弹性动力学轴对称问题的理论解

本文给出了弹性动力学轴对称问题基本方程的一种理论解。它由满足非齐次边界条件的准静态解和满足齐次边界条件的动态解的叠加构成。在求得准静态解后,代入基本方程,得到动态解所需满足的非齐次方程。由相应的齐次方程的特征值问题,定义了有限Hankel变换。通过这种变换及Laplace变换,求得动态解,从而得到了一个完整的理论解。文中通过对一个实例求解,表明该方法求解过程简便,实用,求解结果精确。

A THEORETICAL SOLUTION FOR AXIALLY SYMMETRIC PROBLEMS IN ELASTODYNAMICS

The paper presents a theoretical solution for the basic equation of axial-ly symmetric problems in elastodynamics. The solution consists of a quasi-static solution which meets inhomogeneous boundary conditions and a dynamic solution which meets homogenerous boundary conditions. After the quasi-static solution has been solved, an inhomogenerous equation on dynamic solution is found from the basic equation. By making use of eigenvalue problem of homogenerous equation, the finite Hankel transform is defind. The dynamic solution which fulfils homogenerous boundary condition is obtained by means of the finite Hankel transform and Laplace transform. Thus, the theoretical solution is gained. Through an example of hollow circular cylinder, it is seen that the solving method, solving process and computing results are simple, useful and accurate.