Volume 8, Issue 4

Adv. Appl. Math. Mech., 8 (2016), pp. 536-555.

Published online: 2018-05

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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.

74S30, 65M99

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@Article{AAMM-8-536, author = {Wang , Xinwei and Jin , Chunhua}, title = {Differential Quadrature Analysis of Moving Load Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {4}, pages = {536--555}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m844}, url = {http://global-sci.org/intro/article_detail/aamm/12102.html} }
TY - JOUR T1 - Differential Quadrature Analysis of Moving Load Problems AU - Wang , Xinwei AU - Jin , Chunhua JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 536 EP - 555 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2014.m844 UR - https://global-sci.org/intro/article_detail/aamm/12102.html KW - Differential quadrature method, Dirac-delta function, moving point load, dynamic response, work-equivalent load. AB -

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.

Xinwei Wang & Chunhua Jin. (2020). Differential Quadrature Analysis of Moving Load Problems. Advances in Applied Mathematics and Mechanics. 8 (4). 536-555. doi:10.4208/aamm.2014.m844
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