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Computational time reversal method based on finite element method: influence of temperature
Mračko, Michal ; Kolman, Radek ; Kober, Jan ; Převorovský, Zdeněk ; Plešek, Jiří
Time reversal method is used to focus elastic waves to the location of the original source and reconstruct its source time function. The procedure consists of two steps: Frontal task and Reversal task. In the Frontal task, the medium is excited by an arbitrary source, elastic waves propagate through a body of interest and the dynamic response at few points on boundary is recorded. In the second step (say the Reversal task) the response signal is reversed in time and transmitted back into the medium resulting in focusing in the original source location. It is of practical importance to investigate a case when the medium changes its properties between the frontal and reversal wave propagation steps. An example is a problem of transferring experimentally recorded data to a computational model, where discrepancies in geometry, elastic properties and boundary conditions are expected. Our motivation is to develop a methodology for computation of time reversal problems in commercial finite element software. The results prove that this method is extremely sensitive to the change of temperature and one have to pay special attention to tuning of elastic parameters relevant to the\nexperiment.
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On finite element modelling in time reversal problems
Mračko, Michal ; Kober, Jan ; Kolman, Radek ; Převorovský, Zdeněk ; Plešek, Jiří ; Masák, Jan ; Kruisová, Alena
In this paper we analyse suitability and accuracy of computational techniques in time reversal applications based on finite element method (FEM) for detection and localization of defects, cracks or other acoustic emission sources in bodies and structures. As it is known, a classical explicit integration scheme - central difference is reversible. The central difference scheme as a time integrator is widely used for linear and nonlinear finite element analyses and it is also implemented in commercial and open-source finite element software. In the paper properties of the explicit FEM in time reversal problems are studied and analysed. We use the standard Galerkin FEM formulation with linear shape functions, one-point Gauss integration and lumped mass matrix. Loading by the Ricker pulse was applied for modelling of the acoustic source in an elastic square domain. A special attention is paid to the choice of boundary conditions in reverse problem which keep the reversibility of problems of interest. Finally, we show the quality of refocusing of the original acoustic source.
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Comparative study of finite element method, isogeometric analysis, and finite volume method in elastic wave propagation of stress discontinuities
Berezovski, A. ; Kolman, Radek ; Blažek, Jiří ; Kopačka, Ján ; Gabriel, Dušan ; Plešek, Jiří
A comparative study of Finite Element Method, Isogeometric Analysis, and Finite Volume Method in numerical simulation of one-dimensional wave propagation problems of stress discontinuities in elastic solids is presented. The special attention is paid to accuracy, convergence, and stability of tested numerical methods and the appearance of spurious oscillations and damping effects occurring close to theoretical sharp wavefronts.
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