Inverse problem of thermoelectricity for a functionally graded layer

A. O. Vatulyan ; S. A. Nesterov

Vladikavkazskij matematičeskij žurnal, Tome 26 (2024) no. 1, pp. 68-84

Résumé

The formulation of the inverse problem of identification the variable material characteristics of a transversely inhomogeneous thermoelectroelastic layer, the lower face of which is rigidly pinched, shorted and maintained at zero temperature, and an unsteady load is applied on the upper non-electrodated face. Using the Fourier transform, the two-dimensional inverse problem is reduced to a number of one-dimensional problems similar to those for an elastic and thermoelastic rod with modified characteristics. A step-by-step approach is proposed to identify the material characteristics of the layer. Dimensionless direct problems after applying the Laplace transform are solved on the basis of the apparatus of Fredholm integral equations of the 2nd kind and the conversion of transformants based on the theory of residues. Using the linearization method, operator equations of the 1st kind are obtained to solve the inverse problems at each stage. Computational experiments have been carried out to reconstruct the material characteristics of a thermoelectroelastic layer, both in the absence of noise input information and at 1% noise. Effective time intervals for the identification of additional information have been identified. The analysis of the results of the identification of the thermomechanical characteristics of the layer is carried out.