Numerical method for analyzing steady-state oscillation in trumpets

IF 0.6 Q4 ACOUSTICS

Acoustical Science and Technology Pub Date : 2023-05-01 DOI:10.1250/ast.44.269

Tokihiko Kaburagi, Chiho Kuroki, Shunsuke Hidaka, Satoshi Ishikawa

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Abstract

Interactions between the airflow, elastic body of the lips, and acoustic resonator of the instrument cause self-sustained oscillation of the lips when generating sound using brass instruments, and the steady-state oscillation of the instrument can be expected to be periodic. However, quasi-periodic oscillation or period doubling can also occur, and a cascade of period doublings may further introduce chaos. Therefore, given a set of dynamic equations representing the acoustic behaviors of the airflow, lips, and instrument, a method for detecting and obtaining the periodic solution by adopting a shooting method that relies on the match between the initial and terminal states after the time corresponding to the oscillation period has passed is presented in this paper. Experiments were performed for a trumpet model, where the resonance frequency of the lips and the blowing pressure were used as the main control parameters. The minimum blowing pressure was estimated using a linear stability analysis. The method could capture the corresponding changes in the periodic solution very finely when a small perturbation was successively applied to the control parameters; however, it was less effective when the acoustic load of the instrument was capacitive at the oscillation frequency.

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喇叭稳态振荡分析的数值方法

在使用铜管乐器发声时，气流、唇部弹性体和乐器的声学谐振器之间的相互作用导致了唇部的自持续振荡，并且可以预期乐器的稳态振荡是周期性的。然而，准周期振荡或周期加倍也可能发生，而周期加倍的级联可能进一步引入混沌。因此，本文给出了一组表征气流、唇部和仪器声学特性的动力学方程，提出了一种基于振荡周期对应时间后初始状态与终端状态匹配的射击法检测并获得周期解的方法。以小号模型为实验对象，以吹唇共振频率和吹风压力为主要控制参数。最小吹气压力用线性稳定性分析估计。当控制参数连续施加一个小的扰动时，该方法可以很好地捕捉到周期解的相应变化;然而，当仪器的声负荷在振荡频率为电容性时，其效果较差。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acoustical Science and Technology ACOUSTICS-

CiteScore

1.60

自引率

14.30%

发文量

期刊介绍： Acoustical Science and Technology(AST) is a bimonthly open-access journal edited by the Acoustical Society of Japan and was established in 1980 as the Journal of Acoustical Society of Japan (E). The title of the journal was changed to the current title in 2001. AST publishes about 100 high-quality articles (including papers, technical reports, and acoustical letters) each year. The scope of the journal covers all fields of acoustics, both scientific and technological, including (but not limited to) the following research areas. Psychological and Physiological Acoustics Speech Ultrasonics Underwater Acoustics Noise and Vibration Electroacoustics Musical Acoustics Architectural Acoustics Sonochemistry Acoustic Imaging.