Springer Online Journal Archives 1860-2000
Abstract A new HB (Harmonic Balance)/AFT (Alternating Frequency Time) method is further developed to obtain synchronous and subsynchronous whirling response of nonlinear MDOF rotor systems. Using the HBM, the nonlinear differential equations of a rotor system can be transformed to algebraic equations with unknown harmonic coefficients. A technique is applied to reduce the algebraic equations to only those of the nonlinear coordinates. Stability analysis of the periodic solutions is performed via perturbation of the solutions. To further reduce the computational time for the stability analysis, the reduced system parameters (mass, damping, and stiffness) are calculated in terms of the already known harmonic coefficients. For illustration, a simple MDOF rotor system with a piecewise-linear bearing clearance is used to demonstrate the accuracy of the calculated steady-state solutions and their bifurcation boundaries. Employing ideas from modern dynamics theory, the example MDOF nonlinear rotor system is shown to exhibit subsynchronous, quasi-periodic and chaotic whirling motions.
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