瞬态波在层合板中传播的粘弹比拟法

本文发展了粘弹比拟理论,并将之用于求解半无限空间三层复合材料在垂直层合方向传播的瞬态波问题。对于层合板中应力波的传播问题,寻找到了一等效粘弹体,并用一种较好的Laplace变换的数值反演法求得了等效松弛函数和其它一些必要的辅助函数。用特征线法求得了等效粘弹体的应力和速度,进而得到了三层复合材料中心的应力、速度,进一步就得到了层中任意点的应力和速度。对于一个可由精确理论(射线理论)给出计算结果的问题,将粘弹比拟理论的结果和射线理论的结果进行了比较,结果表明,粘弹比拟理论对三层复合材料的瞬态波传播问题是相当成功的。

THE METHOD OF VISCOELASTIC ANALOGY FOR RANSIENT WAVE PROPAGATION IN LAYERED COMPOSITES

This paper develops the theory of viscoelastic analogy and uses the theory for transient wave propagation normal to the layering direction of a semi-infinite composite with three layers as a period. We have found an "equivalent" homogeneous viscoelastic material and obtained the "equivalent" relaxation function and some other "auxiliary" functions by a better method of numerical inversion of Laplace transform. By solving the transient waves in the "equivalent" viscoelastic medium by the characteristics method, we can obtain the stress and particle velocity at the layer centers of the composites, and then obtain the stress and particle velocity at any points in the composites through the "auxiliary" functions. For an illustrative problem, which can be solved by the exact ray theory, the comparison between the results of the viscoelastic analogy theory and those of the ray theory shows that the theory of viscoelastic analogy is very successful in soloving the transient waves in semi-infinite composites with a period of three layers.