有限振幅脉冲波在管道中的传播

Propagation of finite amplitude sound pulses in tubes

本文分析有限振幅声波在刚性管道中的传播.首先讨论忽略管壁阻尼影响时Burgers方程的解,以反对称N波解为基础,获得了非对称的N波解,能更好地适配实际产生的N波。然后把管壁阻尼的影响作为小量进行修正,获得了广义Burgers方程的近似解.文中对实验测试作了扼要介绍,表明理论预测与实验结果良好相符.

In this paper, the nonlinear propagation properties of finite amplitude sound pulses in tubes with rigid wall is studied. At first, we discuss the solutions of Burgers equation in which dissipation due to wall effect is neglected. Based on the antisymmetric N shaped waveform solution, we obtain an asymmetric one which can fit the actual N wave better. Secondly, we assume that the wall effect is much smaller than the nonlinear effect of acoustic wave, and hence, the approximate solution of the generalized Burgers equation is obtained by perturbation method. Finally, the experimental investigation is described and discussed briefly. It is shown that the experimental data are in good agreement with the theoretical calculations proposed in the paper.