Publication Type

Journal Article

Publication Date

2009

Abstract

The occurrence of spurious complex eigenvalues is a serious stability problem in many differential quadrature methods (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 (LaDQM). The other has banded matrices without using fictitious grids to facilitate boundary conditions, called finite difference differential quadrature methods (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 (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

Discipline

Physical Sciences and Mathematics

Research Areas

Quantitative Finance

Publication

International Journal of Engineering and Applied Sciences

Volume

1

Issue

4

First Page

1

Last Page

25

ISSN

2010-3980

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