| 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)
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| 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
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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
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