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Concerning an approach to identifying the Lamé parameters of an elastic functionally graded cylinder
Author(s) -
Dudarev Vladimir V.,
Vatulyan Alexander O.,
Mnukhin Roman M.,
Nedin Rostislav D.
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6428
Subject(s) - mathematics , mathematical analysis , inverse problem , cylinder , elasticity (physics) , boundary value problem , rotational symmetry , fredholm integral equation , linear elasticity , variable (mathematics) , displacement field , integral equation , displacement (psychology) , geometry , finite element method , materials science , physics , composite material , thermodynamics , psychology , psychotherapist
Based on the general linear elasticity relations, an axisymmetric problem on the steady‐state oscillations of a functionally graded hollow cylinder is formulated. The Lamé 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 Lamé parameters on acoustic characteristics is analysed. The inverse coefficient problem on the identification of the variable Lamé 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 Lamé parameters change. The solution is built by means of an iterative process. A reconstruction of various laws of changing the Lamé 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.