Resonant Oscillations and Stability of Asymmetric Rotors

Abstract

Abstract Non-stationary oscillations of an asymmetric rotor while passing through primary resonance and the associated stability behaviour are analyzed. Solutions are developed based on a Jeffcott rotor model and the equations of motion are rewritten in a form suitable for applying the method of multiple scales. The many-variable version using “slow” and “fast” lime scales is applied to obtain the uniform expansions of amplitudes of motion. Similar general expressions for amplitude and frequency modulation functions are explicitly obtained and are specialized to yield steady-state solutions. Frequency-amplitude relationships resulting from combined parametric and mass unbalance excitations, for the nonlinear vibration are derived. Stability regions in the parameter space are obtained for a stable solution in terms of the perturbed steady-state solutions of the governing equations of motion. Also, trivial solutions are examined for stability. The sensitivity of vibration amplitudes to various rotor-dynamic system parameters is illustrated through a numerical study.