Please use this identifier to cite or link to this item: https://doi.org/10.1016/S0020-7403(01)00052-2
Title: In-plane vibration analyses of circular arches by the generalized differential quadrature rule
Authors: Liu, G.R. 
Wu, T.Y. 
Keywords: Collocation method
Differential equation
Differential quadrature method
Free vibration
Polynomial approximation
Structural arch
Issue Date: Nov-2001
Source: Liu, G.R., Wu, T.Y. (2001-11). In-plane vibration analyses of circular arches by the generalized differential quadrature rule. International Journal of Mechanical Sciences 43 (11) : 2597-2611. ScholarBank@NUS Repository. https://doi.org/10.1016/S0020-7403(01)00052-2
Abstract: In-plane free vibrations of circular arches are investigated using the generalized differential quadrature rule (GDQR) proposed recently. The Kirchhoff assumptions for thin beams are considered, and the neutral axis is taken as inextensible. Several examples of arches with uniform, continuously varying, and stepped cross-sections are presented to illustrate the validity and accuracy of the GDQR. The necessary domain decomposition technique is used for some cases. The obtained frequencies are compared with those calculated from a number of other approaches from the Rayleigh-Ritz, Rayleigh-Schmidt and Galerkin methods to the finite element technique and the cell discretization method. The GDQR frequencies are always greater than those obtained from the cell discretization method that produces the lower bounds to the exact results, and are also in agreement with the upper bounds to the exact results. © 2001 Elsevier Science Ltd. All rights reserved.
Source Title: International Journal of Mechanical Sciences
URI: http://scholarbank.nus.edu.sg/handle/10635/60548
ISSN: 00207403
DOI: 10.1016/S0020-7403(01)00052-2
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