In‐plane free vibrations of shallow cables with cross‐ties

Abstract

Summary Connecting stay cables with cross‐ties is the most promising solution for vibration control of long cables in cable‐stayed bridges. Existing studies have been focusing on the influences of the cross‐tie configurations and properties on the dynamics of the formed cable networks, mostly based on the taut‐string model of cables. However, the cross‐ties are particularly aimed at long cables whose in‐plane vibrations can be significantly affected by the sag effect. This paper therefore presents an analytical method to investigate free in‐plane vibrations of shallow cable networks with cross‐ties, using the linear theory of shallow cables. A two‐shallow‐cable network with one viscoelastic cross‐tie is studied in detail to appreciate the sag effect on the dynamics of the cable network. It is shown that the sag effect couples vibrations of the cable segments divided by the cross‐ties and changes the modal interactions substantially. When the cross‐tie is rigid, curve veering occurs between frequency curves of the system with respect to varying cross‐tie location, as compared with curve intersection in the absence of the sag effect. When the cross‐tie is flexible, generally, mode shapes of the cable segments and the whole cable are not antisymmetric nor symmetric, and the sag then affects nearly all the vibration modes. Furthermore, taking into account the damping effect of the cross‐tie, the frequency loci in the complex plane regarding the increment of cross‐tie damping coefficient can still be categorized by the corresponding undamped and clamped frequencies while the modal interaction becomes more complicated. Quantitatively speaking, when the sag parameter is in the practical range of existing cable‐stayed bridges, the first and second vibration modes of the cable networks are considerably affected and need to be considered for practice.

In‐plane dynamic behaviors of two‐cable networks with a pretensioned cross‐tie

“…Note that the cable sag only has a considerable influence on the first mode for most stay cables in cable-stayed bridges. 15,34 As the mode order increases, the effect of cross-tie pretension on the cable modal frequency becomes more significant. Besides, when the position of the pretensioned cross-tie is close to the midpoint of the cable, the effect of cross-tie pretension on cable tension is more obvious as analyzed at the beginning of this section, which further makes the cable frequencies increase more significantly.…”

“…These characteristics are different from those observed in previous studies where the pretension of cross-ties is ignored, for example, the study on shallow cable networks. 34 The mode shapes in Figure 6 are discussed to further understand such behaviors. In Figure 6, the parameters are κ ¼ 10 and μ ¼ 0:3.…”

“…[30][31][32][33] Recently, cable sag has been considered for the first time in the framework of complex modal analysis. 34 The effect of cable bending stiffness on the modal response of cable networks has also been studied. 35,36 Practical application of cross-ties in existing bridges appeared much earlier than the comprehensive theoretical investigation of interconnected cable systems, and experiences show that cross-ties are effective in suppressing various types of cable vibrations.…”

“…The cable bending stiffness is ignored in the modeling as it is negligible for the long stays which are desirable to be interconnected for vibration control. 34 The rest of this paper is organized as follows. Section 2 formulates the characteristic equation of a two-cable system with a cross-tie considering the pretension in the cross-tie, via complex modal analysis method.…”

Multimode cable vibration control using a viscous‐shear damper: Case studies on the Sutong Bridge

“…A comprehensive analysis of a sagged cable with bending stiffness attached with a viscous damper considering support flexibility or a high damping rubber was performed by Fujino and Hoang, and the damper stiffness was further considered by Javanbakht et al Apparently, the cable‐damper system has been extensively studied using numerical and analytical methods in the last decades. Recent studies tend to focus on enhancing the damping effect of near‐anchorage dampers to compensate for the inadequate supplemental damping for long cables due to the limited damper installation distance from the cable anchorage and the sag effect, for example, using inerter or negative stiffness mechanism and so on and characterizing complex cable networks with cross‐ties . Meanwhile, numerical methods have been applied to precisely appreciate the influences of damper nonlinearity on the damping effects …”