This research introduces a non-linear dynamical model containing Jeffcott rotor with flexible properties and an unbalanced rotating disc. The rotor is supported on two short journal bearings. The disk is surrounded with an elastic snubber ring with significant radial clearance between the disc and the snubber ring. This work considers the dynamic interaction between the rotor disc and the much stiffer snubber ring (stator) using a four degree-of-freedom model to account for inherent nonlinearities. The bearing forces are evaluated by solving Reynolds equation considering short bearing approximation. The system equations of motion are solved numerically by direct integration using the state-space technique. The nonlinear dynamic response results due to the changes in the frequency ratio arising from rotor disk–snubber ring (stator) interactions are evaluated. The present work results show that the system’s response is highly dependent on the frequency ratio, which is defined as η = Ω/ω (forced frequency/natural frequency. Rich dynamics are recorded ranges from periodic, quasi periodic and chaotic.