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Errors in response calculations for beams
Author(s) -
Wada H.,
Warburton G. B.
Publication year - 1985
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.4290130304
Subject(s) - newmark beta method , finite element method , cantilever , beam (structure) , direct integration of a beam , laplace transform , vibration , mathematical analysis , matrix (chemical analysis) , mathematics , structural engineering , acceleration , normal mode , damping matrix , engineering , physics , classical mechanics , stiffness matrix , acoustics , materials science , composite material
When the finite element method is used to idealize a structure, its dynamic response can be determined from the governing matrix equation by the normal mode method or by one of the many approximate direct integration methods. In either method the approximate data of the finite element idealization are used, but further assumptions are introduced by the direct integration scheme. It is the purpose of this paper to study these errors for a simple structure. The transient flexural vibrations of a uniform cantilever beam, which is subjected to a transverse force at the free end are determined by the Laplace transform method. Comparable responses are obtained for a finite element idealization of the beam, using the normal mode and Newmark average acceleration methods; the errors associated with the approximate methods are studied. If accuracy has priority and the quantity of data is small, the normal mode method is recommended; however, if the quantity of data is large, the Newmark method is useful.