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的管中传播时，壁屈服于内部压力，并且随之而来的壁的振动导致几何分散的大量产生和不可避免的声音能量耗散，特别是如果声音频率与一致。目前的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，初始波会产生大量谐波并使其失真。然而，由于这些谐波以每个相应的速度传播，因此所产生的失真可能与声学刚性管中发生的失真不同，在声学刚性管中，耗散可以忽略不计。在理论上，假设是：只有没有任何更高模式的平面波在圆柱形管中传播，我们还强调壁会响应内部压力而局部移动，并且径向方向上的小位移是线性的。建模为由一系列三个机械元件组成的单自由度谐振器；在相对较高的频率下，管壳中传播的粘弹性运动由于橡胶的内摩擦而衰减得更快。材料，因此局部反应的假设虽然是合理的，但不能严格满足非线性波动方程是从无粘性气体的基本控制方程推导出来的，这是由于壁面效应以及经典和松弛损失造成的。由于很难解析地求解非线性波动方程，因此使用根据普通有限差分格式的数值计算技术来深入了解不同空间点的时域波形的演变。在远低于共振频率的低频激励的情况下，波动方程被简化为 Burgers-Korteweg-de Vries(BKdV) 方程，该方程在松弛介质和介质中的压力扰动传播中是已知的。气液混合物较少。