๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Response and bifurcation analysis of a MDOF rotor system with a strong nonlinearity

โœ Scribed by Young B. Kim; Sherif T. Noah

Publisher
Springer Netherlands
Year
1991
Tongue
English
Weight
882 KB
Volume
2
Category
Article
ISSN
0924-090X

No coin nor oath required. For personal study only.

โœฆ Synopsis

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.

๐Ÿ“œ SIMILAR VOLUMES

HOPF BIFURCATION ANALYSIS OF A ROTOR/SEA
HOPF BIFURCATION ANALYSIS OF A ROTOR/SEAL SYSTEM
โœ Q. DING; J.E. COOPER; A.Y.T. LEUNG ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 268 KB

The Hopf bifurcation behaviour of a symmetric rotor/seal system was investigated using Muszynska's non-linear seal #uid dynamic force model. For a perfectly balanced system, the instability from certain critical equilibrium positions is proved to be the result of Hopf bifurcation and only the superc

Bifurcations of a generalized van der Po
Bifurcations of a generalized van der Pol oscillator with strong nonlinearity
โœ Jiashi Tang; Jinqi Qin; Han Xiao ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 228 KB

A generalized van der Pol oscillator with parametric excitation is studied for its bifurcation. On the basis of the MLP method, we enable a strongly nonlinear system to be transformed into a small parameter system. The bifurcation response equation of a 1/2 subharmonic resonance system is determined

Subtle bifurcation in the vibration of a
Subtle bifurcation in the vibration of a system with an interface nonlinearity
โœ J.A. Brandon; E. Benoit; L. Jezequel ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 427 KB

The authors have investigated bifurcation behaviour in vibrating structures where the discrete branches of the trajectories in the phase plane are so close that it could easily occur that their discrimination would not be achieved. The analysis of such subtle bifurcations required prior expectations