A dynamic model for a defective periodic viaduct under harmonic seismic waves

An analytical model for the dynamic response of a defective periodic viaduct (DPV) (i.e. an infinite periodic viaduct containing a defective span) to harmonic seismic waves is proposed. In the proposed model, the viaduct is divided into three parts – left and right semi-infinite ordered periodic viaducts (SOPVs) and the defective span. The total responses of the left and right SOPVs consist of two parts – a free part and a scattered part. The free-part responses are associated with the forced vibration of the corresponding SOPVs due to seismic waves, while the scattered-part responses are relevant to the scattered characteristic waves of the ordered periodic viaduct (OPV) in the SOPVs. The amplitudes of the scattered characteristic waves in the left and right SOPVs can be determined by using the transfer matrix of the defective span. The numerical results suggest that when a DPV is subjected to harmonic seismic waves, a resonance-type response will occur. It was also found that, for the DPV, there are two kinds of resonance frequencies: the frequencies associated with the corresponding OPV and additional frequencies due to the presence of the defective span.