Development and application of incremental harmonic balance for nonlinear vibration in rotating machinery

Abstract

In this thesis, a harmonic balance study of nonlinear dynamic systems and a squeeze film damper embedded Jeffcott rotor is considered. For comparative analysis of results, the Duffing equation is solved via harmonic balance and the Runge-Kutta methods. Generalized harmonic balance in tandem with its iterative counterparts which include the incremental and alternating frequency and time approaches of the harmonic balance are applied to two multi degree of freedom oscillator systems incorporating multiple nonlinearities. Applicable to rotor bearing systems, this thesis develops an incremental solution methodology of harmonic balance to handle the complex nonlinear behaviour of fluid film forces localized in squeeze film dampers. These forces are evaluated by integration of the Reynold’s equation for a short bearing with pi-film approximation handled accordingly via alternating frequency and time method of the harmonic balance. The unbalance frequency response plots for the Jeffcott rotor in tandem with nonlinear fluid film forces are evaluated utilizing the proposed methodology. The dynamic response of the Jeffcott rotor is analysed for both symmetric and unsymmetric variation of the parameters utilized to model the squeeze film dampers. The analysis of the acquired results in sight of the literature previously published effectively depicts the validity of the proposed methodology thereby providing way forward for its implementation on complex nonlinear rotor dynamic systems.