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Weakly nonlinear gas oscillations in air-filled tubes; Solutions and experiments

机译：充气管中的气体非线性微弱振荡;解决方案和实验

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摘要

The results of a theoretical and experimental investigation into the nonlinear, planar propagation of an acoustic signal in a cylindrical air-filled tube is presented. Assuming weakly nonlinear propagation and the distance of propagation smaller than the shock formation distance, the validity of the generalised Burgers' equation is analysed. The theoretical study is based on a dimensional analysis of the conservation equations followed by a calculation using asymptotic expansions. The deduced generalised Burgers' equations are solved whatever the boundary conditions are, with a numerical-finite-difference method and using a harmonic balance method. Two cases are investigated experimentally: the purely progressive case, and the standing wave with an unknown termination. The results are compared successfully with theoretical predictions on the three first harmonics of a periodic signal in a high degree of accuracy, when the effects of the thermoviscous dissipation and of the non-linear propagation have the same order of magnitude. [References: 25]
机译：给出了在圆柱形充气管中声学信号的非线性平面传播的理论和实验研究结果。假设非线性传播较弱，且传播距离小于激波形成距离，则分析了广义伯格斯方程的有效性。理论研究基于对守恒方程的维分析，然后使用渐近展开进行计算。无论边界条件如何，都可以利用数值有限差分法和谐波平衡法求解推导的广义Burgers方程。实验研究了两种情况：纯渐进式情况和未知终止的驻波。当热粘性耗散和非线性传播的影响具有相同数量级时，可以将结果与高精度的周期信号的三个一次谐波的理论预测成功地进行比较。 [参考：25]

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