Calculation of the steady‐state oscillations of a clarinet using the harmonic balance technique

1989 ◽  
Vol 86 (1) ◽  
pp. 35-41 ◽  
Author(s):  
J. Gilbert ◽  
J. Kergomard ◽  
E. Ngoya
Keyword(s):  
Steady State ◽  
Harmonic Balance ◽  
Balance Technique ◽  
Harmonic Balance Technique

scholarly journals Steady State Analysis Of Single Phase IPM Motors By D-Q Harmonic Balance Method

2021 ◽  
Vol 12 (1) ◽  
pp. 43-51
Author(s):  
Asogwa Jude C. ◽  
Obe Emeka S. ◽  
Nnadi Damian B. ◽  
Oti Stephen E.
Keyword(s):  
Steady State ◽  
Harmonic Balance ◽  
Single Phase ◽  
Harmonic Balance Method ◽  
Phase Variable ◽  
Steady State Analysis ◽  
Q Model ◽  
Balance Technique ◽  
Harmonic Balance Technique ◽  
State Analysis

A concise steady-state analysis of a single-phase line-start permanent magnet (SPLSPM) machine is conducted from a developed d-q model using the d-q harmonic balance technique. The d-q model was developed in rotor reference frame from a phase variable model of the machine. SPLSPM whose performance indices were characterized by high torque ripples has detailed analysis docile mostly in computer simulations quite unlike the three-phase types. The main cause is not far-fetched, it was due to nonexistence of precise mathematical model in d-q rotor frame of the motor due to the unbalanced field winding, the rotor saliency and the presence of the capacitor in the auxiliary windings. Even after model has been developed, the simple traditional procedure of setting all time varying component to zero for steady-state analysis fails because the rotor position dependence on the inductance expressions could not be eliminated. The d-q harmonic-balance technique was then applied. An important feature of the harmonic balance technique was that it decoupled all equations to simple sine waveforms in a style that resembled Fourier series. Results yield torque pulsation, current and load characteristics in the steady state.

Aerodynamic Asymmetry Analysis of Unsteady Flows in Turbomachinery

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Kivanc Ekici ◽  
Robert E. Kielb ◽  
Kenneth C. Hall
Keyword(s):  
Harmonic Balance ◽  
Coupling Effect ◽  
Unsteady Flows ◽  
Unsteady Aerodynamic ◽  
Blade Row ◽  
Balance Technique ◽  
Turbomachinery Blades ◽  
Aerodynamic Asymmetry ◽  
Frequency Domain Approach ◽  
Harmonic Balance Technique

A nonlinear harmonic balance technique for the analysis of aerodynamic asymmetry of unsteady flows in turbomachinery is presented. The present method uses a mixed time-domain/frequency-domain approach that allows one to compute the unsteady aerodynamic response of turbomachinery blades to self-excited vibrations. Traditionally, researchers have investigated the unsteady response of a blade row with the assumption that all the blades in the row are identical. With this assumption the entire wheel can be modeled using complex periodic boundary conditions and a computational grid spanning a single blade passage. In this study, the steady/unsteady aerodynamic asymmetry is modeled using multiple passages. Specifically, the method has been applied to aerodynamically asymmetric flutter problems for a rotor with a symmetry group of 2. The effect of geometric asymmetries on the unsteady aerodynamic response of a blade row is illustrated. For the cases investigated in this paper, the change in the diagonal terms (blade on itself) dominated the change in stability. Very little mode coupling effect caused by the off-diagonal terms was found.

Aerodynamic Asymmetry Analysis of Unsteady Flows in Turbomachinery

2008 ◽  
Author(s):  
Kivanc Ekici ◽  
Robert E. Kielb ◽  
Kenneth C. Hall
Keyword(s):  
Harmonic Balance ◽  
Coupling Effect ◽  
Unsteady Flows ◽  
Unsteady Aerodynamic ◽  
Blade Row ◽  
Balance Technique ◽  
Turbomachinery Blades ◽  
Aerodynamic Asymmetry ◽  
Frequency Domain Approach ◽  
Harmonic Balance Technique

A nonlinear harmonic balance technique for the analysis of aerodynamic asymmetry of unsteady flows in turbomachinery is presented. The present method uses a mixed time-domain/frequency-domain approach that allows one to compute the unsteady aerodynamic response of turbomachinery blades to self-excited vibrations. Traditionally, researchers have investigated the unsteady response of a blade row with the assumption that all the blades in the row are identical. With this assumption the entire wheel can be modeled using complex periodic boundary conditions and a computational grid spanning a single blade passage. In this study, the steady/unsteady aerodynamic asymmetry is modeled using multiple passages. Specifically, the method has been applied to aerodynamically asymmetric flutter problems for a rotor with a symmetry group of two. The effect of geometric asymmetries on the unsteady aerodynamic response of a blade row is illustrated. For the cases investigated in this paper, the change in the diagonal terms (blade on itself) dominated the change in stability. Very little mode coupling effect caused by the off-diagonal terms was found.

Using Transfer Matrices for Parametric System Forced Response

1987 ◽  
Vol 109 (4) ◽  
pp. 356-360 ◽  
Author(s):  
J. W. David ◽  
L. D. Mitchell ◽  
J. W. Daws
Keyword(s):  
Harmonic Balance ◽  
Forced Response ◽  
Computational Techniques ◽  
Computational Technique ◽  
Transfer Matrices ◽  
Frequency Branch ◽  
Balance Technique ◽  
Systems Analysts ◽  
The Many ◽  
Harmonic Balance Technique

For many years, engineers and scientists have sought to deal with the many phenomena exhibiting parametric characteristics. While many approximate techniques are available for the analysis of such systems, the harmonic balance technique can be used to accurately model the response of systems where the coefficient variation is large. Also, in analyzing complex physical systems, analysts have sought to develop efficient computational techniques that are sufficiently general for the analysis of arbitrary systems. In this paper, it is shown that combining the harmonic balance technique with transfer matrices produces an efficient computational technique for the analysis of parametric systems where the coefficient variations can be large. The technique is demonstrated by considering a single-degree-of-freedom system with time varying stiffness. The harmonic balance technique is used to frequency-branch the transfer matrices, thus allowing multifrequency response calculations to be done simultaneously. The results are compared with direct numerical integrations of the equations. Lastly, this technique is applied to a simple gear coupled rotor system to demonstrate the application of this technique to large order systems of more engineering relevance.

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