On the Accuracy and Stability of a Variety of Differential Quadrature Formulations for the Vibration Analysis of Beams

Authors : C. H. W. Ng, Y. B. Zhao, Y. Xiang, G. W. Wei

Pages : 1-25

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Publication Date : 2009-12-01

Article Type : Research Paper

Abstract :The occurrence of spurious complex eigenvalues is a serious stability problem in many differential quadrature methods insert ignore into journalissuearticles values(DQMs);. This paper studies the accuracy and stability of a variety of different differential quadrature formulations. Special emphasis is given to two local DQMs. One utilizes both fictitious grids and banded matrices, called local adaptive differential quadrature method insert ignore into journalissuearticles values(LaDQM);. The other has banded matrices without using fictitious grids to facilitate boundary conditions, called finite difference differential quadrature methods insert ignore into journalissuearticles values(FDDQMs);. These local DQMs include the classic DQMs as special cases given by extending their banded matrices to full matrices. LaDQMs and FDDQMs are implemented on a variety of treatments of boundary conditions, distributions of grids insert ignore into journalissuearticles values(i.e., uniform grids and Chebyshev grids);, and lengths of stencils. A comprehensive comparison among these methods over beams of six different combinations of supporting edges sheds light on the stability and accuracy of DQMs
Keywords : Stability analysis, Local adaptive differential quadrature method, Differential quadrature method, Beam, Vibration analysis