In-plane free vibration of a two-cable network with multiple flexible cross-ties considering the effects of dynamic axial forces of the cables

Abstract

Equipping cross-ties on the cables of cable-stayed bridges to form a cable network is regarded as an effective measure to suppress large cable vibrations and has been realized in practical engineering. However, most of the existing studies on the suspended cable (small sag) network have ignored the contributions of dynamic axial forces to transverse forces of the cables. More importantly, the dimension of the characteristic matrix is relatively large. Therefore, the current study introduces the transfer matrix method (TMM) to solve the in-plane free vibration problem of a two-cable network with dynamic axial forces of the cables considered simultaneously. Compared with the methodology utilized by the previous studies, the dimension of the resulting characteristic matrix is smaller and is independent of the number of cross-ties. Three cases, i.e., a two-cable network with two cross-ties, with three cross-ties and with four cross-ties, are explored in detail. Their frequencies and mode shapes are compared with those obtained by finite element model (FEM) to demonstrate the validity of the results in this paper. Meanwhile, the effects of dynamic axial forces on the first two frequencies and mode shapes are analyzed. The results show that the contributions of dynamic axial forces should be taken into account in transverse forces when calculating the first two frequencies of the cable network with flexible cross-ties.