“…The dynamic and nonlinear behavior of a flexible rotor supported by a relatively short herringbone-grooved gas journal bearing system, comprising periodic and quasi-periodic responses and varying with bearing number and rotor mass, was proposed [24][25][26][27][28]. In Wang and Yau's study [29], the behavior of the high speed spindle air bearing system, combining the differential transformation method and the finite difference method, was studied in order to analyze the complex dynamic behavior of periodic, sub-harmonic and quasi-periodic responses. Limitedly, the conventional constitutive models generally seen as a short rotor were proposed only to describe two-degree-of-freedom motions of a spindle, i.e.…”