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.