“…Most of the studies mentioned above focus on a linear analysis, which is based on the small perturbation approach. A linear gas bearing model, indifferent from its complexity, can only predict the linear concept threshold speed of instability and cannot forecast the evolution of the orbits when sub-synchronous vibration start to appear [39][40][41]. Considering gas foil bearing supported rigid rotor systems, both predictions by Bonello et al [38] and Larsen et al [42] suggest the presence of a speed range, where the orbits continuously evolve towards limit cycles after the stable state (orbit converge to equilibrium position).…”