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 - <p style="text-align: justify;">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.</p>