Concerning an approach to identifying the Lame parameters of an elastic functionally graded cylinder

摘要

Based on the general linear elasticity relations, an axisymmetric problem on the steady-state oscillations of a functionally graded hollow cylinder is formulated. The Lame parameters are considered variable in radial coordinate. Oscillations are caused by the distributed load applied to the outer part of the cylinder boundary. Using the variable separation method, the direct problem on determining the radial and longitudinal components of the displacement field is investigated. The influence of the laws of variation for the Lame parameters on acoustic characteristics is analysed. The inverse coefficient problem on the identification of the variable Lame parameters from the data on the amplitude-frequency characteristic is stated. Based on the weak formulation of the problem for an elastic inhomogeneous body, a general linearised relation for the desired and given characteristics is obtained. A system of the Fredholm integral equations of the first kind is formulated with respect to two unknown corrections to the restored laws of the Lame parameters change. The solution is built by means of an iterative process. A reconstruction of various laws of changing the Lame parameters is carried out. The accuracy of the presented algorithm is estimated, and recommendations for the most efficient implementation of the reconstruction procedure are proposed.