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Vibration analysis for elastic multi‐beam structures by the C 0 ‐continuous time‐stepping finite element method
Author(s) -
Lai Junjiang,
Huang Jianguo,
Shi Zhongci
Publication year - 2010
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1143
Subject(s) - discretization , finite element method , galerkin method , mathematics , mathematical analysis , nonlinear system , hermite polynomials , vibration , beam (structure) , displacement field , spectral element method , numerical analysis , physics , geometry , mixed finite element method , quantum mechanics , thermodynamics , optics
Some C 0 ‐continuous time‐stepping finite element method is proposed for investigating vibration analysis of elastic multi‐beam structures. In the time direction, the C 0 ‐continuous Galerkin method is used to discretize the generalized displacement field. In the space directions, the longitudinal displacements and rotational angles on beams are discretized using conforming linear elements, while the transverse displacements on beams are discretized by the Hermite elements of third order. The error of the method in the energy norm is proved to be O ( h + k 3 ), where h and k denote the mesh sizes of the subdivisions in the space and time directions, respectively. The finite difference analysis in time is developed to discuss the spectral behavior of the algorithms as well as their dissipation and dispersion properties in the low‐frequency regime. The method has also been extended to study some nonlinear problems. A number of numerical tests are included to illustrate the computational performance of the method. Copyright © 2008 John Wiley & Sons, Ltd.