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A frequency dependent rectangular plate finite dynamic element for high precision transverse vibration analysis of simply supported plates
Author(s) -
Downs B.
Publication year - 1991
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620310508
Subject(s) - eigenvalues and eigenvectors , finite element method , normal mode , vibration , transverse plane , square (algebra) , mathematical analysis , deflection (physics) , degrees of freedom (physics and chemistry) , element (criminal law) , frequency response , mathematics , geometry , structural engineering , physics , acoustics , engineering , classical mechanics , electrical engineering , quantum mechanics , political science , law
The need for adding to the many existing rectangular plate elements is justified and the inclusion of the twist parameter, in the degrees of freedom selected, is shown to be essential. Using a rational choice of parameters to form the deflection functions for a simply supported plate element, a constant term, sixteen degrees of freedom rectangular element is developed which is shown to predict exactly the first mode frequency and mode shape when used in whole plate modelling. The properties of this ‘dynamic’ element are combined with the properties of an existing ‘static’ element to obtain the frequency dependent properties of a ‘blended’ element. It is demonstrated that in order to obtain high accuracy in eigenvalue determination it is necessary to use three separate modellings of the plate using a square element and two rectangular elements which are oriented orthogonally. From 3 × 3 and 2 × 5 modelling, it is shown that the frequencies of the first 20 modes of a simply supported square plate, resulting from matrix eigenvalue determinations are obtainable within one per cent of the exact values. Modes 11 and 18 are determined exactly. Mode shape distortions associated with frequency errors are examined and shown to be minimal for the first 20 modes.