scholarly journals Use and Limitations of the Harmonic Balance Method for Rub-Impact Phenomena in Rotor-Stator Dynamics

2012 ◽  
Author(s):  
Loïc Peletan ◽  
Sebastien Baguet ◽  
Georges Jacquet-Richardet ◽  
Mohamed Torkhani
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Current Form ◽  
Transient Simulations ◽  
Future Extension ◽  
Periodic Behaviour ◽  
State Behaviour ◽  
Impact Phenomena ◽  
Time Marching

In the present paper, a Harmonic Balance Method (HBM) coupled with a pseudo-arc length continuation algorithm is presented for the prediction of the steady state behaviour of a rotor-stator contact problem. The ability of the HBM to reproduce the four most common phenomena encountered during rotor to stator contact situations (i.e. ‘no-rub’, ‘full annular rub’, ‘partial rub’ and ‘backward whirl/whip’) is investigated. A modified Jeffcott rotor model is used and results of the proposed algorithm are compared with traditional time marching solutions and analytical predictions. The advantages and limitations of the HBM for this kind of problem are analyzed. It is shown that the HBM is orders of magnitude faster than transient simulations, and provides very accurate results. However, in its current form it is unable to predict quasi-periodic behaviour. Detailed analysis of the transient solutions yields valuable information for the future extension of the HBM to efficient quasi-periodic simulations.

Nonlinear vibration analysis of forced response for rubbing problems using the automatic differential frame

2021 ◽  
pp. 095440892110396
Author(s):  
Tianyuan Liu ◽  
Lei Sun ◽  
Yonghui Xie
Keyword(s):  
Nonlinear Vibration ◽  
Harmonic Balance ◽  
Vibration Analysis ◽  
Automatic Differentiation ◽  
Jacobian Matrix ◽  
Harmonic Balance Method ◽  
Degree Of Freedom ◽  
Balance Method ◽  
Time Marching ◽  
Marching Method

The multi-harmonic balance method is widely applied to obtain the forced responses of nonlinear systems undergoing rubbing problems. Despite large-scale time savings compared with the time marching method, it suffers from the complicated derivations of the Jacobian matrix. To solve this problem, this paper focuses on applying the automatic differentiation frame to the multi-harmonic balance method to implement the nonlinear vibration analysis of systems subjected to the rub phenomena. By establishing computational graph and utilizing the automatic differentiation process, tedious works such as the derivations of the complicated analytical expressions of the Jacobian matrix are avoided, which guarantees the efficiency and applicability of the presented method. A single-degree-of-freedom system with nonlinear force in the form of cubic is used to verify the accuracy of the method, and numerical analysis results reveal that the method is accurate enough compared with the time marching method. Furthermore, for the purpose of application, the responses of two common friction models, which are of great concern in some practical engineering fields, including a two-degree-of-freedom system containing a friction damper and a rotor disk system with circumferential rubbing, are obtained utilizing the presented approach. The influences of several model parameters on their responses are investigated as well. Numerical investigations demonstrate that the automatic differential solution framework developed in this research for solving nonlinear vibration equations has high accuracy and eliminates the need for a complicated partial derivative analytical formula derivation.

Analysis of Oscillator Injection Locking by Harmonic Balance Method

2008 ◽  
Author(s):  
M.M. Gourary ◽  
S.G. Rusakov ◽  
S.L. Ulyanov ◽  
M.M. Zharov ◽  
B.J. Mulvaney ◽  
...  
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Injection Locking ◽  
Balance Method

Closed-Form Expression for the Exact Period of a Nonlinear Oscillator Typified by a Mass Attached to a Stretched Wire

2011 ◽  
Vol 3 (6) ◽  
pp. 689-701
Author(s):  
Malik Mamode
Keyword(s):  
Harmonic Balance ◽  
Nonlinear Oscillator ◽  
Harmonic Balance Method ◽  
Elliptic Functions ◽  
Oscillatory System ◽  
Balance Method ◽  
Closed Form Expression ◽  
Form Expression ◽  
Polynomial Potential ◽  
Exact Analytical Expression

AbstractThe exact analytical expression of the period of a conservative nonlinear oscillator with a non-polynomial potential, is obtained. Such an oscillatory system corresponds to the transverse vibration of a particle attached to the center of a stretched elastic wire. The result is given in terms of elliptic functions and validates the approximate formulae derived from various approximation procedures as the harmonic balance method and the rational harmonic balance method usually implemented for solving such a nonlinear problem.

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