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Spectral Super Elements for Beams with Arbitrary Cross Section
Author(s) -
Greim Axel,
Müller Gerhard
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900043
Subject(s) - ansatz , finite element method , cross section (physics) , mathematical analysis , discretization , eigenvalues and eigenvectors , beam (structure) , fourier transform , mathematics , physics , wavenumber , mixed finite element method , geometry , optics , quantum mechanics , thermodynamics
Spectral Super Elements are semi‐analytical elements for the calculation of the wave propagation in structures with a constant cross section. They base on a finite element discretization in the cross‐sectional directions and wave functions as ansatz for the longitudinal direction. No discretization in the latter direction has to be carried out and therefore the number of degrees of freedom is independent of the length the structure. The wave functions used as ansatz are gained as eigenvalues (wave numbers) and –vectors (wave forms) from a quadratic eigenvalue problem of the infinite structure (in longitudinal direction). The infinite structure is reduced to a 2D problem with the help of a Fourier transformation in longitudinal direction. This method is called Waveguide Finite Element Method or 2,5D Finite Element Method in literature. In this study we compare the performance of Spectral Super Elements for beams with arbitrary cross sections with analytical solutions for the Euler‐Bernoulli beam at low frequencies and with results form a 3D Finite Element analysis with commercial software for higher frequencies.