External vibration can drive high-speed rotors on gas bearings into high-excursion orbits, risking damage or functional failure and making forced-response predictions essential. This work examines the periodic base-excited response of a rigid rotor on herringbone-grooved journal bearings. The role of stiffness and damping of compliant bearing supports in containing forced-response orbits is also assessed.

We present a non-intrusive algorithm for constructing efficient frequency-domain surrogates of (nonlinear) parametric dynamical systems. The approach combines rational approximation in frequency with smooth interpolation over the remaining parameters. The method is instantiated for a herringbone-grooved journal bearing by constructing a surrogate of the reaction forces and linearized force coefficients from an eccentric perturbation model. In numerical tests, the surrogate achieves a two-order-of-magnitude speedup, enabling fast bearing evaluations in larger rotor--bearing simulations.

We extend a nonlinear transient rotor--bearing model based on narrow-groove theory to arbitrary periodic excitation and propose an efficient alternative, the mixed-linearization approach. This approach couples time-domain rigid-body motion with a frequency-domain bearing surrogate queried at the instantaneous eccentricity to update linearized force coefficients. The rotor--bearing equations of motion are decomposed into incremental excitation-frequency contributions, enabling use of the surrogate.

A dedicated experimental setup enables validation against shaker-table measurements for four test unit configurations: one rigidly supported case and three undamped support-stiffness cases. Each configuration is tested at more than 300 operating points spanning compressibility numbers up to 34, two base-acceleration amplitudes and pure-unbalance conditions.

Base excitation strongly influences rotor and relative rotor--bushing excursions. Compared at the same base-excitation amplitude, compliant supports can reduce the relative rotor--bushing orbit size when excitation is sufficiently above, and for higher compressibility numbers also below, the rotor--bearing eigenfrequencies, but can significantly amplify it near the modal-interaction region. The mixed-linearization model closely matches the nonlinear transient predictions, with average orbit-size and shape errors at the 1% level and mean speedups of 7.8x and 12.3x for the rigid and flexible support configurations, respectively. For the rigid support configuration, a modest frequency and amplification bias between the models and test setup explains model--measurement errors within 10% of the nominal clearance for orbit size at most test points and isolated peaks within 30% near modal crossings. For the flexible support configurations, model--model agreement remains strong, and although model--measurement errors increase near the system eigenfrequencies, agreement away from resonance remains strong and the time-domain trends are encouraging. The stiffness study shows that orbit size is reduced most consistently in the super-modal region, whereas support compliance carries an orbit-size penalty near the modal-interaction region. Damping has little effect on forced-response orbit size for a given support-stiffness level relative to the rigid support configuration.