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

局部反应管中有限振幅声波的波形畸变

基本信息

批准号：
02650234
负责人：
KAMAKURA Tomoo
金额：
$ 0.83万
依托单位：
University of Electro-Communications
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1990
资助国家：
日本
起止时间：
1990 至 1991
项目状态：
已结题

项目摘要

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

当声音在橡胶类材料管道中传播时，管壁屈服于内压，由此引起的管壁振动导致大量的几何弥散和不可避免的声能耗散。具体地说，如果声音频率与共振频率一致，则波能被强烈吸收。本研究描述了有限振幅声波在这种屈服管中的传播。由于空气的非线性，初始波产生大量的谐波并使其波形失真。然而，由于这些谐波以每个相应的速度传播，由此产生的失真可能以不同于在声学刚性管中发生的失真的方式来看待，后者的耗散可以忽略不计。在理论中，假设只有没有任何高模的平面波在圆柱管中传播。我们还强调假设墙在局部移动是对…的响应内压较大，径向位移较小，由柔度、质量和机械阻力三个力学要素组成的单自由度谐振器模型被线性化。在相对较高的频率下，由于橡胶材料的内耗，管壳中传播的壁面的粘弹性运动衰减得更快，因此局部反应的假设是合理的，尽管不是严格满足的。从无粘气体的基本控制方程出发，导出了非线性波动方程。墙上效应引起的能量耗散以及声音的经典和松弛损失以特别的方式被包括在内。针对非线性波动方程难以解析求解的问题，采用了基于普通有限差分格式的数值计算技术，深入研究了时间域波形在不同空间点上的演化规律。在低频激励远低于共振频率的情况下，波动方程被简化为Burgers-Korteweg-de Vries(BKdV)方程，该方程在松弛介质和气液混合物中的压力扰动传播中是已知的。较少