Dynamic Response of a Defected Periodic Viaduct to a Moving Point Load

Abstract

A defected periodic viaduct (DPV) is an infinite viaduct consisting of a left and a right semi-infinite ordered periodic viaducts (OPV) and one or several in-between defected spans different from the standard span of the OPV. Currently, no methodology is available in the literature for assessing the dynamic response of a DPV to a moving load, as the presence of the defected spans breaks the periodicity of the OPV. In this study, a new FEM model for estimating the dynamic response of a DPV with one defected span to a moving load is proposed. To establish the model, the time-space domain (TSD) moving load is decomposed into the sum of its constituent frequency wavenumber domain (FWD) load components first. For the DPV subjected to the FWD load component, the response of the left and right semi-infinite OPVs of the DPV can be divided into two parts, namely, the free wave field and the scattered wave field. To determine the free wave field of the left and right semi-infinite OPVs of the DPV, the FEM equations for an individual span of the viaduct are established and applied to the two OPVs. The scattered wave field in the two semi-infinite OPVs consists of the characteristic waves of the OPV and can be determined using the FEM eigenvalue equations for the OPV free of external loads. Applying the span FEM equations to the defected span and using the expressions for the free wave field and the scattered wave field yield the FWD response of the DPV. The time-space domain response of the DPV can then be retrieved by superposing all the FWD responses of the DPV. Numerical simulations are conducted to investigate the influence of the defected span on the dynamic response of the DPV. For the DPV, there are two kinds of the resonant frequencies, namely, the resonant frequencies common to the corresponding OPV and the additional resonant frequencies due to the presence of the defected span. In some cases, the magnitudes of the responses at the additional resonant frequencies may be larger than those at the common resonance frequencies. Therefore, when conducting the design for a periodic viaduct, it is important to account for the influence of the defected span on the dynamic response of the periodic viaduct.