Ungar微分变换在弹性动力学中的一个应用

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An Application of Ungar’s Differential Transform to Elastodynamics

摘要: 近些年来,在求解弹性波方面的一些问题时,许多著者都应用了Cagniard—de Hoop方法^[1][2].但是,在使用该法时,定要进行一些比较复杂的改变积分路径的工作.A.Ungar所提出的一种微分变换^[3~6]可以避免这种困难.本文应用Ungar微分变换来求解Lamb问题^[1][2]的一情形.

Abstract: In recent years, a lot of writers have used Cagniard-de Hoop's method^[1][2] to solve some problems of elastic wave. But it is a difficult and complicated task to change the path of integration when we use this method. A differential transform by A.Ungar^[3,6] can obviate this difficulty. In this paper, weuse Ungar's differential transform to solve a case of Lamb's problem^[1][2].

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[2]	Achenbach,J.D.,Wave Propagation in Elastic Solids,North-Holland(1973),298,289.
[3]	Ungar,A.,Wave generation in an elastic half-space by a normal point load moving uniformly over the free surface,International Journal of Engineering Science,14,10(1976),935-945.
[4]	Ungar,A.and N.I.Robinson,The application of the differential transform technique to point source problems of elasticity,International Journal of Engineering Science,15,3(1977), 157-170.
[5]	Ungar,A.,The propagation of elastic waves from moving normal point loads in layered media,Pure and Applied Geophysics.114,5(1976),845-861.
[6]	Ungar,A.,The differential transform technique for solving problems of wave propagation,in Modern Problems in Elastic Wave Propagation(edited by J.Miklowitz and J.D.Achenbach),John Wiley & Sons(1978).
[7]	Eason,G.,Dynamical problems of the theory of elasticity,in Application of Integral Transforms in the Theory of Elasticity(edited by I.N.Sneddon),Springer-Verlag(1975),318.