Premium
A discontinuous enrichment method for the efficient solution of plate vibration problems in the medium‐frequency regime
Author(s) -
Massimi Paolo,
Tezaur Radek,
Farhat Charbel
Publication year - 2010
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.2888
Subject(s) - discretization , lagrange multiplier , biharmonic equation , finite element method , mathematics , mathematical analysis , vibration , displacement (psychology) , transversal (combinatorics) , physics , mathematical optimization , boundary value problem , acoustics , psychology , psychotherapist , thermodynamics
A discontinuous enrichment method (DEM) is presented for the efficient discretization of plate vibration problems in the medium‐frequency regime. This method enriches the polynomial shape functions of the classical finite element discretization with free‐space solutions of the biharmonic operator governing the elastic vibrations of an infinite Kirchhoff plate. These free‐space solutions, which represent flexural waves and decaying modes, are discontinuous across the element interfaces. For this reason, two different and carefully constructed Lagrange multiplier approximations are introduced along the element edges to enforce a weak continuity of the transversal displacement and its normal derivative, and discrete Lagrange multipliers are introduced at the element corners to enforce there a weak continuity of the transversal displacement. The proposed DEM is illustrated with the solution of sample plate vibration problems with different types of harmonic loading in the medium‐frequency regime, away from and close to resonance. In all cases, its performance is found to be significantly superior to that of the classical higher‐order finite element method. Copyright © 2010 John Wiley & Sons, Ltd.