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Modelling approaches to the stress wave propagation in a cracked specimen
Kruisová, Alena ; Kopačka, Ján ; Kober, Jan
One of the essential tasks of non-destructive testing is to detect a crack in a specimen. It is well known that a component with a crack exposed to a harmonic excitation of a given frequency\nhas a nonlinear response as a function of the excitation amplitude. The focus of this paper is the numerical modelling of this phenomenon using the finite element method with the consideration\nof the contact constraint at the crack interface. In addition to the nonlinear transient dynamic problem solved by explicit time integration, a more efficient procedure based on the harmonic\nbalance method is developed. The results of numerical simulations are also compared with experimentally obtained data.
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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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The 2nd International Conference on Advanced Modelling of Wave Propagation in Solids
Kolman, Radek ; Berezovski, A. ; Kruisová, Alena
The proceeding of the 2nd International Conference on Advanced Modelling of Wave Propagation in Solids presents papers related to analytical, numerical and experimental studies of linear and non-linear waves in conventional, advanced and modern materials like metamaterials and auxetic materials, to strongly dispersive wave propagation in inhomogeneous solids and to waves in materials with microstructure, etc. The recent advances and properties of analytical and numerical approaches and strategies are also included. Theoretical, computational as well as experimental contributions on the wave propagation are related to the proceeding.
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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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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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Vliv volby konstitutivního vztahu na modelování šíření vln v předepjatém prostředí
Kruisová, Alena ; Plešek, Jiří ; Červ, Jan
Nejznámější konstitutivní vztah používaný v akustoelasticitě je rovnice druhého řádu vyjádřená pomocí Greenova -- Lagrangeova tenzoru přetvoření. Tento materiálový model je charakterizován vysokou citlivostí materiálových parametrů na malé chyby měření. Tato vlastnost vedla k návrhu nového materiálového modelu s konstitutivními vztahy druhého řádu, vyjádřeného pomocí logaritmického tenzoru přetvoření. Pro tento materiálový model byly odvozeny rychlosti šíření akustoelastických vln pro tři druhy homogenního předpjetí.
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