兰姆波在自由端面上的反射

对于板材的内部缺陷,常用兰姆波作超声无损检测。兰姆波在板材自由端面上的反射呈现复杂现象,即使在纯模入射条件下,通常也要产生无数个其它模式的反射兰姆渡。由于兰姆波本征模式正交关系同时涉及位移和应力,使其反射问题的分析较复杂,我们采用了一种新方法,应用最小二乘原理,将兰姆波本征模式作为试验函数,实现了一种较简单的分析方法。在一般情形下,利用8位微处理机就可取得满意的结果。应用该方法,给出了兰姆波在自由端面上反射时各模式的反射系数,阐明了纯模反射条件,并发现了关于模式转换的一些有趣的新现象。

Reflection of the Lamb wave in a semi-infinite plate

The Lamb wave technique is used in the detection of internal defects in plates. The reflection of the Lamb wave at the free edge of the plate is shown to be more complicated. The reflected waves are usually composed of infinite number of modes of the Lamb waves even in the case of one mode of Lamb wave incidence. The analysis of the reflection problem is complicated, as the orthogonal relation of the eigen-modes of the Lamb wave concerns both the components of the stresses and displacements. The principle of the least squares is applied as a new analysis method, in which the eigen-modes are taken as the trial function. It is simple and effective. In most cases satisfactory results could be obtained by using 8-bit micro-computers. The coefficients of various reflected modes of the Lamb wave are calculated by this method and some interesting phenomena on the mode conversion are indicated and the conditions on the pure mode reflection are given as well.