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<p>The inverse problem of poroelasticity for a&#xa0;rod within the Cowin-Nunziato model is investigated. Vibrations of a&#xa0;rigidly clamped elastic rod with voids under the action of a&#xa0;non-stationary mechanical load are considered. The direct problem in the Laplace transform space is solved based on the apparatus of Fredholm integral equations of the 2nd kind. The inversion of the transformants is performed based on the residue theory. Verification of the numerical solution of the direct problem for a&#xa0;homogeneous rod was carried out by comparison with a&#xa0;finite element solution in the FlexPDE package. The influence of power-law inhomogeneities of the physical and mechanical characteristics on the displacement is investigated. For solving the inverse problem, operator equations of the 1st kind were obtained. To simplify its solution, the class of sought reconstructed characteristics was narrowed down to polynomial functions. The polynomial coefficients were refined by solving a&#xa0;system of algebraic equations arising from the discretization of the operator equations. The physical and mechanical characteristics were refined stepwise during the iterative process: first among constants, then linear, and then quadratic functions. The proposed approach showed fast convergence of the iterative scheme with a&#xa0;small reconstruction error.</p>

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Identification of Inhomogeneous Characteristics of an Elastic Rod with Voids

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • Sergey A. Nesterov,
  • Vladimir V. Dudarev

摘要

The inverse problem of poroelasticity for a rod within the Cowin-Nunziato model is investigated. Vibrations of a rigidly clamped elastic rod with voids under the action of a non-stationary mechanical load are considered. The direct problem in the Laplace transform space is solved based on the apparatus of Fredholm integral equations of the 2nd kind. The inversion of the transformants is performed based on the residue theory. Verification of the numerical solution of the direct problem for a homogeneous rod was carried out by comparison with a finite element solution in the FlexPDE package. The influence of power-law inhomogeneities of the physical and mechanical characteristics on the displacement is investigated. For solving the inverse problem, operator equations of the 1st kind were obtained. To simplify its solution, the class of sought reconstructed characteristics was narrowed down to polynomial functions. The polynomial coefficients were refined by solving a system of algebraic equations arising from the discretization of the operator equations. The physical and mechanical characteristics were refined stepwise during the iterative process: first among constants, then linear, and then quadratic functions. The proposed approach showed fast convergence of the iterative scheme with a small reconstruction error.