Convergence rates of Harmonic Balance Method for periodic solution of smooth and non-smooth systems

2021 ◽  
pp. 105826
Author(s):  
Li Wang ◽  
Zhong-Rong Lu ◽  
Jike Liu
Keyword(s):  
Periodic Solution ◽  
Harmonic Balance ◽  
Convergence Rates ◽  
Harmonic Balance Method ◽  
Balance Method

Oscillations in an x(2n+2)/(2n+1) Potential via He’s Frequency-Amplitude Formulation

2009 ◽  
Vol 64 (12) ◽  
pp. 877-878 ◽  
Author(s):  
Abd Elhalim Ebaid
Keyword(s):  
Periodic Solution ◽  
Fractional Order ◽  
Harmonic Balance ◽  
Nonlinear Oscillator ◽  
Harmonic Balance Method ◽  
Solution Procedure ◽  
Present Approach ◽  
Balance Method

A recent technique, known as He’s frequency-amplitude formulation approach, is proposed in this letter to obtain an analytical approximate periodic solution to a nonlinear oscillator equation with potential of arbitrary fractional order. The solution procedure of the present approach is very simple and more convenient in comparison with the harmonic balance method

scholarly journals Convergence Acceleration of the Harmonic Balance Method Using a Time-Level Preconditioner

AIAA Journal ◽  
2020 ◽  
Vol 58 (11) ◽  
pp. 4908-4922
Author(s):  
Daniel Lindblad ◽  
Niklas Andersson
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Convergence Acceleration ◽  
Balance Method ◽  
Time Level

Some Remarks on the Harmonic Balance Method for Mixed-Parity Non-Linear Oscillations

1994 ◽  
Vol 170 (4) ◽  
pp. 571-576 ◽  
Author(s):  
A.Venkateshwar Rao ◽  
B.Nageswara Rao
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Non Linear

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.

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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