scholarly journals Nonlinear Aeroelastic in-Plane Behavior of Suspension Bridges under Steady Wind Flow

2020 ◽  
Vol 10 (5) ◽  
pp. 1689 ◽  
Author(s):  
Simona Di Nino ◽  
Angelo Luongo
Keyword(s):  
Elastic Beam ◽  
Suspension Bridge ◽  
Multiple Scale ◽  
Continuous Model ◽  
Suspension Bridges ◽  
Wind Flow ◽  
Aeroelastic System ◽  
Natural Modes ◽  
Structural Nonlinearities ◽  
Limit Cycle Amplitude

The nonlinear aeroelastic behavior of suspension bridges, undergoing dynamical in-plain instability (galloping), is analyzed. A nonlinear continuous model of bridge is formulated, made of a visco-elastic beam and a parabolic cable, connected each other by axially rigid suspenders, continuously distributed. The structure is loaded by a uniform wind flow which acts normally to the bridge plane. Both external and internal damping are accounted for the structure, according to the Kelvin-Voigt rheological model. The nonlinear aeroelastic effects are evaluated via the quasi-static theory, while structural nonlinearities are not taken into account. First, the free dynamics of the undamped bridge are addressed, and the natural modes determined. Then, the nonlinear equations ruling the dynamics of the aeroelastic system, close to the bifurcation point, are tackled by the Multiple Scale Method. This is directly applied to the partial differential equations, and provides the finite-dimensional bifurcation equations. From these latter, the limit-cycle amplitude and its stability are evaluated as function of the mean wind velocity. A case study of suspension bridge is analyzed.

scholarly journals Nonlinear Dynamics of an Internally Resonant Base-Isolated Beam under Turbulent Wind Flow

2021 ◽  
Vol 11 (7) ◽  
pp. 3213
Author(s):  
Simona Di Nino ◽  
Daniele Zulli ◽  
Angelo Luongo
Keyword(s):  
Nonlinear Dynamics ◽  
Base Isolation ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Multiple Scale ◽  
Wind Flow ◽  
Isolation System ◽  
Turbulent Wind ◽  
The Mean ◽  
Limit Cycle Amplitude

A base isolation system, aimed to passively control the nonlinear dynamics of an internally resonant tower, exposed to turbulent wind flow, is studied. A continuous visco-elastic beam, constrained at the bottom end by a nonlinear visco-elastic device and free at the top end, is considered. All the nonlinearities, structural, inertial and aeroelastic, these latter computed via the quasi-static theory, are accounted in the model. The interaction between self- and parametric excitations, triggered by the mean wind velocity and the turbulent component, respectively, are analyzed. The Multiple Scale Method is applied to the partial differential equations of motion, to investigate critical and post-critical behaviors, when two modes in internal 1:3 resonance are involved in the response. The first mode is found to lead the phenomenon, while the second mode is marginally involved. The effectiveness of the visco-elastic nonlinear isolation system is assessed, both in increasing the mean wind bifurcation value and in reducing the limit-cycle amplitude. The contribution of structural nonlinearities is found to weakly affect the response.

Unsteady Aerodynamic Modeling and Flutter Analysis of Long-Span Suspension Bridges

2012 ◽  
Author(s):  
Andrea Arena ◽  
Walter Lacarbonara ◽  
Pier Marzocca
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Equations Of Motion ◽  
Suspension Bridge ◽  
Longitudinal Direction ◽  
Lagrangian Formulation ◽  
Suspension Bridges ◽  
Equilibrium Equations ◽  
Aeroelastic System ◽  
Flutter Analysis

A parametric one-dimensional model of suspension bridges is employed to investigate their static and dynamic aeroelastic behavior in response to a gust load and at the onset of flutter. The equilibrium equations are obtained via a direct total Lagrangian formulation where the kinematics for the deck, assumed to be linear, feature the vertical and the chord-wise displacements of the deck mean axis and the torsional rotations of the deck cross sections, while preserving their shape during rotation. The cables elasto-geometric stiffness contribution is obtained by condensing the equilibrium in the longitudinal direction assuming small horizontal displacements and neglecting the cable kinematics along the bridge chord-wise direction. The equations of motion are linearized about the prestressed static aeroelastic configuration and are obtained via an updated Lagrangian formulation. The equations of motion governing the structural dynamics of the bridge are coupled with the incompressible unsteady aero-dynamic model obtained by a set of reduced-order indicial functions developed for the cross section of a suspension bridge, here represented by a rectangular cross-section. The space dependence of the governing equations is treated using the Galerkin approach borrowing as set of trial functions, the eigenbasis of the modal space. The time integration is subsequently performed by using a numerical scheme that includes the modal reduced dynamic aeroelastic Ordinary Differential Equations (ODEs) and the added aerodynamic states also represented in ODE form, the latter being associated with the lag-state formulation pertinent to the unsteady wind-induced loads. The model is suitable to analyze the effect of a time and space non uniform gust load distributed on the bridge span. The obtained aeroelastic system is also suitable to study the onset of flutter and to investigate the sensitivity of the flutter condition on geometrical and aerodynamic parameters. The flutter instability is evaluated using appropriate frequency and time domain characteristics. The parametric continuum model is exploited to perform dynamic aeroelastic flutter analysis and gust response of the Runyang Suspension Bridge over the Yangtze river in China.

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.

Analysis and Test on Mechanical Properties of a Flexible Suspension Bridge

2013 ◽  
Vol 405-408 ◽  
pp. 1616-1622
Author(s):  
Guo Hui Cao ◽  
Jia Xing Hu ◽  
Kai Zhang ◽  
Min He
Keyword(s):  
Mechanical Properties ◽  
Suspension Bridge ◽  
Experimental Results ◽  
Suspension Bridges ◽  
Loading Test ◽  
Main Cable ◽  
Element Simulation ◽  
Static Loading Test ◽  
Geometric Nonlinear Analysis ◽  
Test Process

In order to research on mechanical properties of flexible suspension bridges, a geometric nonlinear analysis method was used to simulate on the experimental results, and carried on static loading test finally. In the loading test process, the deformations were measured in critical section of the suspension bridge, and displacement values of measured are compared with simulation values of the finite element simulation. Meanwhile the deformations of the main cable sag are observed under classification loading, the results show that the main cable sag increment is basically linear relationship with the increment of mid-span loading and tension from 3L/8 and 5L/8 to L/2 section, the main cable that increasing unit sag required mid-span loads and tension are gradually reduce in near L/4 and 3L/4 sections and gradually increase in near L/8 and 7L/8 sections and almost equal in near L/2, 3L/8 and 5L/8 sections. From the experimental results, the flexible suspension bridge possess good mechanical properties.

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.

Theoretical Study on Space Coupling Free Vibration Analysis of Self-Anchored Cable-Stayed Suspension Bridge

2014 ◽  
Vol 501-504 ◽  
pp. 1107-1111
Author(s):  
Miao Feng
Keyword(s):  
Free Vibration ◽  
Strain Energy ◽  
Coupling Effect ◽  
Longitudinal Vibration ◽  
Free Vibration Analysis ◽  
Flexural Vibration ◽  
Suspension Bridge ◽  
Large Displacement ◽  
Generalized Variational Principle ◽  
Suspension Bridges

Based on Large-displacement Non-linear Elastic Generalized Variational Principle, coupling effect of axial and flexural action, shearing strain energy, torsional strain energy of stiffening girder were considered, the large-displacement incomplete generalized potential energy functional of space coupling free vibration of a three-span self-anchored cable-stayed suspension bridge was presented. By constraint variation, fundamental differential equations of vertical flexural vibration, lateral flexural vibration, longitudinal vibration and torisional vibration were formulated, also presented the equations for the main tower with respect to longitudinal and lateral vibration. The linear free vibration differential equation was obtained when the nonlinear items were discarded. This approach provides theoretical basis for analysis of natural vibration character of self-anchored cable-stayed suspension bridges.

Experimental Study on Mass Transfer Coefficient of Dry Air in Main Cable of Suspension Bridge

2012 ◽  
Vol 461 ◽  
pp. 151-154
Author(s):  
Dai Yong Jia ◽  
Lu Yan Sui ◽  
Ming Lai He
Keyword(s):  
Mass Transfer ◽  
Transfer Coefficient ◽  
Mass Transfer Coefficient ◽  
Experimental Studies ◽  
Suspension Bridge ◽  
Suspension Bridges ◽  
Dry Air ◽  
Experiment Platform ◽  
Main Cable ◽  
Key Parameter

In this study, an experiment platform was built up to determine the key parameter, mass transfer coefficient, of the ventilation and dehumidification process in main cable of suspension bridge. On the basis of experimental studies, an empirical formula of the mass transfer coefficient was obtained, which can greatly contribute to control the content of moisture in the main cable of suspension bridges.

scholarly journals Performance of a Suspension Bridge with Active Vibration Dampers

2018 ◽  
Vol 196 ◽  
pp. 01017
Author(s):  
Anatolij Konovalov ◽  
Marina Pustovalova
Keyword(s):  
Cross Sections ◽  
Dynamic Properties ◽  
Suspension Bridge ◽  
Suspension Bridges ◽  
Initial Model ◽  
Strain Behavior ◽  
Pedestrian Bridges ◽  
Active Vibration ◽  
Active Damper ◽  
Vibration Dampers

Suspended structures that are used extensively in construction of motorway and pedestrian bridges allow bridging wide spans without having to install intermediate supports. Being less stiff in comparison to girder and arch bridges, suspension bridges require their dynamic properties to be controlled [1, 2]. This is a vital task when it comes to suspension bridges. Several engineering arrangements are available to control the dynamic properties of the structures [3]. This paper addresses the use of active dampers [4] installed on the tops of the towers as the means to control vibrations of a suspension bridge. To this end, a planar 3D model of suspension bridge was built using ANSYS software. The authors compared stress-strain behavior and dynamic properties of the models with and without active vibration dampers. In contrast to the initial model, the model of a bridge equipped with active dampers exhibits less displacement in all cross-sections. Thus, the displacements are reduced 1.7 times in the middle of the central span of suspended stiffening truss; 2.7 times in the middle of the end span; and displacements of the top of the bridge tower are 1.6 times less. The modal analysis has shown that in the model with active dampers the frequency of transverse vibrations at the tower tops has increased 1.9 times, while vertical vibrations have increased within 23%. Under maximum applied overpressure in the active damper, torsional vibrations of the structure have increased 2.4 times as compared to the initial model. The results obtained by the authors allow for the conclusion that active dampers are useful tools for controlling the dynamic properties of a suspension bridge.

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>

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