Free vibration analysis of plates using least-square-based finite difference method

Shu, C., Wu, W. X., Ding, H. and Wang, C. M. (2007) Free vibration analysis of plates using least-square-based finite difference method. Computer Methods in Applied Mechanics and Engineering, 196 7: 1330-1343. doi:10.1016/j.cma.2006.09.008


Author Shu, C.
Wu, W. X.
Ding, H.
Wang, C. M.
Title Free vibration analysis of plates using least-square-based finite difference method
Journal name Computer Methods in Applied Mechanics and Engineering   Check publisher's open access policy
ISSN 0045-7825
Publication date 2007-01-10
Year available 2006
Sub-type Article (original research)
DOI 10.1016/j.cma.2006.09.008
Open Access Status Not yet assessed
Volume 196
Issue 7
Start page 1330
End page 1343
Total pages 14
Place of publication Amsterdam, Netherlands
Publisher Elsevier BV
Language eng
Abstract In this paper, we apply the two-dimensional least-square-based finite difference (LSFD) method for solving free vibration problems of isotropic, thin, arbitrarily shaped plates with simply supported and clamped edges. Using the chain rule, we show how the fourth-order derivatives of the plate governing equation can be discretized in two or three steps as well as how the boundary conditions can be implemented directly into the governing equation. By analyzing vibrating plates of various shapes and comparing the solutions obtained against existing results, we clearly demonstrate the effectiveness of LSFD as a mesh-free method for computing vibration frequencies of generally shaped plates accurately.
Keyword Chain rule
Finite difference
Least squares
Plates
Vibration
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: ResearcherID Downloads
School of Civil Engineering Publications
 
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Citation counts: TR Web of Science Citation Count  Cited 14 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 16 times in Scopus Article | Citations
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