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Waveform distortions of finite amplitude sound wave in a locally reacting tube

Research Project

Project/Area Number 02650234
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 電子通信系統工学
Research InstitutionUniversity of Electro-Communications

Principal Investigator

KAMAKURA Tomoo  University of Electro-Communications Department of Electro-Communications Associate Professor, 電気通信学部, 助教授 (50109279)

Project Period (FY) 1990 – 1991
Project Status Completed (Fiscal Year 1991)
Budget Amount *help
¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1991: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1990: ¥600,000 (Direct Cost: ¥600,000)
KeywordsNonlinear acoustics / velocity dispersion / Elastic tube / Finite amplitude wave / 非線形 / 弾性チュ-ブ / 音波パルス / 波形歪 / 非線形効果 / BKdV方程式
Research Abstract

When sound propagates in a tube of rubber-like material, the wall yields to the internal pressure, and the consequent vibration of the wall results in the substantial generation of geometrical dispersion and inevitable sound energy dissipation. In particular, if the sound frequency coincides with the resonance frequency the wave energy is strongly absorbed. The present research describes the propagation of finite amplitude sound waves in such yielding tubes. Due to the nonlinearity of air, the initial waves generate plenty of harmonics and distort their waveforms. Since these harmonics, however, propagate with each corresponding speed, the resultant distortions might be seen in a different way from those that take place in an acoustically rigid tube, where the dissipation is negligibly weak.
In the theory the assumption is made that only plane waves without any higher modes are propagating in a cylindrical tube. We also assume emphatically that the wall moves locally in response to the … More internal pressure and the small displacement in radial direction is linearly modeled as a single freedom of resonator which consists of a series of three mechanical elements; compliance, mass and mechanical resistance. At relatively high frequencies, the visco-elastic motion of wall propagating in the tube shell decays more fast by the internal friction for rubber materials, so the assumption of local reaction would be resonable, although not be rigorously satisfied. The nonlinear wave equation is derived from the basic governing equations for an inviscid gas. The energy dissipations due to the on wall effect and the classical and relaxational losses of sound are included in an ad hoc manner. Since it is difficult to solve the nonlinear wave equation analytically, the numerical calculation technique according to an ordinary finite difference scheme is used for giving insight into the evolution of the time domain waveform at various space points. In the case of low frequency excitation much below the resonance frequency, the wave equation is reduced to the Burgers- Korteweg-de Vries(BKdV) equation, which is known in the propagation of pressure disturnances in a relaxing medium and in a gas-liquid mixture. Less

Report

(3 results)
  • 1991 Annual Research Report   Final Research Report Summary
  • 1990 Annual Research Report
  • Research Products

    (11 results)

All Other

All Publications (11 results)

  • [Publications] T.Kamakura et.al.: "Suitable modulation of the carrier ultrasound for a parametric loudspeaker" ACUSTICA. 73. 215-217 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Kamakura et.al: "Harmonic generation in finite amplitude sound beams from a rectangular aperture source." J.Acoust.Soc.Am.(1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 長谷川 光司,鎌倉 友男: "粘弾性チューブ内での音波伝搬" 日本音響学会誌. (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Kamakura et.al.: "Waveform distortions of finite amplitude sound wave in an elastic tuke" Proc.of 12th International Symposium on Nonlinear Acoustics.Elsevier. 333-338 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Kamakura, K.Aoki, and Y.Kumamoto: "Suitable modulation of the carrier ultrasound for a parametric loudspeaker" ACUSTICA,. 73. 215-217 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Kamakura, M.Tani, Y.Kumamoto, and K.Ueda: "Harmonic generation in finite amplitude sound beams from a rectangular aperture source" J.Acoust.Soc.Am.91(6).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] H.Hasegawa, T.Kamakura, and Y.Kumamoto,: "On the propagation in a viscoelasic tube" J.Acoust.Soc.Jpn.48. (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Kamakura and Y.Kumamoto: "Waveform distortions of finite amplitude sound wave in an elasic tube" Proceedings of 12th ISNA, edited by M.F. Hamilton and D.T. Blackstock, Elsevier. 333-338 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Kamakura et.al: "Harmonic generation in finte amplitude sound beams from a rectangular apernre source." J.Acoust.Soc.Am.91(6). (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] T.Kamakura,K.Matuda,and Y.Kumamoto: "Waveform distortions of finite ampitude sound wave in a locally reacting tube" J.Sound and Vibration.

    • Related Report
      1990 Annual Research Report
  • [Publications] T.Kamakura,K.Aoki and Y.Kumamoto: "Harmonic generation in bounded beams by a rectangular aperture source" J.Sound and Vibration.

    • Related Report
      1990 Annual Research Report

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Published: 1990-04-01   Modified: 2016-04-21  

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