Analysis of Harmonically Forced Duffing Oscillator with Time Delay State Feedback by Incremental Harmonic Balance Method

2021 ◽  
Author(s):  
Han Wu ◽  
Xiaohui Zeng ◽  
Yubiao Liu ◽  
Jiang Lai
Keyword(s):  
Time Delay ◽  
Harmonic Balance ◽  
State Feedback ◽  
Duffing Oscillator ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Incremental Harmonic Balance ◽  
Harmonically Forced Duffing Oscillator

Higher-order approximate steady-state solutions for strongly nonlinear systems by the improved incremental harmonic balance method

2017 ◽  
Vol 24 (16) ◽  
pp. 3744-3757 ◽  
Author(s):  
Jiangchuan Niu ◽  
Yongjun Shen ◽  
Shaopu Yang ◽  
Sujuan Li
Keyword(s):  
Nonlinear Systems ◽  
Harmonic Balance ◽  
Duffing Oscillator ◽  
Harmonic Balance Method ◽  
Higher Order ◽  
Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Strongly Nonlinear ◽  
Incremental Harmonic Balance ◽  
Steady State Solutions

Combining the harmonic balance method with the incremental harmonic balance approach, an improved incremental harmonic balance method is presented to obtain the higher-order approximate steady-state solutions for strongly nonlinear systems, which can simplify the calculation process for high-order nonlinear terms. Taking a strongly nonlinear Duffing oscillator with cubic nonlinearity and a strongly nonlinear Duffing oscillator with quintic nonlinearity as examples, the forced vibrations under harmonic excitation are investigated. Based on the first-order approximate analytical solutions obtained by the harmonic balance method, the higher-order approximate solutions are obtained by the improved incremental harmonic balance method. The correctness of the approximate analytical results is verified by the numerical results. The comparison results show that the approximations obtained by the improved incremental harmonic balance method agree with the numerical solutions well, and the improved method is effective to analyze the dynamical response for strongly nonlinear systems.

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.

scholarly journals A Modified Incremental Harmonic Balance Method for 2-DOF Airfoil Aeroelastic Systems with Nonsmooth Structural Nonlinearities

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Ying-Ge Ni ◽  
Wei Zhang ◽  
Yi Lv ◽  
Stylianos Georgantzinos
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Free Play ◽  
Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Aeroelastic System ◽  
Structural Nonlinearity ◽  
Incremental Harmonic Balance

A modified incremental harmonic balance method is presented to analyze the aeroelastic responses of a 2-DOF airfoil aeroelastic system with a nonsmooth structural nonlinearity. The current method, which combines the traditional incremental harmonic balance method and a fast Fourier transform, can be used to obtain the higher-order approximate solution for the aeroelastic responses of a 2-DOF airfoil aeroelastic system with a nonsmooth structural nonlinearity using significantly fewer linearized algebraic equations than the traditional method, and the dominant frequency components of the response can be obtained by a fast Fourier transform of the numerical solution. Thus, periodic solutions can be obtained, and the calculation process can be simplified. Furthermore, the nonsmooth nonlinearity was expanded into a Fourier series. The procedures of the modified incremental harmonic balance method were demonstrated using systems with hysteresis and free play nonlinearities. The modified incremental harmonic balance method was validated by comparing with the numerical solutions. The effect of the number of harmonics on the solution precision as well as the effect of the free-play and stiffness ratio on the response amplitude is discussed.

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