一维波在水下多层介质中传播的时域解析解

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振动与冲击 ›› 2014, Vol. 33 ›› Issue (13) : 6-12.

论文

一维波在水下多层介质中传播的时域解析解

金泽宇;殷彩玉;谌勇;黄修长;华宏星

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A time-domain analytical method of one-dimensional wave propagating through underwater multilayer mediums

JIN Ze-yu, YIN Cai-yu, CHEN Yong, HUANG Xiu-chang，HUA Hong-xing

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摘要

为研究水中压力波在覆盖层-钢板等介质中多次反射透射后对输入压力波的影响，采用波动理论建立一维多层介质声学模型，提出一种计算湿表面（水与覆盖层的交界面）压力的时域解析方法。该方法可以考虑波在多层介质中发生多次反射和透射的复杂情况，并得到时域解析解。针对输入为指数衰减波的情况，该方法的结果通过与有限元结果进行对比，验证了结果的正确性，将该方法的结果与只计及一、两次反射透射影响的近似结果进行对比，结果表明，对于刚性边界条件，该结果与近似结果相比吻合较好；对于气背边界和水背边界，与近似结果相比误差较大。为研究覆盖层参数的影响，对指数衰减波进行无量纲化和参数分析，分析结果表明，随着覆盖层特性阻抗的减小，压力波峰值先减小后增大再减小；随着覆盖层厚度的增大，压力波峰值逐渐减小；入射压力波衰减速度快，压力波峰值减小。该方法对于q(q≥3)层介质中波的多次反射透射分析依然适用。

Abstract

The underwater pressure wave will generate a series of complex reflection and transmission waves when it spreads between the coating and the steel plate which would influence the input pressure wave. A time-domain analytical method to calculate the pressure of the wetted surface (the interface of water and coating) is developed based on the wave theory. The method can take all complicated reflections and transmissions into account and obtain the analytical solution. For the exponential decay wave input, comparisons between the analytical results and FEM results indicate the correctness of the method. At the same time, the results are also compared with the approximate results whose effects merely counted once or twice reflection and transmission for the exponential decay wave input. Through the comparison, the results are highly consistent with the approximate results for the rigid boundary, but obtain large error for the air-back and the water-back boundary. Furthermore, dimensional analysis for exponential decay wave is done to study the influence of the coating parameters to the results. The results of the analysis indicate that the peak pressure will decrease first, then increase and again decrease with the decreasing of the coating characteristic impedance. Besides, the peak pressure will decrease as the thickness of the coating increases or the input wave decay speed increases. The method is still applicable for q-layers (q≥3)medium.

导出引用

金泽宇;殷彩玉;谌勇;黄修长;华宏星. 一维波在水下多层介质中传播的时域解析解[J]. 振动与冲击, 2014, 33(13): 6-12

JIN Ze-yu;YIN Cai-yu;CHEN Yong;HUANG Xiu-chang;HUA Hong-xing. A time-domain analytical method of one-dimensional wave propagating through underwater multilayer mediums[J]. Journal of Vibration and Shock, 2014, 33(13): 6-12