Effects of longitudinal girder vibration on non-linear cable responses in cable-stayed bridges

Abstract

In order to ascertain the effects of longitudinal girder vibration on the non-linear cable responses in cable-stayed bridges, this study established a mechanical model of a cable which is subjected to three excitations at each anchorage. Non-linear governing equations were derived by Galerkin method and solved numerically. Three longitudinal girder vibration amplitudes were selected to illustrate their effect on cable non-linear response under primary and sub-harmonic resonance. The numerical results show that partially releasing the longitudinal constraint between the girder and pylons ensures that longitudinal girder vibration eases cable vibrations. This provides scientific basis for designing cable-stayed bridge as floating or half-floating system from a non-linear vibrations of view. Two basic and mutually orthogonal excitation mechanisms were identified under the sub-harmonic resonance: external excitation and parametric excitation. Effects of global excitation amplitude and cable inclined angle on response distribution under sub-harmonic resonance were found.

Nonlinear vibrations of CFRP cables excited by periodic motions of supports in cable-stayed bridges

“…In this model, the curve of the gravitational sag of the cable is assumed as a parabola. The two supports are subjected to excitations at horizontal, vertical, and transverse directions simultaneously (Sun et al., 2017). The excitations are denoted by X , Y , and Z which refer to the global coordination O-XYZ .…”

“…One of the typical global vibration modes of cable-stayed bridges is illustrated in Figure 2. Actually, the beam end of the cables is subjected to longitudinal excitations X b (Sun et al., 2017). However, large X b generally appears in longitudinal floating modes of cable-stayed bridges.…”

“…They developed theoretical models for the vibrations of the cables subjected to support excitations, respectively. In general, vibration models can be classified into a single-cable vibration model (Lilien and Pinto Da Costa, 1994; Chen et al., 2002; Sun et al., 2003; Wu et al., 2003; Mei et al., 2007; Ying et al., 2007; Wang and Zhao, 2009; Kang et al., 2016; Ouni and Kahla, 2012; Brzakala and Herbut, 2014; Sun et al., 2014; Qian et al., 2014; Guo et al., 2016; Warminski et al., 2016) and cable-deck coupling vibration model (Luo et al, 2010; Kang et al., 2012; Sun et al., 2017). In addition, support excitations include the following: horizontal excitation at the upper support of the cable, vertical excitation at the lower support or axial excitation.…”

“…In addition, support excitations include the following: horizontal excitation at the upper support of the cable, vertical excitation at the lower support or axial excitation. Only a few researchers considered the combination of horizontal excitation at the upper support and vertical excitation at the lower support (Ying et al., 2007; Mei et al., 2007; Sun et al., 2017). The governing equations were discretized with the Galerkin method and then solved with a numerical time integration algorithm.…”

“…In general, the cables were assumed to be subjected to excitation at the upper anchorage or lower anchorage in most previous studies. In fact, the upper and lower anchorages are subjected to excitations at horizontal, vertical, and transverse directions simultaneously (Sun et al., 2017). Moreover, many researches only focused on in-plane parametric vibrations of cables.…”