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Symmetric modes of vibration for A circular plate using finite dynamic elements
Author(s) -
Fergusson N. J.,
Pilkey W. D.
Publication year - 1993
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290220504
Subject(s) - finite element method , vibration , rotational symmetry , stiffness , matrix (chemical analysis) , stiffness matrix , mathematics , mathematical analysis , structural engineering , taylor series , dynamic problem , beam (structure) , geometry , physics , engineering , mathematical optimization , materials science , acoustics , composite material
The dynamic element method has been shown previously to provide a computational advantage over the ordinary finite element method for various beam elements. The Taylor expansions are computed here for the dynamic shape functions (two terms) and dynamic stiffness matrix (four terms) for the axisymmetric vibrations of an annular plate element. The complicated matrices which result are made more tractable by expressing them as power series in powers of the aspect ratio. The percentage error in the natural frequencies is then calculated using both the two‐ and the three‐term dynamic stiffness matrix, demonstrating the increased accuracy for a given number of elements.