A symbolic algorithm for the automatic computation of multitone-input harmonic balance equations for nonlinear systems

2008 ◽  
Vol 56 (1-2) ◽  
pp. 179-191 ◽  
Author(s):  
D. Akgün ◽  
İ. Çankaya ◽  
J. C. Peyton Jones
Keyword(s):  
Nonlinear Systems ◽  
Harmonic Balance ◽  
Balance Equations ◽  
Automatic Computation ◽  
Symbolic Algorithm

THE NEW ALGORITHM OF SOLVING HARMONIC BALANCE EQUATIONS

2019 ◽  
Author(s):  
Vladimir Lantsov ◽  
A. Papulina
Keyword(s):  
Harmonic Balance ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Balance Equations ◽  
Model Order ◽  
Cad Systems ◽  
Computational Costs ◽  
Reduction Methods ◽  
Model Equations

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.

Generalized Harmonic Analysis of Nonlinear Ship Roll Dynamics

1996 ◽  
Vol 40 (04) ◽  
pp. 316-325
Author(s):  
J. C. Peyton Jones ◽  
I. Cankaya
Keyword(s):  
Harmonic Analysis ◽  
Harmonic Balance ◽  
Initial Conditions ◽  
Balance Equations ◽  
Validation Process ◽  
Algebraic Expressions ◽  
Resonant Modes ◽  
Ship Roll ◽  
Righting Moment ◽  
Simulation Time

Algebraic expressions are presented which enable the harmonic balance equations to be written down directly in terms of the coefficients of a general nonlinear ship roll equation, without restriction on the number of harmonics considered. The rolling response is then readily computed, as illustrated by an investigation of the resonant modes of ships with angle-dependent cubic damping, or quintic terms in the righting moment. Details are also given of the validation process, showing how simulation time can be reduced by an appropriate choice of initial conditions.

Symbolic computation of harmonic balance equations

1997 ◽  
Vol 68 (3) ◽  
pp. 449-460 ◽  
Author(s):  
J. C. Peyton ◽  
Jones M. Zhuang ◽  
I. Cankaya
Keyword(s):  
Symbolic Computation ◽  
Harmonic Balance ◽  
Balance Equations
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