Out-of-plane natural vibration characteristic and parameter analysis of curved girders based on DQM

Based on the DQM (Differential Quadrature Method), the frequency equations and boundary conditions of curved girder are discretized respectively. By the choice of the unequal spacing form of the sampling grid points and the replaced equation approach of boundary conditions, the out-of-plane natural vibration characteristic of the one-span circular curved girder and the one-span cyclotron transition curved girder are computed respectively. Through a comparison with the exact solutions, the high effectiveness of DQM is verified and the influence of grid point quantity on the solving precision is discussed. Based on the solution of natural vibration characteristic of curved girder, the influences of stiffness ratio of bending and torsion, warping coefficient and boundary constraint form on natural vibration frequency of curved girder are studied respectively and the parameter influence laws of circular curved girder and cyclotron transition curved girder are compared. The research shows that the natural vibration characteristic of curved girder can be computed conveniently and efficiently by the DQM and the stiffness ratio of bending and torsion, warping coefficient and boundary constraint form have obvious influence on the vibration frequency of curved girder. The computation results show that the fundamental frequencies of the two types of curved girders are both reduced with the decrease of boundary constraint conditions and the parameter influence laws are similar in most boundary constraint conditions; however, the parameter influence of the cantilever type cyclotron transition curved girder reflects a reversed law compared to the most boundary constraint conditions.