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Dispersion errors for wave propagation in thin plate due to the finite element method
Kruisová, Alena ; Kolman, Radek ; Mračko, Michal
In modelling of wave propagation by finite element method, both the spatial and temporal discretization lead to dispersion errors. For 2D plane strain elements these errors can be stated analytically. These analytical relations derived for harmonical waves in the infinite continuum can be used for error estimation on an example of simulation of Lamb's wave in plate using the implicit time integration method. So the analytical relations for dispersion errors can serve for determination of element size and time step size in wave propagation.
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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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Finite element modeling of the signal propagation in a thin tube and comparison with experimental data
Kruisová, Alena ; Kolman, Radek ; Trnka, Jan ; Mračko, Michal
In finite element modeling of wave propagation problems, both the spatial and temporal discretization lead to dispersion errors. It means that the phase velocity of propagated wave is related to its frequency. In framework of temporal-spatial dispersion analysis, the time step size for implicit time integration method based on the Newmark method is proposed for linear and quadratic serendipity plane finite elements. In this paper, we verify the theoretical dispersion analysis by elastic wave propagation in thin tube, where experimental results are known. Such time step size was used in finite element modeling of the stress wave propagating in this thin steel tube, the results of simulations were compared with experimental results.
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Metodika pro modelování dynamických deju metodou konecných prvku - fáze II
Mochar, Dominik ; Mračko, Michal ; Gabriel, Dušan ; Kolman, Radek ; Kopačka, Ján
Zpráva navazuje na metodiku Z-1546/15 popisující základní metody, algoritmy a postupy pro numerické rešení MKP úloh rázové dynamiky pri vývoji komponent zbraní. V této práci byly testovány disperzní vlastnosti bilineárních ctyruzlových prvku s redukovanou integrací na úloze rázu dvou elastických válcu, pro které je k dispozici analytické rešení. Pozornost byla zamerena na zkoumání vlivu velikosti prvku a casového integracního kroku na presnost numerického rešení. Výsledky získané z MKP programu PMD, Abaqus a Ansys byly diskutovány a porovnány s analytickým rešením.
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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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