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Analysis of classical and spectral finite element spatial discretization in one-dimensional elastic wave propagation
Kolman, Radek ; Plešek, Jiří ; Okrouhlík, Miloslav ; Gabriel, Dušan
The spatial discretization of continuum by finite element method introduces the dispersion error to numerical solutions of stress wave propagation. For higher order finite elements there are the optical modes in the spectrum resulting in spurious oscillations of stress and velocity distributions near the sharp wavefront. Spectral finite elements are of h-type finite element, where nodes have special positions along the elements corresponding to the numerical quadrature schemes, but the displacements along element are approximated by Lagrangian interpolation polynomials. In this paper, the classical and Legendre and Chebyshev spectral finite elements are tested in the one-dimensional wave propagation in an elastic bar.
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Determination of elastic moduli by the resonant ultrasound spectroscopy method
Kolman, Radek ; Plešek, Jiří ; Landa, Michal
An optimization method for the determination of elastic moduli by resonant ultrasound spectrocopy (RUS) was proposed. All components of the fourth-order tensor of elastic moduli for a general anisotropic material is determined from the knowledge of the resonance responce(spectrum) of the mechanical system. This spectrum is obtained from experimental measurements, using the RUS method on the prismatic specimen. For the iterative computation of elastic moduli an identification algorithm based on the direct iteration method is used. Spatial discretisation is performed by the finite element method.
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