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Accuracy in finite element computation for eigenfrequencies
Author(s) -
Ladeveze P.,
Pelle J. P.
Publication year - 1989
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.1620280815
Subject(s) - eigenvalues and eigenvectors , finite element method , discretization , mathematics , computation , subspace topology , dimension (graph theory) , upper and lower bounds , mathematical analysis , quotient , vibration , numerical analysis , constant (computer programming) , algorithm , pure mathematics , computer science , physics , thermodynamics , programming language , quantum mechanics
In this paper we propose an original numerical method to get upper and lower bounds for the eigenfrequencies of an elastic structure. This method is based on a ‘static’ formulation for eigenvalue problems built up from a new quotient R s which is defined on a load space. From R s properties, upper and lower bounds for the exact eigenfrequencies are proved. The application of the method requires the solution of an eigenvalue problem of finite dimension and the computation of a constant which is characteristic of the discretization subspace. Results of numerical tests are given for the vibration problem of an elastic clamped membrane.