中文摘要：

介绍两种方法,即沿特征线的有线差分数值方法、采用Laplace变换及数值反变换的半解析方法,分析典型一维粘弹性应力波传播问题。对这两种方法所得结果进行比较表明：特征线差分方法将材料的非弹性响应部分分解,可以有效处理强间断扰动在非弹性（粘性）介质中的传播问题,是一种较便利的分析工具;而Laplace变换方法具有简洁和快速特点,对于一些线性耦合边界问题结合数学分析软件MATHEMATICA可以迅速得到初步答案。

英文摘要：

Two approaches for analyzing the viscoelastic stress wave propagations in a bar are provided. The first approach applies the finite difference scheme to the characteristic differential equations derived from the governing wave propagation equations. The second one uses the Laplace transform and the numerical inverse technique to solve the equations directly. It is shown that the characteristic finite difference scheme effectively handles strong discontinuities on a wave front as well as the material’s non-elasticity, while the Laplace transform approach is concise and neat in a mathematical form, and can be used effectively in combination with mathematical software.