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Hybrid cross-tie system with passive dampers study

The authors have investigated the use of passive vibration dampers through the implementation of concentrated masses in the hybrid cross-tie system of a cable-stayed bridge. A 3D model of a cable-stayed bridge was built in ANSYS suite. The authors have studied the stress-strain behavior and dynamic characteristics of the model under the gravity load. The study has shown that the most effective model appears to be the one with passive dampers implemented by means of six concentrated masses. The increased stiffness of links of the concentrated masses had stronger effect on the model with passive dampers implemented by means of ten concentrated masses, however the model where passive dampers were implemented by six concentrated masses displayed comparable values of natural vibration frequencies with deflections in the spans being 3% lower, displacements of the towers being 8% lower, and longitudinal forces in the main cable being 6% lower. The results obtained by the authors allow for the conclusion that all models of a hybrid cross-tie system with passive dampers reviewed have high aerodynamic stability.


Introduction
Hybrid systems in which the roadway comprises a girder with tower supports and staying system are widely used in bridge engineering. This kind of structures provide high load-bearing capacity to cablestayed bridges, are lightweight, and allow for covering long bridge spans without having to install additional supports. Yet, such systems are sensitive to dynamic loading. Different dampening devices are used for the prevention of wind-induced vibrations in bridge structures. This study is intended as the study of stress-strain behavior, evaluation of wind-induced vibration critical velocities and aerodynamic stability of the structures when passive dampers are used in the form of additional concentrated masses attached by elastic constraint. To that end, a 3D model of a cable-stayed bridge was built in ANSYS suite. The dimensions of the model were assigned as per the contemplated design of a bridge across the Kuznechikha River in Arkhangelsk [1].
The influence of passive vibration dampers on the strain-stress behavior and dynamic characteristics of the structure were studied for a cable-stayed bridge with the end spans each 200 m long and 450 m central span, 90 m high towers, and the bridge height of 30 m. Stiffeners, dimensions and configuration of a hybrid system meets the model described in ref. [2].

Stress-Strain Analysis and Modal Analysis
Three cases of passive vibration dampers modeling were analyzed: ten, six and two concentrated masses fixed at the ends of the stiffening truss in the central span on elastic elements by means of constraint EI = 2.46•10 11 Nm 2 , EА = 2.51•10 8 N. Passive dampers implemented by means of ten concentrated masses are shown on figure 1. The distance from the tower to the nearest concentrated mass is 80 meters; the IOP Publishing doi:10.1088/1757-899X/1015/1/012011 2 distance between the masses along the stiffening truss is 60 meters, while the distance between the masses across the stiffening truss is 30 meters. Initially, the effect of the weight of concentrated masses on the stress-strain behavior of the model was analyzed. The variation was between 0 and 8% of the bridge structure weight without dampers. The calculations showed that increase of the weight of 10 passive dampers to 8% of the weight of the original bridge structure will increase the deflections at midspan by 35%. A 40% increase was noted in the displacement of the tops of towers.
The modal analysis of a cable-stayed bridge model with different concentrated masses has shown that the use of passive dampers has no significant effect on the variation of natural torsional frequencies and natural transverse frequencies of a cable-stayed bridge. The transverse frequency has changed by 1.25%, and the torsional frequency has changed by 2.9 %. The frequency of vertical motions has decreased by 6%.  At the next phase of the study, the value of additional concentrated masses was assumed to be constant and equal to 8% of the original weight of the bridge structure. The modal analysis of a cablestayed bridge with varying stiffness of links of the concentrated masses has shown that the increased stiffness of links of additional masses has resulted in 60% increase of transverse vibrational frequency. The changes in the stiffness of links of the concentrated masses have no effect on the frequencies of vertical and torsional vibrations ( figure 4). displacements and internal forces in the structural elements were confirmed to be tending to increase as an effect of the increased load by means of additional concentrated masses. In contrast, the frequencies of natural vibrations of the structure showed very small change. In all cases reviewed using 2, 6 and 10 additional concentrated masses, considerable effect on transverse frequency of the structure was caused only by the increase in the stiffness of links that attached these masses to the structure (Figure 4).
On the basis of the analysis completed on the models, the most efficient model appears to be the model with passive dampers implemented by means of six concentrated masses. As compared to the models having passive dampers implemented by two and ten concentrated masses, the model with dampers represented by six concentrated masses has lower deflections in the spans, lower displacements of the towers, lower stress in the stiffening truss, and lower longitudinal forces in the main cable (table  1).

Aerodynamic Stability
The change of aerodynamic characteristics of the structure has an effect on its aerodynamic stability [3]. Aerodynamic stability condition is written as [4,5] 1.5 where is the design wind speed, i.e. the maximum wind speed that can be expected in this bridge construction area (normally, WND v = 25…35 m/s); 1.5 is specific safety factor [6, para. 2.24]. In the practice of cable-stayed bridges structural analysis, aerodynamic stability is evaluated using various methods and criteria that are based on the natural vibrational frequency of the bridge structures. where ℎ is the stiffening truss height, (m); B is the bridge breadth, (m); ω is the natural vibrational frequency of the structure, (Hz). Table 2 is the summary of results obtained by the calculation of windinduced vibrations critical velocities using the formula (3) for the models reviewed in this study.