitude surface in the state space; (2) the touch of the periodic solutions of subsystems with the switching surface occurs always simultaneously at all points of the solution to make it different from gazing bifurcations or phenomena in the usual nonsmooth systems; (3) there is no periodic solution formed through connection of trajectories from two subsystems. So some techniques developed for the bifurcation analysis of equilibriums or periodic solutions are not directly applicable to the system. Thus, according to the dynamical characteristics of subsystems, this paper tries to classify the parameter regions into the switching sensitive and insensitive regions. In this way, the responses of whole system in the switching insensitive regions can be obtained from the analysis of the responses of subsystems. For some responses of the whole systems in the switching sensitive regions, explanation is given for their occurrence based on the dynamical characteristics of subsystems.