Solution of the problem of diffraction of a plane acoustic pulse on an elastic inhomogeneous cylinder using the finite element method

A. E. Belkin   ; D. R. Biryukov

Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2024), pp. 68-83

Résumé

The article poses the problem of scattering a finite plane non-stationary acoustic pulse by an elastic inhomogeneous isotropic cylinder located in an ideal fluid. To solve the problem, the integral Fourier transform was used. To solve the problem, the space is divided into an external region, in which the image of the desired scattered wave is sought in the form of an infinite series with unknown coefficients, and an internal region containing an elastic cylinder and subject to discretization. The solution of a system of linear algebraic equations, which is constructed on the basis of a finite element model in accordance with the Galerkin method, allows one to determine the image coefficients of the scattered wave. The problem and the algorithm for solving it are of interest for further study of the possibility of determining scattered wave fields in cases in which it is not possible to use analytical methods.

Détail

Keywords: finite element method, system of linear equations, acoustic pulse, unsteady wave, elastic cylinder, inhomogeneous cylinder, isotropic cylinder.

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