Numerical method for analyzing steady-state oscillation in trumpets

被引:0
作者
Kaburagi, Tokihiko [1 ]
Kuroki, Chiho [2 ]
Hidaka, Shunsuke [2 ]
Ishikawa, Satoshi [3 ]
机构
[1] Kyushu Univ, Fac Design, 4-9-1 Shiobaru,Minami ku,, Fukuoka 8158540, Japan
[2] Kyushu Univ, Grad Sch Design, 4-9-1 Shiobaru,Minami ku, Fukuoka 8158540, Japan
[3] Kyushu Univ, Fac Engn, 744 Motooka,Nishi ku, Fukuoka 8190395, Japan
关键词
Trumpet; Two-dimensional lip model; Steady-state oscillation; Shooting method; Linear stability analysis; LINEAR-STABILITY ANALYSIS; VOCAL-TRACT; BRASS; INSTRUMENTS; SIMULATION; PHONATION; VIBRATION; BEHAVIOR; VOICE; CHEST;
D O I
10.1250/ast.44.269]
中图分类号
O42 [声学];
学科分类号
070206 ; 082403 ;
摘要
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.
引用
收藏
页码:269 / 280
页数:12
相关论文
共 22 条
  • [1] Trumpet sound simulation using a two-dimensional lip vibration model
    Adachi, S
    Sato, MA
    [J]. JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 1996, 99 (02) : 1200 - 1209
  • [2] COMPUTER ALGORITHM TO DETERMINE STEADY-STATE RESPONSE OF NONLINEAR OSCILLATORS
    APRILLE, TJ
    TRICK, TN
    [J]. IEEE TRANSACTIONS ON CIRCUIT THEORY, 1972, CT19 (04): : 354 - &
  • [3] INPUT IMPEDANCE CURVES FOR BRASS INSTRUMENTS
    BACKUS, J
    [J]. JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 1976, 60 (02) : 470 - 480
  • [4] Cullen JS, 2000, ACUSTICA, V86, P704
  • [5] A Minimal Model of a Single-Reed Instrument Producing Quasi-Periodic Sounds
    Doc, J. -B.
    Vergez, C.
    Missoum, S.
    [J]. ACTA ACUSTICA UNITED WITH ACUSTICA, 2014, 100 (03) : 543 - 554
  • [6] FLETCHER NH, 1979, ACUSTICA, V43, P63
  • [7] AUTONOMOUS VIBRATION OF SIMPLE PRESSURE-CONTROLLED VALVES IN GAS-FLOWS
    FLETCHER, NH
    [J]. JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 1993, 93 (04) : 2172 - 2180
  • [8] Gibiat V, 2000, ACUSTICA, V86, P746
  • [9] NONLINEAR VIBRATIONS IN THE AIR COLUMN OF A CLARINET ARTIFICIALLY BLOWN
    IDOGAWA, T
    KOBATA, T
    KOMURO, K
    IWAKI, M
    [J]. JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 1993, 93 (01) : 540 - 551
  • [10] Control of the vocal tract when experienced saxophonists perform normal notes and overtones
    Kaburagi, Tokihiko
    Kato, Ayame
    Fukuda, Yuri
    Taguchi, Fumiaki
    [J]. ACOUSTICAL SCIENCE AND TECHNOLOGY, 2021, 42 (02) : 83 - 92