Nonlinear Response of a Dynamic System due to Oscillatory Flow

1987 ◽  
Vol 109 (4) ◽  
pp. 345-356 ◽  
Author(s):  
Y. M. Huang ◽  
C. M. Krousgrill ◽  
A. K. Bajaj
Keyword(s):  
Harmonic Balance ◽  
Nonlinear Response ◽  
Oscillatory Flow ◽  
Nonlinear Stiffness ◽  
Method Of Averaging ◽  
Secondary Resonances ◽  
Incremental Harmonic Balance ◽  
Nonzero Mean ◽  
Stiffness Characteristics ◽  
Solution Formulation

The dynamic response of a structure exhibiting nonlinear stiffness characteristics and excited by a nonzero mean oscillatory fluid flow is investigated. Both the method of averaging and a multi-frequency incremental harmonic balance approach are used in understanding the primary and secondary resonances in the response. Several parameter studies are presented where the results of these two methods are compared with those obtained by numerical integration and are discussed in detail. The results point to the need for a multi-frequency solution formulation for accurate representation of the response offset and to the difficulties of using the standard method of averaging formulation for investigation of secondary resonances in the response of this system.

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 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.

Nonlinear stiffness characteristics of the annular ligament

2014 ◽  
Vol 136 (4) ◽  
pp. 1756-1767 ◽  
Author(s):  
M. Lauxmann ◽  
A. Eiber ◽  
F. Haag ◽  
S. Ihrle
Keyword(s):  
Annular Ligament ◽  
Nonlinear Stiffness ◽  
Stiffness Characteristics

An Efficient Galerkin Averaging-Incremental Harmonic Balance Method Based on the Fast Fourier Transform and Tensor Contraction

2020 ◽  
Author(s):  
R. Ju ◽  
W. Fan ◽  
W. D. Zhu
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Harmonic Balance ◽  
High Efficiency ◽  
Jacobian Matrix ◽  
Sampling Rate ◽  
Harmonic Balance Method ◽  
Incremental Harmonic Balance ◽  
Tensor Contraction ◽  
Ihb Method

Abstract An efficient Galerkin averaging-incremental harmonic balance (EGA-IHB) method is developed based on the fast Fourier transform (FFT) and tensor contraction to increase efficiency and robustness of the IHB method when calculating periodic responses of complex nonlinear systems with non-polynomial nonlinearities. As a semi-analytical method, derivation of formulae and programming are significantly simplified in the EGA-IHB method. The residual vector and Jacobian matrix corresponding to nonlinear terms in the EGA-IHB method are expressed using truncated Fourier series. After calculating Fourier coefficient vectors using the FFT, tensor contraction is used to calculate the Jacobian matrix, which can significantly improve numerical efficiency. Since inaccurate results may be obtained from discrete Fourier transform-based methods when aliasing occurs, the minimal non-aliasing sampling rate is determined for the EGA-IHB method. Performances of the EGA-IHB method are analyzed using several benchmark examples; its accuracy, efficiency, convergence, and robustness are analyzed and compared with several widely used semi-analytical methods. The EGA-IHB method has high efficiency and good robustness for both polynomial and nonpolynomial nonlinearities, and it has considerable advantages over the other methods.

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