scholarly journals Comparison of ANM and Predictor-Corrector Method to Continue Solutions of Harmonic Balance Equations

2019 ◽  
pp. 239-242
Author(s):  
Lukas Woiwode ◽  
Nidish Narayanaa Balaji ◽  
Jonas Kappauf ◽  
Fabia Tubita ◽  
Louis Guillot ◽  
...  
Keyword(s):  
Harmonic Balance ◽  
Balance Equations ◽  
Predictor Corrector

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

A Note on the Computation of Maximum Roll Amplitudes in Regular Beam Seas

1997 ◽  
Vol 41 (03) ◽  
pp. 224-229
Author(s):  
J. C. Peyton Jones ◽  
I. Qankaya
Keyword(s):  
Harmonic Balance ◽  
Wide Frequency Range ◽  
Phase Constraint ◽  
Frequency Range ◽  
Balance Equations ◽  
Efficient Tool ◽  
Beam Seas ◽  
At Resonance ◽  
Ship Roll ◽  
Cubic Stiffness

Generalized methods for deriving the harmonic balance equations are illustrated using a ship roll model with angle dependent cubic damping, and cubic stiffness terms. The balance equations are then solved subject to a phase constraint which identifies the resonant solution only. The amplitude of the response at resonance, and the frequency at which resonance occurs, can therefore be obtained without needing to compute the response over a wide frequency range. This provides an efficient tool for investigating the dependence of the resonant response on the level of input excitation, with results which agree well with more time-consuming simulation methods.

Development of a Harmonic Balance Method-Based Numerical Strategy for Blade-Tip/Casing Interactions: Application to NASA Rotor 37

2021 ◽  
Author(s):  
Yann Colaïtis ◽  
Alain Batailly
Keyword(s):  
Harmonic Balance ◽  
Time Integration ◽  
Harmonic Balance Method ◽  
Gibbs Phenomenon ◽  
Contact Forces ◽  
Balance Method ◽  
Blade Tip ◽  
Model Reduction Technique ◽  
Predictor Corrector ◽  
Numerical Strategy

Abstract In this study, a frequency-domain approach based on the harmonic balance method coupled to a predictor-corrector continuation algorithm is implemented for the qualitative analysis of blade-tip/casing contacts in aircraft engines. Unilateral contact and dry friction are taken into account through a regularized penalty law. To enhance the robustness of the methodology, particular attention is paid to the mitigation of the Gibbs phenomenon. To this end, the employed Alternating Frequency/Time scheme features a Lanczos σ-approximation so that spurious oscillations of the computed nonlinear contact forces become negligible. This approach is applied in combination with a model reduction technique on an industrial compressor blade: NASA rotor 37. In order to assess the influence of both the contact law regularization and the Lanczos σ-approximation, obtained results are thoroughly compared to an existing time integration-based numerical strategy relying on a Lagrange multiplier-based approach for contact treatment and that was previously confronted to experimental results. Presented results underline the very good agreement between the proposed methodology and the reference time integration numerical strategy. The proposed developments thus complement existing results on blade-tip/casing contact adding a much needed qualitative understanding of the interaction and an accurate assessment of the contact stiffening phenomenon.

Development of a Harmonic Balance Method-Based Numerical Strategy for Blade-Tip/Casing Interactions: Application to NASA Rotor 37

2021 ◽  
Author(s):  
Yann Colaïtis ◽  
Alain Batailly
Keyword(s):  
Harmonic Balance ◽  
Time Integration ◽  
Harmonic Balance Method ◽  
Gibbs Phenomenon ◽  
Contact Forces ◽  
Balance Method ◽  
Blade Tip ◽  
Model Reduction Technique ◽  
Predictor Corrector ◽  
Numerical Strategy

Abstract In this study, a frequency-domain approach based on the harmonic balance method coupled to a predictor-corrector continuation algorithm is implemented for the qualitative analysis of blade-tip/casing contacts in aircraft engines. Unilateral contact and dry friction are taken into account through a regularized penalty law. To enhance the robustness of the methodology, particular attention is paid to the mitigation of the Gibbs phenomenon. To this end, the employed Alternating Frequency/Time scheme features a Lanczos σ-approximation so that spurious oscillations of the computed nonlinear contact forces become negligible. This approach is applied in combination with a model reduction technique on an industrial compressor blade: NASA rotor 37. In order to assess the influence of both the contact law regularization and the Lanczos σ-approximation, obtained results are thoroughly compared to an existing time integration-based numerical strategy relying on a Lagrange multiplier-based approach for contact treatment and that was previously confronted to experimental results. Presented results underline the very good agreement between the proposed methodology and the reference time integration numerical strategy. The proposed developments thus complement existing results on blade-tip/casing contact adding a much needed qualitative understanding of the interaction and an accurate assessment of the contact stiffening phenomenon.

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