有限亨克尔(Hankel)变换及其应用

本文主要是把有限变换式的概念,推广到亨克尔变换式的情形,建立相应的反演定理,并利用它求解关于具有轴对称性系统的边值问题。这一类型的问题,通常是采用拉普拉斯变换的方法求解,但此种方法很冗长,且往往要计算复杂的围道积分。而本文所要叙述的有限亨克尔变换的方法,却比较快,而且容易使用,它可避免用留数计算围道积分。

FINITE HANKEL TRANSFORM AND ITS APPLICATION

This paper shows to extend the use of the method of finite transform to Hankel transform. The Kernel "K(p,x)" of the formula of transforma- tion a_a~b k(p,x)f(x)dx" is one of the Solution of the Bessel Equation, The introduction of the transform of the kind may be used to Simplify the pro- cess of the solutions of the initial value problem and boundary value problem in the elastic theory, The paper makes use of Finite Hankel transform and its inversion formula to solve three examples of boundary value prob- lems involved in the axisymmetric system. The advantage of the application of the method, in comparison with that of the Laplace trantform in com- mon use is to avoid using residue calculation of the complicated contour ntegral.