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How Well Can Linear Stability Analysis Predict the Behaviour of an Outward-Striking Valve Brass Instrument Model?

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A physical model of brass instrument is considered in this paper: a one degree-of-freedom outward-striking valve for the lips, non-linearly coupled to a modal representation of the air column. It is studied through Linear Stability Analysis (LSA) of the equilibrium solution. This approach provides the threshold blowing pressure value, at which instability occurs, and the instability frequency value. The relevance of the results of this method is theoretically limited to the neighbourhood of the equilibrium solution. This paper checks the efficiency of LSA to understand the behaviour of the model computed through time-domain simulations. As expected, a good agreement is observed between LSA and numerical simulations of the complete nonlinear model around the oscillation threshold. For blowing pressures far above the oscillation threshold, the picture is more contrasted. In most of the cases tested, a periodic regime coherent with the LSA results is observed, but over-blowing, q uasi-periodicity and period-doubling also occur. Interestingly, LSA predicts the production of the pedal note by a trombone, for which only nonlinear hypotheses have been previously proposed. LSA also predicts the production of a saxhorn note which, although known to musicians, has barely been documented.
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Document Type: Research Article

Publication date: 2017-01-01

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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