粗糙界面板Lamb波的传播特征

Propagation of elastic waves in a plate with rough surfaces

弹性波在粗糙界面板中的传播问题对无损检测、地震波传播等问题有实际意义,但是多年来的研究限于相屏近似等方法。本文从严格的理论出发,把粗糙界面起伏看作空间位置变量的随机过程,在粗糙表面起伏很小的条件下,用多次散射相互独立假设得到了平均意义下的Rayleigh-Lamb频散方程。通过对方程进行求解,得到了Lamb波在粗糙界面板中传播时的衰减。结果表明Lamb波的衰减和界面的粗糙起伏方差近似成正比,和粗糙起伏相关长度关系不大。在理论分析的基础上,进行了实验验证。

Propagation of Lamb waves in plates with rough surfaces is important to practical problems of nondestructive evaluation and study of seismic waves and, however, is very diffcult that the research till now has been limited to the approximate techniques such as phase screen model. The problem is studied in this paper by the stochastic theory and the elevation variation of the rough surfaces is considered as a stochastic procedure. The dispersive relation of the stochastic average of the Lamb wave, Rayleigh-Lamb equation is deduced based on the assumptions that the variation is small and the multi-reflections are independent from each other. The attenuation of the Lamb waves caused by the surface roughness is analyzed by the equation and it is found that the attenuation is approximately proportional to the variance of the roughness and is independent from its correltion length. Experimental measurement is carried out to verify the theoretical predictions.