The dynamics of a long hydrodynamic gas bearing is investigated for periodic variations of the rotational speed. The analysis is divided into two regions of interest, namely: (1) for small eccentricities the system is represented by a pair of linear differential equations with time-dependent coefficients. Investigation for a sinusoidally varying rotational speed proves that an unloaded bearing can be stable, though it is known not to be stable at all constant speeds. An approximate analytical solution is given for the orbit of a stable journal whirling about its equilibrium position. (2) For higher eccentricities the nonlinear equations describing the motion of the journal center are derived. When the speed perturbation is small, the equations may be linearized, and analytical expressions are obtained for the calculation of journal response. At given speed and eccentricity resonance is reached at the critical mass of instability threshold, but even for smaller mass the amplitudes are liable to endanger safe operation of the system.

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