Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.cma.2006.09.008
Title: Free vibration analysis of plates using least-square-based finite difference method
Authors: Shu, C. 
Wu, W.X.
Ding, H.
Wang, C.M. 
Keywords: Chain rule
Finite difference
Least squares
Plates
Vibration
Issue Date: 10-Jan-2007
Citation: Shu, C., Wu, W.X., Ding, H., Wang, C.M. (2007-01-10). Free vibration analysis of plates using least-square-based finite difference method. Computer Methods in Applied Mechanics and Engineering 196 (7) : 1330-1343. ScholarBank@NUS Repository. https://doi.org/10.1016/j.cma.2006.09.008
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. © 2006 Elsevier B.V. All rights reserved.
Source Title: Computer Methods in Applied Mechanics and Engineering
URI: http://scholarbank.nus.edu.sg/handle/10635/60369
ISSN: 00457825
DOI: 10.1016/j.cma.2006.09.008
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