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Differential Quadrature Analysis of Moving Load Problems

Part of: Numerical methods Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  27 May 2016

Xinwei Wang  and
Chunhua Jin
Xinwei Wang*
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Chunhua Jin*
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China School of Civil Engineering and Architecture, Nantong University, Nantong 224019, China
*
*Corresponding author. Email:wangx@nuaa.edu.cn (X. W. Wang), jinch@ntu.edu.cn (C. H. Jin)
*Corresponding author. Email:wangx@nuaa.edu.cn (X. W. Wang), jinch@ntu.edu.cn (C. H. Jin)
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Abstract

The differential quadrature method (DQM) has been successfully used in a variety of fields. Similar to the conventional point discrete methods such as the collocation method and finite difference method, however, the DQM has some difficulty in dealing with singular functions like the Dirac-delta function. In this paper, two modifications are introduced to overcome the difficulty encountered in solving differential equations with Dirac-delta functions by using the DQM. The moving point load is work-equivalent to loads applied at all grid points and the governing equation is numerically integrated before it is discretized in terms of the differential quadrature. With these modifications, static behavior and forced vibration of beams under a stationary or a moving point load are successfully analyzed by directly using the DQM. It is demonstrated that the modified DQM can yield very accurate solutions. The compactness and computational efficiency of the DQM are retained in solving the partial differential equations with a time dependent Dirac-delta function.

Keywords

Differential quadrature methodDirac-delta functionmoving point loaddynamic responsework-equivalent load

MSC classification

Secondary: 74S30: Other numerical methods 65M99: None of the above, but in this section
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 4 , August 2016 , pp. 536 - 555
Copyright
Copyright © Global-Science Press 2016 

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