Post-Flutter Bifurcation Behavior in Long-Span Suspension Bridges

2013 ◽  
Author(s):  
Andrea Arena ◽  
Walter Lacarbonara ◽  
Pier Marzocca
Keyword(s):  
Limit Cycle ◽  
Equations Of Motion ◽  
Suspension Bridge ◽  
Sensitivity Analyses ◽  
Design Parameters ◽  
Suspension Bridges ◽  
Limit Cycle Oscillations ◽  
Stability Range ◽  
Long Span ◽  
Fold Bifurcation

A linearized parametric continuum model of a long-span suspension bridge is coupled with a nonlinear quasi-steady aerodynamic model giving the aeroelastic partial differential equations of motion reduced to the state-space ordinary differential form by adopting the Galerkin method. Numerical time-domain simulations are performed to investigate the limit cycle oscillations occurring in the range of post-flutter wind speeds. Continuation tools are thus employed to path follow the limit cycles past the flutter speed where the Hopf bifurcation occurs. The stable post-flutter behavior, which can significantly affect the bridge by fatigue, terminate at a fold bifurcation. This result represents an important assessment of the conducted aeroelastic investigations. The stability range of the limit cycle oscillations is evaluated by carrying out sensitivity analyses with respect to the main design parameters, such as the structural damping and the initial wind angle of attack.

Post-Critical Behavior of Suspension Bridges Under Nonlinear Aerodynamic Loading

2015 ◽  
Vol 11 (1) ◽  
Author(s):  
Andrea Arena ◽  
Walter Lacarbonara ◽  
Pier Marzocca
Keyword(s):  
Reduction Process ◽  
Design Parameters ◽  
Suspension Bridges ◽  
Long Span ◽  
Fold Bifurcation ◽  
Speed Up ◽  
The Stability ◽  
Parametric Analyses ◽  
Bifurcation Behavior ◽  
Nonlinear Aerodynamic

The limit cycle oscillations (LCOs) exhibited by long-span suspension bridges in post-flutter condition are investigated. A parametric dynamic model of prestressed long-span suspension bridges is coupled with a nonlinear quasi-steady aerodynamic formulation to obtain the governing aeroelastic partial differential equations adopted herewith. By employing the Faedo–Galerkin method, the aeroelastic nonlinear equations are reduced to their state-space ordinary differential form. Convergence analysis for the reduction process is first carried out and time-domain simulations are performed to investigate LCOs while continuation tools are employed to path follow the post-critical LCOs. A supercritical Hopf bifurcation behavior, confirmed by a stable LCO, is found past the critical flutter condition. The analysis shows that the LCO amplitude increases with the wind speed up to a secondary critical speed where it terminates with a fold bifurcation. The stability of the LCOs within the range bracketed by the Hopf and fold bifurcations is evaluated by performing parametric analyses regarding the main design parameters that can be affected by uncertainties, primarily the structural damping and the initial wind angle of attack.

Control of Vibrations due to Moving Loads on Suspension Bridges

2006 ◽  
Vol 11 (3) ◽  
pp. 293-318 ◽  
Author(s):  
M. Zribi ◽  
N. B. Almutairi ◽  
M. Abdel-Rohman
Keyword(s):  
Bridge Deck ◽  
Suspension Bridge ◽  
Lyapunov Theory ◽  
Dynamic Responses ◽  
Suspension Bridges ◽  
Control Force ◽  
Moving Loads ◽  
Hydraulic Actuator ◽  
Long Span ◽  
Suspended Cables

The flexibility and low damping of the long span suspended cables in suspension bridges makes them prone to vibrations due to wind and moving loads which affect the dynamic responses of the suspended cables and the bridge deck. This paper investigates the control of vibrations of a suspension bridge due to a vertical load moving on the bridge deck with a constant speed. A vertical cable between the bridge deck and the suspended cables is used to install a hydraulic actuator able to generate an active control force on the bridge deck. Two control schemes are proposed to generate the control force needed to reduce the vertical vibrations in the suspended cables and in the bridge deck. The proposed controllers, whose design is based on Lyapunov theory, guarantee the asymptotic stability of the system. The MATLAB software is used to simulate the performance of the controlled system. The simulation results indicate that the proposed controllers work well. In addition, the performance of the system with the proposed controllers is compared to the performance of the system controlled with a velocity feedback controller.

scholarly journals Probabilistic Assessment of the Safety of Main Cables for Long-Span Suspension Bridges considering Corrosion Effects

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Hao Tian ◽  
Jiji Wang ◽  
Sugong Cao ◽  
Yuanli Chen ◽  
Luwei Li
Keyword(s):  
Probability Model ◽  
Steel Wire ◽  
Suspension Bridge ◽  
Element Model ◽  
Traffic Load ◽  
Suspension Bridges ◽  
Accelerated Corrosion ◽  
Long Span ◽  
Accelerated Corrosion Tests ◽  
Main Cables

This paper presents a reliability analysis to assess the safety of corroded main cables of a long-span suspension bridge. A multiscale probability model was established for the resistance of the main cables considering the length effect and the Daniels effect. Corrosion effects were considered in the wire scale by relating the test results from accelerated corrosion tests to the corrosion stages and in the cable scale by adopting a corrosion stage distribution of the main cable section in NCHRP Report 534. The load effects of temperature, wind load, and traffic load were obtained by solving a finite element model with inputs from in-service monitoring data. The so-obtained reliability index of the main cables reduces significantly after operation for over 50 years and falls below the design target value due to corrosion effects on the mechanical properties of the steel wire. Multiple measures should be taken to delay the corrosion effects and ensure the safety of the main cables in the design service life.

Building 8500+ Trail Bridges in the Himalayas

2021 ◽  
Author(s):  
Robert Groeli
Keyword(s):  
International Development ◽  
Technical Assistance ◽  
Local Level ◽  
Cost Effective ◽  
Suspension Bridge ◽  
Development Cooperation ◽  
Design Parameters ◽  
Suspension Bridges ◽  
Teaching Resources ◽  
Economic Output

<p>Mobility is one of the most challenging fundamentals of rural livelihood in the Himalayan hills and mountains. More than 8500 trail bridges, comprising an overall span-length of about 650 kilometers have been constructed to date, saving millions of walking hours for people living in the rural Himalayan areas. Previously, crossing rivers was dangerous and sometimes impossible, especially in the rainy season. These bridges created vital connections which enabled children to go to school and people to access public services and visit medical centers and sanctuaries. They also boost local economic output by reducing the effort required to run local farms, gather crops and visit regional markets.</p><p>Fig. 1:The struggles and dangers of crossing a river and its solution</p><p>Swiss technical assistance for rural trail bridges started in the early sixties with the construction of a few suspension bridges in the hill areas of Nepal. In 1964 the Nepalese Government established the Suspension Bridge Division (SBD), and starting in 1972 the Swiss Government began providing continuous technical and financial assistance. Similarly, the Public Works Department in Bhutan initiated a country wide trail bridge construction program in 1971 for which assistance was provided from 1985-2010. Exchanges of experiences between these programs created a collaborative environment where new ideas could be evaluated and tested in the field. After SBD initially developed the basic technical norms, design parameters and standard designs suitable for long-span bridges, demand for simpler shorter span bridges rose tremendously. This prompted the program to develop “community executable bridge designs” adapted to the local skills and materials while conforming to established engineering standards. As a result, cost-effective, easy to implement technologies and community-based approaches were developed, which have been replicated in numerous countries leading to multiple successful partnerships in international development cooperation.</p><p>The purpose of this paper is to highlight the following outcomes of the trail bridge-program:</p><ul><li><p>Standardized cost-effective trail bridge designs based on local capabilities and bridge-building techniques</p></li><li><p>Published of manuals, technical drawings and teaching resources for design, construction and fabrication</p></li><li><p>Engaged local communities in the construction, operation and maintenance of trail bridges</p></li><li><p>Compiled comprehensive trail bridge directory for planning, monitoring and maintenance</p></li><li><p>Established Sector Wide Approach (SWAp) with institutional frameworks at national and local level</p></li><li><p>‘South-South Cooperation’ with Bhutan, Tanzania, Ethiopia, Indonesia, Laos, Burundi, Honduras, Guatemala</p></li></ul>

scholarly journals A Master Digital Model for Suspension Bridges

2020 ◽  
Vol 10 (21) ◽  
pp. 7666
Author(s):  
Ngoc-Son Dang ◽  
Gi-Tae Rho ◽  
Chang-Su Shim
Keyword(s):  
Suspension Bridge ◽  
Geometrical Model ◽  
Information Modeling ◽  
Digital Model ◽  
Suspension Bridges ◽  
Actual Behavior ◽  
Data Generation ◽  
Element Analysis ◽  
Long Span ◽  
Bridge System

Long-span suspension bridges require accumulated design and construction technologies owing to challenging environmental conditions and complex engineering practices. Building information modeling (BIM) is a technique used to federate essential data on engineering knowledge regarding cable-supported bridges. In this study, a BIM-based master digital model that uses a data-driven design for multiple purposes is proposed. Information requirements and common data environments are defined considering international BIM standards. A digital inventory for a suspension bridge is created using individual algorithm-based models, and an alignment-based algorithm is used to systematize them and generate the entire bridge system. After assembling the geometrical model, metadata and various BIM applications are linked to create the federated master model, from which the mechanical model is derived for further stages. During the construction stage, the advantage of this digital model lies in its capability to perform efficient revisions and updates with respect to varying situations during the erection process. Stability analyses of the bridge system can be performed continuously at each erection step while considering the geometric control simulation. Furthermore, finite element analysis models for any individual structural member can be extracted from the master digital model, which is aimed at estimating the actual behavior of bridge members. In addition, a pilot master digital model was generated and applied to an existing suspension bridge; this model exhibited significant potential in terms of bridge data generation and manipulation.

Compositive Optimal Control for the Seismic Response of a Long-Span Triple-Tower Suspension Bridge

2018 ◽  
Vol 18 (08) ◽  
pp. 1840009 ◽  
Author(s):  
Hao Wang ◽  
Yifeng Wu ◽  
Ben Sha ◽  
Wenzhi Zheng ◽  
Yuqi Gao
Keyword(s):  
Optimal Control ◽  
Suspension Bridge ◽  
Suspension Bridges ◽  
Seismic Responses ◽  
Viscous Dampers ◽  
Analytic Hierarchy ◽  
Expansion Joints ◽  
Elastic Links ◽  
Long Span ◽  
Floating System

In the design of super-long-span suspension bridges, the floating system is commonly adopted. However, this system may lead to the excessive earthquake-excited longitudinal displacement (LD) at the end of the main girder, which in return could result in pounding damage at expansion joints. In this paper, Taizhou Bridge, the triple-tower suspension bridge with the longest main span in the world, is taken as an example to demonstrate the effectiveness of three different approaches (elastic links, viscous dampers, and their combination) of mitigating the possible excessive LD. The finite element code ABAQUS is used to build the numerical model of the bridge and calculate the dynamic characteristics as well as the seismic responses. Then, 24 cases with different parameters of elastic links and viscous dampers are investigated and it is observed that the mitigation effect of the 24 cases varies significantly with different parameters. To obtain the optimized mitigation effect for seismic responses, including the LD of the girder, the LD and shear force of all towers, in the 24 cases, the modified analytic hierarchy process (AHP) method is introduced to realize the compositive optimal control of the triple-tower suspension bridge. Results show that the 24th case is the optimal one in which the LD of the girder is reduced significantly while the inner force of towers does not get excessive increase.

Damper Optimization for Long-Span Suspension Bridges

2013 ◽  
pp. 112-125
Author(s):  
Hao Wang ◽  
Aiqun Li ◽  
Zhouhong Zong ◽  
Teng Tong ◽  
Rui Zhou
Keyword(s):  
Seismic Response ◽  
Optimization Method ◽  
Sensitivity Analyses ◽  
Suspension Bridges ◽  
Seismic Responses ◽  
Control Effect ◽  
Analytic Hierarchy ◽  
First Order ◽  
Traveling Wave Effect ◽  
Long Span

Long-span suspension bridges are becoming prevalent globally with the rapid progress in design methodologies and construction technologies. Although with apparent progress, the balance between excessive displacement and inner forces, under dynamic loads, is still a main concern because of increased flexibility and low structural damping. Therefore, effective controllers should be employed to control the seismic responses to ensure their normal operation. In this chapter, the combination of the analytic hierarchy process (AHP) and first-order optimization method are formulated to optimize seismic response control effect of the Runyang suspension bridge (RSB) under earthquakes, considering traveling wave effect. The compositive optimal parameters of dampers are achieved on the basis of 3-dimensional nonlinear seismic response analyses for the RSB and parameters sensitivity analyses. Results show that the dampers with rational parameters can reduce the seismic responses of the bridge significantly, and the application of the AHP and first-order optimization method can lead to accurate optimization effects.

Limit–cycle oscillations of a heavy whirling cable subject to aerodynamic drag

2005 ◽  
Vol 461 (2055) ◽  
pp. 875-893 ◽  
Author(s):  
James David Clark ◽  
Wynstone Barrie Fraser ◽  
Christopher David Rahn ◽  
Arun Rajamani
Keyword(s):  
Limit Cycle ◽  
Aerodynamic Drag ◽  
Equations Of Motion ◽  
Experimental System ◽  
Angular Speed ◽  
Full Time ◽  
Limit Cycle Oscillations ◽  
Rotating Disc ◽  
Linearized Stability ◽  
Fixed End

In this paper a simple experimental system consisting of a length of cable, fixed to the edge of a rotating disc at its upper end, and free at its lower end or with a point mass ( drogue ) attached there, is described. This system exhibits a rich variety of bifurcation behaviours as the length of cable, angular speed of the fixed end, mass of the drogue and elasticity of the cable is varied. Bifurcation diagrams for the quasistationary configurations (cable shapes that appear stationary with respect to the rotating reference frame) are described. Linearized stability analyses of these quasistationary balloons are compared with solutions to the full time–dependent equations of motion. It is shown that there is an exchange of stability at the turning points of the quasi–stationary bifurcation curves, and that Hopf bifurcations occur at otherwise undistinguished points of these curves. It is shown that limit–cycle oscillations of the system occur at angular speeds corresponding to points on the bifurcations curves in the neighbourhood of the Hopf bifurcation points. These oscillations have been observed experimentally.

Wind Tunnel Studyon Vortex-Induced Vibration Characteristics of Long-Span Suspension Bridges with Single Cable Plane

2014 ◽  
Vol 633-634 ◽  
pp. 1263-1266
Author(s):  
Huang Yu
Keyword(s):  
Wind Tunnel ◽  
Suspension Bridge ◽  
Wind Tunnel Experiment ◽  
Vibration Characteristics ◽  
Torsional Stiffness ◽  
Suspension Bridges ◽  
Vortex Induced Vibration ◽  
Long Span Bridges ◽  
Wind Speeds ◽  
Long Span

For modern long-span bridges, both the optimization of aerodynamic shape and the increase of torsional stiffness according to the result of the wind tunnel experiment could avoid the flutter instability.Vortex-inducedvibration with relatively large amplitude happens easily at low wind speeds. In this paper, based on wind tunnel experiment, by studying on the vortex-induced vibration characteristics of a long-span suspension bridge with single cable plane, aerodynamic measures for easing the vortex-induced vibration are given.

scholarly journals Fragility-Based Improvement of System Seismic Performance for Long-Span Suspension Bridges

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Guanya Lu ◽  
Kehai Wang ◽  
Wenhua Qiu
Keyword(s):  
Seismic Performance ◽  
Fragility Curves ◽  
Suspension Bridge ◽  
System Level ◽  
Suspension Bridges ◽  
Fragility Function ◽  
Long Span ◽  
Damage Indices ◽  
Composite Damage ◽  
Demand Models

In this study, a procedure is developed to evaluate and improve the seismic performance of long-span suspension bridges based on the performance objectives under the fragility function framework. A common type of suspension bridge in China was utilized in the proposed procedure, considering its approach structures according to earthquake damage experience and fortification criteria. Component-level fragility curves were derived by probabilistic seismic demand models (PSDMs) using a set of nonlinear time-history analyses that incorporated the related uncertainties such as earthquake motions and structural properties. In addition, one step that was covered was to pinpoint the capacity limit states of critical components including bearings, pylons, and columns. The stepwise improved seismic designs were proposed in terms of the component fragility results of the as-built design. Results of the comparison of improved designs showed that the retrofit measure of the suspension span should be selected based on two attributes, i.e., displacement and force, and the restraint system of the approach bridges was a key factor affecting the reasonable damage sequence. Necessarily, from the comparison of different system vulnerability models, the mean values of earthquake intensity of system-level fragility function developed by the composite damage state indices were used to assess the overall seismic performance of the suspension bridge. The results showed that compared to the absolutely serial and serial-parallel assumptions, the defined composite damage indices incorporating the thought of component classification and structural relative importance between the main bridge and approach structures were necessary and were able to derive a good indicator of seismic performance assessment, hence validating the point that the different damage states were dominated by the seismic demands of different structures for the retrofitted bridges.

Sign in / Sign up

Export Citation Format

Share Document