楔形杆中弹塑性波的一种渐近展开式

据我们所知,楔形杆中弹塑性波尚未有很好的分析方法。对弹性波有文献1,2]等,其中文献1]研究了圆锥壳轴向撞击的波动问题,发现楔形杆是其很好的近似,故后者的研究对圆锥壳具有重要意义。文中采用拉氏变换方法求得两种特殊情况下(波阵面和冲击端附近,的渐近解,而一般情形下的解未能得到。也有人用WKB方法讨论了类似问题,但仅限于波长很短的情形,局限性很大。另外,文献5]用正则摄动法研究了楔形杆的自振问题。 本文针对楔形杆(和圆锥壳)的特点建议了一种渐近展开式,并求解了弹性波和弹塑性波问题,并与其他一些方法及其结果进行了比较。

AN ASYMPTOTIC EXPANSION FOR ELASTIC-PLASTIC WAVES IN A WEDGE ROD

As far as we know,there are no satisfactory analytic methods to the elastic-plastic wave problem in a wedge rod.In the paper 1],the elastic wave propagation in a conical shell has been studied.and it has been found that the wedge rod is a good approximation for a conical shell under axial impulsive loading.In I],the Laplace transformation was used to obtain an asymptotic solution for two special cases (the neighbourhoods of the wave front and the impact end).Also,the WKB methods has been employed to discuss this kind of problems,which is valid only when the wave-length is very short (see 3.4]).In this paper,an asymptotic expansion is proposed in accordance with the peculiarities of the wedge rod (and the conical shell),and the elastic and elastic-plastic wave problem in a wedge rod are discussed.