Differential quadrature procedure for in-plane vibration analysis of variable thickness circular arches traversed by a moving point load

Point discretization methods such as the differential quadrature method (DQM) are well known to have difficulties in solving partial differential equations that involve the Dirac-delta function because the Dirac-delta function is a generalized singularity function and it cannot be discretized directly using the DQM. To overcome this difficulty, a simple differential quadrature methodology is proposed in this study, where the Dirac-delta function is expanded into a Fourier trigonometric series. By expanding the Dirac-delta function into a Fourier trigonometric series, this singular function is treated as non-singular functions, which can be discretized easily and directly using the DQM. The applicability of the proposed method is demonstrated by the in-plane vibration analysis of variable thickness circular arches traversed by a moving point load. The numerical results show that the proposed method is highly accurate and reliable.