Differential Quadrature Analysis of Moving Load Problems (Advances in Applied Mathematics and Mechanics, 2018)
The differential quadrature method (DQM) has been successfully used in avariety of fields. Similar to the conventional point discrete methods such as the collocationmethod and finite difference method, however, the DQM has some difficultyin dealing with singular functions like the Dirac-delta function. In this paper, twomodifications are introduced to overcome the difficulty encountered in solving differentialequations with Dirac-delta functions by using the DQM. The moving point loadis work-equivalent to loads applied at all grid points and the governing equation isnumerically integrated before it is discretized in terms of the differential quadrature.With these modifications, static behavior and forced vibration of beams under a stationaryor 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 compactnessand computational efficiency of the DQM are retained in solving the partialdifferential equations with a time dependent Dirac-delta function.