Nonlinear vibrations of dynamical systems with a general form of piecewise-linear viscous damping by incremental harmonic balance method

2002 ◽  
Vol 301 (1-2) ◽  
pp. 65-73 ◽  
Author(s):  
L. Xu ◽  
M.W. Lu ◽  
Q. Cao
Keyword(s):  
Dynamical Systems ◽  
Harmonic Balance ◽  
Nonlinear Vibrations ◽  
Piecewise Linear ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Viscous Damping ◽  
Incremental Harmonic Balance Method ◽  
Incremental Harmonic Balance

Nonlinear Vibrations of Piecewise-Linear Systems by Incremental Harmonic Balance Method

1992 ◽  
Vol 59 (1) ◽  
pp. 153-160 ◽  
Author(s):  
S. L. Lau ◽  
W.-S. Zhang
Keyword(s):  
Harmonic Balance ◽  
Nonlinear Vibrations ◽  
Piecewise Linear ◽  
Practical Interest ◽  
Harmonic Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Incremental Harmonic Balance ◽  
Stiffness Characteristics ◽  
Ihb Method ◽  
Piecewise Linear Stiffness

The incremental harmonic balance (IHB) method is extended to analyze the periodic vibrations of systems with a general form of piecewise-linear stiffness characteristics. An explicit formulation has been worked out. This development is of significance as many structural and mechanical systems of practical interest possess a piecewise-linear stiffness. Typical examples show that the IHB method is very effective for analyzing this kind of systems under steady-state vibrations.

scholarly journals Calculation of nonlinear vibrations of piecewise-linear systems using the shooting method

2012 ◽  
Vol 34 (3) ◽  
pp. 157-167
Author(s):  
Nguyen Van Khang ◽  
Hoang Manh Cuong ◽  
Nguyen Thai Minh Tuan
Keyword(s):  
Harmonic Balance ◽  
Shooting Method ◽  
Piecewise Linear ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Periodic Attractors ◽  
Incremental Harmonic Balance ◽  
Excited Oscillator ◽  
Ihb Method

In this paper, an explicit formulation of the shooting scheme for computation of multiple periodic attractors of a harmonically excited oscillator which is asymmetric with both stiffness and viscous damping piecewise linearities is derived. The numerical simulation by the shooting method is compared with that by the incremental harmonic balance method (IHB method), which shows that the shooting method is in many respects distinctively advantageous over the incremental harmonic balance method.

Bearing Looseness Fault Characteristics Analysis of Rotor System Based on Incremental Harmonic Balance Method

2013 ◽  
Vol 397-400 ◽  
pp. 517-523 ◽  
Author(s):  
Guo Liang Xiong ◽  
Qin Xiang ◽  
Qing Song Cao
Keyword(s):  
Harmonic Balance ◽  
Piecewise Linear ◽  
Harmonic Balance Method ◽  
Analytic Solutions ◽  
Rotor System ◽  
Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Characteristics Analysis ◽  
Incremental Harmonic Balance ◽  
The Time Domain

Support or pedestal looseness fault exists in mechanical system typically.A new dynamical model of an eccentric motor rotor system with a piecewise-linear stiffness was proposed, and the incremental harmonic balance method was employed to obtain analytic solutions of the model. Then, the time domain waveform and amplitude spectrogram were achieved by applying the analytic solutions to program and iterate in the MATLAB software. Finally, the characteristics of looseness was analyzed. Results show that this research method is feasible, and this paper may provide a theoretical basis for the solution of complex bearing looseness model analytically and the diagnosis of its fault.

scholarly journals Comparison of Common Methods in Dynamic Response Predictions of Rotor Systems with Malfunctions

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongliang Yao ◽  
Qian Zhao ◽  
Qi Xu ◽  
Bangchun Wen
Keyword(s):  
Frequency Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Newmark Method ◽  
Incremental Harmonic Balance Method ◽  
Rotor Systems ◽  
Double Frequency ◽  
Frequency Domain Methods ◽  
Incremental Harmonic Balance

The efficiency and accuracy of common time and frequency domain methods that are used to simulate the response of a rotor system with malfunctions are compared and analyzed. The Newmark method and the incremental harmonic balance method are selected as typical representatives of time and frequency domain methods, respectively. To improve the simulation efficiency, the fixed interface component mode synthesis approach is combined with the Newmark method and the receptance approach is combined with the incremental harmonic balance method. Numerical simulations are performed for rotor systems with single and double frequency excitations. The inherent characteristic that determines the efficiency of the two methods is analyzed. The results of the analysis indicated that frequency domain methods are suitable single and double frequency excitation rotor systems, whereas time domain methods are more suitable for multifrequency excitation rotor systems.

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