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

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实质性产生和不可避免的声能耗散。特别地，如果声音频率与共振频率一致，则波能量被强烈地吸收。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，初始波会产生大量的谐波，使波形发生畸变。然而，由于这些谐波以各自相应的速度传播，因此所产生的失真可能与在声学刚性管中发生的失真不同，在声学刚性管中，耗散弱到可以忽略不计。在理论中，假设只有平面波没有任何更高的模式在圆柱形管中传播。我们还着重假设，壁响应于 ...更多信息 内部压力和径向方向上的小位移被线性地建模为谐振器的单自由度，该谐振器由一系列三个机械元件组成：柔度、质量和机械阻力。对于橡胶材料，在较高的频率下，管壁的粘弹性运动由于内摩擦力的作用而衰减得更快，因此局部反应的假设虽然不能严格满足，但也是合理的。从无粘气体的基本控制方程出发，导出了非线性波动方程。能量耗散由于在墙上的效果和经典的和松弛的声音损失包括在一个特设的方式。由于它是很难解决的非线性波动方程解析，数值计算技术根据一个普通的有限差分格式被用来洞察的演变的时域波形在不同的空间点。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弗里斯（BKdV）方程，该方程在松弛介质和气液混合物中的压力扰动的传播中是已知的。少

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