Some aspects of the harmonic balance method applied to the clarinet

Fritz, Claudia; Farner, Snorre; Kergomard, Jean

doi:10.1016/j.apacoust.2004.04.006

Cited by 9 publications

(14 citation statements)

References 9 publications

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“…Widely used in many scientific fields, methods dedicated to computation of periodic solutions of nonlinear dynamical systems have demonstrated, in several previous works [10,11,12,16,17], their benefits for the study of musical instruments. However, no available software (such as AUTO [8], Manlab [18], or DDE-Biftool [19]) is suitable for neutral delayed systems, involved in the modeling of flute-like instruments.…”

Section: Resultsmentioning

confidence: 99%

“…Particularly, different studies have dealt with both computation and continuation of periodic solutions and bifurcation analysis of reed instruments with the software AUTO [16], Harmbal [11,12] or Manlab [17,18]. These software differ in numerical methods they use, both for the calculation of periodic solutions (harmonic balance and collocation for Manlab, collocation for AUTO), and for the continuation algorithm (predictorcorrector method for AUTO, asymptotic numerical method for Manlab).…”

Section: Mathematical Nature Of the Modelmentioning

confidence: 99%

“…This technique has then been used in various works focusing on single reed musical instruments [11,12,13] and brass instruments [14,15]. Recent studies [16,17] have then demonstrated the benefits of combining this technique with numerical continuation methods to understand the behaviour of clarinet-like instruments.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Calculation of the Steady-State Oscillations of a Flute Model Using the Orthogonal Collocation Method

Terrien¹,

Vergez²,

Fabre³

et al. 2014

Acta Acustica united with Acustica

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In this paper we exploit the method of numerical continuation combined with orthogonal collocation to determine the steady-state oscillations of a model of flute-like instruments that is formulated as a nonlinear neutral delay differential equation. The delay term in the model causes additional complications in the analysis of the behaviour of the model, in contrast to models of other wind instruments which are formulated as ordinary differential equations. Fortunately, numerical continuation provides bifurcation diagrams that show branches of stable and unstable static and periodic solutions of the model and their connections at bifurcations, thus enabling an in depth analysis of the global dynamics. Furthermore, it allows us to predict the thresholds of the different registers of the flute-like instrument and thus to explain the classical phenomenon of register change and the associated hysteresis.

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Section: Resultsmentioning

confidence: 99%

Section: Mathematical Nature Of the Modelmentioning

confidence: 99%

See 1 more Smart Citation

Calculation of the Steady-State Oscillations of a Flute Model Using the Orthogonal Collocation Method

Terrien¹,

Vergez²,

Fabre³

et al. 2014

Acta Acustica united with Acustica

View full text Add to dashboard Cite

show abstract

“…The error e i ð Þ is defined as the difference between the measured input impedance Z ð Þ and the estimated input impedance Z 0 À Á in Eq. (8). It is assumed that coefficient of the highest-order term in the denominator is one.…”

Section: Parameter Identification Of the Input Impedance-rational Framentioning

confidence: 99%

Hybrid coupling method to nonlinear acoustic source and linear duct system using parameter identification of the input impedance in fluid machinery

Wang

Cho

2016

Journal of Sound and Vibration

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“…A complete numerical version of the HBT can be found in Refs. [3,7,8], but previously, for small oscillations, Worman [1] suggested that a relationship exists between the amplitude of the higher harmonics, and that of the first one. Grand et al [9], using the model of a reed without dynamics, got important analytical results, confirming the validity of the so-called Worman rule when the equations of the HBT are truncated to a finite number of harmonics.…”

Section: Introductionmentioning

confidence: 99%

Behavior of Reed Woodwind Instruments Around The Oscillation Threshold

Ricaud¹,

Guillemain²,

Kergomard³

et al. 2009

Acta Acustica united with Acustica

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Properties of small amplitude oscillations of the single reed woodwind instruments near the oscillation threshold are investigated. Analytical formulae with explicit dependence on the physical parameters of the instrument and instrumentist allow to determine the bifurcation point, the nature of the bifurcation, the amplitude of the first harmonics and the oscillation frequency. The model, which takes the reed dynamics into account, is entirely expressed in the frequency domain and its behaviour is analysed. An application to a model of saxophone is proposed and compared with numerical results obtained through the harmonic balance technique and a time domain simulation, showing excellent agreements.

show abstract

Some aspects of the harmonic balance method applied to the clarinet

Cited by 9 publications

References 9 publications

Calculation of the Steady-State Oscillations of a Flute Model Using the Orthogonal Collocation Method

Calculation of the Steady-State Oscillations of a Flute Model Using the Orthogonal Collocation Method

Hybrid coupling method to nonlinear acoustic source and linear duct system using parameter identification of the input impedance in fluid machinery

Behavior of Reed Woodwind Instruments Around The Oscillation Threshold

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