Bifurcation and chaos of a harmonically excited oscillator with both stiffness and viscous damping piecewise linearities by incremental harmonic balance method

2003 ◽  
Vol 264 (4) ◽  
pp. 873-882 ◽  
Author(s):  
L. Xu ◽  
M.W. Lu ◽  
Q. Cao
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Viscous Damping ◽  
Incremental Harmonic Balance Method ◽  
Bifurcation And Chaos ◽  
Incremental Harmonic Balance ◽  
Excited Oscillator

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.

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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