Application of Secondary Bifurcations to Large-Amplitude Limit Cycles in Mechanical Systems

Ananthkrishnan, N.; Sudhakar, K.; Sudershan, S.; Aishwarya, Agarwal,

doi:10.1006/jsvi.1998.1623

Cited by 30 publications

(43 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The shape of the curves P s (a) may be easily altered and new bifurcations introduced by adding higher even-powers of x to the nonlinear damping factor (Ananthkrishnan et al, 1998). In a previous work (Lucero, 2005), a fourth-degree polynomial was used to produce an oscillation hysteresis phenomenon.…”

Section: Extension Of the Modelmentioning

confidence: 99%

A lumped mucosal wave model of the vocal folds revisited: Recent extensions and oscillation hysteresis

Lucero

Koenig

Lourenço

et al. 2011

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

This paper examines an updated version of a lumped mucosal wave model of the vocal fold oscillation during phonation. Threshold values of the subglottal pressure and the mean (DC) glottal airflow for the oscillation onset are determined. Depending on the nonlinear characteristics of the model, an oscillation hysteresis phenomenon may occur, with different values for the oscillation onset and offset threshold. The threshold values depend on the oscillation frequency, but the occurrence of the hysteresis is independent of it. The results are tested against pressure data collected from a mechanical replica of the vocal folds, and oral airflow data collected from speakers producing intervocalic /h/. In the human speech data, observed differences between voice onset and offset may be attributed to variations in voice pitch, with a very small or inexistent hysteresis phenomenon.

show abstract

Section: Extension Of the Modelmentioning

confidence: 99%

A lumped mucosal wave model of the vocal folds revisited: Recent extensions and oscillation hysteresis

Lucero

Koenig

Lourenço

et al. 2011

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

show abstract

“…1 whose amplitude starts from zero at the Hopf bifurcation point. Triggered limit cycles are, therefore, also called large-amplitude limit cycles in the literature [37,38]. The onset of triggered limit cycles at a fold bifurcation can be considered to be a nonlinear combustion instability phenomenon.…”

Section: Triggered Liluit Cyclesmentioning

confidence: 99%

Reduced-Order Modeling and Dynamics of Nonlinear Acoustic Waves in a Combustion Chamber

Ananthkrishnan

Deo

Culick

2005

Combustion Science and Technology

Self Cite

View full text Add to dashboard Cite

For understanding the fundamental properties of unsteady motions in combustion chambers, and for applications of active feedback control, reduced-order models occupy a uniquely important position. A framework exists for transforming the representation of general behavior by a set of infinite-dimensional partial differential equations to a finite set of nonlinear second-order ordinary . differential equations in time. The procedure rests on an expansion of the is a criterion for deciding how many modes must be retained to give accurate results. Addressing that problem is the principal purpose of this paper. Our analysis shows that, in case of longitudinal modes, a first mode instability problem requires a minimum of four modes in the modal truncation whereas, for a second mode instability, one needs to retain at least the first eight modes. A second important problem concerns the conditions under which a linearly stable system becomes unstable to sufficiently large disturbances. Previous work has given a partial answer, suggesting that nonlinear gasdynamics alone cannot produce pulsed or 'triggered' true nonlinear instabilities; that suggestion is now theoretically established. Also, a certain form of the nonlinear energy addition by combustion processes is known to lead to stable limit cycles in a linearly stable system. A second form of nonlinear combustion dynamics with a new velocity coupling function that naturally displays a threshold character is shown here also to produce triggered limit cycle behavior.

show abstract

“…5.2) may be easily altered by using suitable even-powered polynomials. This approach has been used to model subcritical Hopf bifurcations and oscillation hysteresis in other mechanical systems, such as axial flow compressors [27]. Here, the simple modification of (3.1) is considered…”

Section: Modification Of the Modelmentioning

confidence: 99%

Bifurcations and limit cycles in a model for a vocal fold oscillator

Lucero¹

2005

Communications in Mathematical Sciences

View full text Add to dashboard Cite

Abstract. This article presents an analysis of the dynamics of a bidimensional oscillator, which has been proposed as a simple model for the vocal fold motion at phonation. The model is capable of producing an oscillation with physiologically realistic values for the parameters. A simple extension of the model using even-powered polynomials in the damping factor is proposed, to permit the occurrence of an oscillation hysteresis phenomenon commonly observed in voice onset-offset patterns. This phenomenon appears from the combination of a subcritical Hopf bifurcation where an unstable limit cycle is produced, with a fold bifurcation between limit cycles, where the unstable limit cycle coalesces and cancels with a stable limit cycle. The results are illustrated with phase plane plots and bifurcation diagrams obtained using numerical continuation techniques.

show abstract

Application of Secondary Bifurcations to Large-Amplitude Limit Cycles in Mechanical Systems

Cited by 30 publications

References 0 publications

A lumped mucosal wave model of the vocal folds revisited: Recent extensions and oscillation hysteresis

A lumped mucosal wave model of the vocal folds revisited: Recent extensions and oscillation hysteresis

Reduced-Order Modeling and Dynamics of Nonlinear Acoustic Waves in a Combustion Chamber

Bifurcations and limit cycles in a model for a vocal fold oscillator

Contact Info

Product

Resources

About