A theoretical solution for axially symmetric problems in elastodynamics

Abstract

This paper presents a theoretical solution for the basic equation of axisymmetric problems in elastodynamics. The solution is composed of a quasi-static solution which satisfies inhomogeneous boundary conditions and a dynamic solution which satisfies homogeneous boundary conditions. After the quasi-static solution has been obtained an inhomogeneous equation for dynamic solution is found from the basic equation. By making use of eigenvalue problem of a corresponding homogeneous equation, a finite Hankel transform is defined. A dynamic solution satisfying homogeneous boundary conditions is obtained by means of the finite Hankel transform and Laplace transform. Thus, an exact solution is obtained. Through an example of hollow cylinders under dynamic load, it is seen that the method, and the process of computing are simple, effective and accurate.