Isogeometric analysis of free vibration of simple shaped elastic samples.
The paper is devoted to numerical solution of free vibration problems for elastic bodies of canonical shapes by means of a spline based finite element method (FEM), called Isogeometric Analysis (IGA). It has an advantage that the geometry is described exactly and the approximation of unknown quantities is smooth due to higher-order continuous shape functions. IGA exhibits very convenient convergence rates and small frequency errors for higher frequency spectrum. In this paper, the IGA strategy is used in computation of eigen-frequencies of a block and cylinder as benchmark tests. Results are compared with the standard FEM, the Rayleigh-Ritz method, and available experimental data. The main attention is paid to the comparison of convergence rate, accuracy, and time-consumption of IGA against FEM and also to show a spline order and parameterization effects. In addition, the potential of IGA in Resonant Ultrasound Spectroscopy measurements of elastic properties of general anisotropy solids is discussed.
Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Dolejskova 5, 182 00 Prague, Czech Republic.
Radek
R
Kolman
Faculty of Engineering and Science, Department of Mechanical and Manufacturing Engineering, Aalborg University, Fibigerstræde 16, 9220 Aalborg, Denmark.
Sergey
S
Sorokin
Faculty of Applied Science, NTIS, University of West Bohemia, Univerzitni 8, 301 00 Pilsen, Czech Republic.
Bohumír
B
Bastl
Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Dolejskova 5, 182 00 Prague, Czech Republic.
Ján
J
Kopačka
Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Dolejskova 5, 182 00 Prague, Czech Republic.
Jiří
J
Plešek