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

Development of an Edge-Based Harmonic Balance Method for Turbomachinery Flows

2011 ◽  
Author(s):  
Roque Corral ◽  
Javier Crespo
Keyword(s):  
Harmonic Balance ◽  
Stokes Equations ◽  
Computational Cost ◽  
Harmonic Balance Method ◽  
Convergence Acceleration ◽  
Balance Method ◽  
Navier Stokes ◽  
Acceleration Techniques ◽  
Edge Based ◽  
The Time Domain

An harmonic balance method for modeling unsteady nonlinear periodic flows in turbomachinery is presented. The method solves the Reynolds Averaged Navier-Stokes equations in the time domain and may be implemented in a relatively simple way into an existing code including all the standard convergence acceleration techniques used for steady problems. The application of the method to vibrating airfoils and rotorstator interaction is discussed. It is demonstrated that the time spectral scheme may achieve the same temporal accuracy at a lower computational cost at the expense of using more memory.

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.

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