Structures from inhomogeneous materials are widely used in various fields of technology with large thermomechanical loads. The efficiency of use of such materials depends on the knowledge of exact laws of inhomogeneity, which requires solution of inverse coefficient thermoelasticity problems. In the present work, we give versions of statement of inverse thermoelasticity problems for an inhomogeneous cylindrical pipe. Investigation of the primal problem on radial oscillations of the pipe is reduced to solution of a system of ordinary differential equations of 1st order in Laplace transforms on the basis of the targeting method and the employment of the inversion technique implemented in accordance with the Durbin method. For solution of a nonlinear inverse problem on the basis of the linearization method, we construct an iterative process each stage of which is used for solution of the Fredholm integral equation of the 1st kind. Consideration is given to specific examples of reconstruction of thermomechanical characteristics of an inhomogeneous cylinder. Computational experiments show the efficiency of this approach to reconstruction of different inhomogeneity laws.
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 88, No. 4, pp. 951–959, July–August, 2015.
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Vatul′yan, A.O., Nesterov, S.A. On Determination of Inhomogeneous Thermomechanical Characteristics of a Pipe. J Eng Phys Thermophy 88, 984–993 (2015). https://doi.org/10.1007/s10891-015-1274-7
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DOI: https://doi.org/10.1007/s10891-015-1274-7