Prediction of the dynamic oscillation threshold in a clarinet model with a linearly increasing blowing pressure : influence of noise
| Autor: | Bergeot, Baptiste, Almeida, André, Vergez, Christophe, Gazengel, Bruno |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Nonlinear Dynamics 74, 3 (2013) 591-605 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11071-013-0991-8 |
| Popis: | This paper presents an analysis of the effects of noise and precision on a simplified model of the clarinet driven by a variable control parameter. When the control parameter is varied the clarinet model undergoes a dynamic bifurcation. A consequence of this is the phenomenon of bifurcation delay: the bifurcation point is shifted from the static oscillation threshold to an higher value called dynamic oscillation threshold. In a previous work [8], the dynamic oscillation threshold is obtained analytically. In the present article, the sensitivity of the dynamic threshold on precision is analyzed as a stochastic variable introduced in the model. A new theoretical expression is given for the dynamic thresholds in presence of the stochastic variable, providing a fair prediction of the thresholds found in finite-precision simulations. These dynamic thresholds are found to depend on the increase rate and are independent on the initial value of the parameter, both in simulations and in theory. Comment: 14 pages |
| Databáze: | arXiv |
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