Stretch and Rotation of a Suspended Cable Subject to Transverse Fluid Excitation

ＩｎｔｒｏｄｕｃｔｉｏｎＣａｂｌｅｓａｒｅｅｘｔｅｎｓｉｖｅｌｙｕｓｅｄｉｎｖａｒｉｏｕｓｆｉｅｌｄｓｏｆｅｎｇｉｎｅｅｒｉｎｇ .Ｔｈｅｏｂｓｅｒｖｅｄｄｙｎａｍｉｃｓｏｆｃａｂｌｅｓｉｎｐｒａｃｔｉｃｅｏｆｔｅｎｅｘｈｉｂｉｔｓｖｅｒｙｃｏｍｐｌｅｘｂｅｈａｖｉｏｒ.Ｈｅｒｅａｒｅａｆｅｗ ,ｂｕｔｔｙｐｉｃａｌｅｘａｍｐｌｅｓ:(ａ)Ｔｈｅｓｔｅｅｌｃａｂｌｅｏｆｓｈｉｐｐｉｎｇｃｒａｎｅｍａｙｈａｖｅｔｈｅａｐｅｒｉｏｄｉｃｓｗｉｎｇｔｈａｔｐｒｏｄｕｃｅｓｐｏｏｒｐｏｓｉｔｉｏｎａｃｃｕｒａｃ…     

Dynamic modeling and simulation of flexible cable with large sag

ＩｎｔｒｏｄｕｃｔｉｏｎＦｌｅｘｉｂｌｅｃａｂｌｅｓｗｉｔｈｌａｒｇｅｓａｇａｒｅａｋｉｎｄｏｆｓｐｅｃｉａｌｅｎｇｉｎｅｅｒｉｎｇｓｔｒｕｃｔｕｒｅｓ.Ｔｈｅｙａｒｅｕｓｅｄｉｎｏｖｅｒｈｅａｄｔｒａｎｓｍｉｓｓｉｏｎｌｉｎｅｓｗｉｔｈｈｉｇｈｖｏｌｔａｇｅ,ａｅｒｉａｌｃａｂｌｅｓｆｏｒｔｒａｎｓｐｏｒｔ,ｌａｒｇｅｓｐａｎｓｔｒｕｃｔｕｒｅｓｉｎｂｒｉｄｇｅｓａｎｄｃｉｖｉｌｅｎｇｉｎｅｅｒｉｎｇ[1,2].Ｔｈｅｙｗｉｌｌｍｏｖｅｉｎｌａｒｇｅｒａｎｇｅｕｎｄｅｒｗｉｎｄ,ｌｏａｄｄｅｓｉｇｎｅｄ…     

A catenary element for the analysis of cable structures

ＩｎｔｒｏｄｕｃｔｉｏｎＣａｂｌｅｓｔｒｕｃｔｕｒｅｓａｒｅｎｏｎｌｉｎｅａｒｓｙｓｔｅｍｓｗｉｔｈｌａｒｇｅｄｉｓｐｌａｃｅｍｅｎｔｓ,ｔｈｅｙｓｈｏｕｌｄｂｅａｎａｌｙｓｅｄｂｙｎｏｎｌｉｎｅａｒｅｌａｓｔｉｃｔｈｅｏｒｙ．Ａｔｐｒｅｓｅｎｔ,ｃ...     

A discrete algorithm for complex frequency-domain convolutions

ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｗｅｌｌ＿ｋｎｏｗｎｔｈａｔｔｈｅＬａｐｌａｃｅｔｒａｎｓｆｏｒｍｏｆｔｈｅｐｒｏｄｕｃｔｏｆｔｗｏｔｉｍｅ＿ｄｏｍａｉｎｓｉｇｎａｌｓｅｑｕａｌｓｔｈｅｃｏｍｐｌｅｘｆｒｅｑｕｅｎｃｙ＿ｄｏｍａｉｎｃｏｎｖｏｌｕｔｉｏｎｏｆｉｎｄｉｖｉｄｕａｌＬａｐｌａｃｅｔｒａｎｓｆｏｒｍｓｏｆｔｗｏｓｉｇｎａｌｓ.Ｇｅｎｅｒａｌｌｙ,ｔｈｅｃｏｎｖｏｌｕｔｉｏｎｏｆｔｗｏｃｏｍｐｌｅｘｆｒｅｑｕｅｎｃｙ＿ｄｏｍａｉｎａｎａｌｙｔｉｃａｌｆｕｎｃｔｉｏｎｓｉｓｃａｌｃｕｌａｔｅ…     

K-ε-T MODEL OF DENSE LIQUID-SOLID TWO-PHASE TURBULENT FLOW AND ITS APPLICATION TO THE PIPE FLOW

ＩｎｔｒｏｄｕｃｔｉｏｎＬｉｑｕｉｄ＿ｓｏｌｉｄｔｗｏ＿ｐｈａｓｅｆｌｏｗｅｘｉｓｔｓｗｉｄｅｌｙｉｎｎａｔｕｒｅａｎｄｍａｎｙｉｎｄｕｓｔｒｉａｌｍｉｎｉｓｔｒｉｅｓ,ｆｏｒｅｘａｍｐｌｅ,ｓｅｄｉｍｅｎｔ＿ｌａｄｅｎｗａｔｅｒｆｌｏｗｉｓａｃｈａｒａｃｔｅｒｉｓｔｉｃｌｉｑｕｉｄ＿ｓｏｌｉｄｔｗｏ＿ｐｈａｓｅｆｌｏｗｉｎｎａｔｕｒｅａｎｄｈｙｄｒａｕｌｉｃｔｒａｎｓｐｏｒｔｏｆｓｏｌｉｄｍａｔｅｒｉａｌｉｓａｃｈａｒａｃｔｅｒｉｓｔｉｃｉｎｄｕｓｔｒｉａｌａｐｐｌｉｃａｔｉｏｎ.Ｔｈｅｓｔｕｄ…     

THE INTERACTION PROBLEM BETWEEN THE ELASTIC LINE INCLUSIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＯｆａｌｌｔｈｅｆｉｂｅｒ＿ｒｅｉｎｆｏｒｃｅｄｃｏｍｐｏｓｉｔｅｍａｔｅｒｉａｌｓ,ｔｈｅｓｈｏｒｔ＿ｆｉｂｅｒｃｏｍｐｏｓｉｔｅｍａｔｅｒｉａｌｎｏｔｏｎｌｙｓｔｒｅｎｇｔｈｅｎｓｔｈｅｍａｔｒｉｘｂｕｔａｖｏｉｄｓｄｅｆｅｃｔｉｏｎｓｏｆｔｈｅｌｏｎｇ＿ｆｉｂｅｒｃｏｍｐｏｓｉｔｅｍａｔｅｒｉａｌａｓｗｅｌｌ.Ｔｈｅｍｉｃｒｏ＿ｍｅｃｈａｎｉｃｓａｂｏｕｔｉｔｓｕｃｈａｓｆｒａｃｔｕｒｅ ,ｆａｔｉｇｕｅａｎｄｄａｍａｇｅｉｓｖｅｒｙｃｏｍｐｌｅｘ .Ｉｎｔｈｅｐｒｅｖｉ…     

A nonlinear Galerkin/Petrov-least squares mixed element method for the stationary Navier-Stokes equations

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｎｏｎｌｉｎｅａｒＧａｌｅｒｋｉｎｍｅｔｈｏｄｉｓａｍｕｌｔｉ＿ｌｅｖｅｌｓｃｈｅｍｅｔｏｆｉｎｄｔｈｅａｐｐｒｏｘｉｍａｔｅｓｏｌｕｔｉｏｎｆｏｒｔｈｅｄｉｓｓｉｐａｔｉｖｅＰＤＥ .ＴｈｉｓｍｅｔｈｏｄｈａｓｆｉｒｓｔｍａｉｎｌｙｂｅｅｎａｄｄｒｅｓｓｅｄｂｙＦｏｉａｓ＿Ｍａｎｌｅｙ＿Ｔｅｍａｍ[1],Ｍａｒｉｏｎ＿Ｔｅｍａｍ[2 ],Ｆｏｉａｓ＿Ｊｏｌｌｙ＿Ｋｅｖｒｅｋｉｄｉｓ＿Ｔｉｔｉ[3]ａｎｄＤｅｖｕｌｄｅｒ＿Ｍａｒｉｏｎ＿Ｔｉｔｉ[4 ]ｉｎｔｈｅｃａｓｅｏｆｓｐｅｃｔ…     

Semi-inverse method and generalized variational principles with multi-variables in elasticity

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ 1 954,Ｈｕ[1,2 ]ｄｅｄｕｃｅｄＨｕ＿Ｗａｓｈｉｚｕｐｒｉｎｃｉｐｌｅｂｙｓｏ＿ｃａｌｌｅｄｔｒｉａｌ＿ａｎｄ＿ｅｒｒｏｒｍｅｔｈｏｄ ,ａｎｄｉｎ1 964 ,Ｃｈｉｅｎ[3]ｓｙｓｔｅｍａｔｉｃａｌｌｙｄｉｓｃｕｓｓｅｄｔｈｅＬａｇｒａｎｇｅｍｕｌｔｉｐｌｉｅｒｍｅｔｈｏｄ ,ｂｙｗｈｉｃｈｈｅｓｕｃｃｅｓｓｆｕｌｌｙｄｅｄｕｃｅｄＨｕ＿Ｗａｓｈｉｚｕｐｒｉｎｃｉｐｌｅ.Ａｆｔｅｒｔｈａｔｇｅｎｅｒａｌｉｚｅｄｖａｒｉａｔｉｏｎａｌｐｒｉｎｃｉｐｌｅｓｃａｎｂｅａｒｒｉｖｅｄａｔ…     

Precise integration method for LQG optimal measurement feedback control problem

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｌｉｎｅａｒｓｙｓｔｅｍｏｆｔｈｅｍｅａｓｕｒｅｍｅｎｔｆｅｅｄｂａｃｋｃｏｎｔｒｏｌ ｘ=Ａｘ Ｂｗ Ｂ2 ｕ , ( 1 )ｙ =Ｃｘ ｖ ,( 2 )ｗｈｅｒｅｘｉｓｔｈｅｎ＿ｄｉｍｅｎｓｉｏｎａｌｓｔａｔｅｖｅｃｔｏｒ,ｙｉｓａｑ＿ｖｅｃｔｏｒｏｆｍｅａｓｕｒｅｍｅｎｔｓ,ｕｉｓａｎｍ＿ｖｅｃｔｏｒｏｆｃｏｎｔｒｏｌｉｎｐｕｔｓ,ｗａｎｄｖａｒｅｌ＿ｖｅｃｔｏｒ,ｑ＿ｖｅｃｔｏｒｏｆｗｈｉｔｅ＿ｎｏｉｓｅｐｒｏｃｅｓｓｗｉｔｈｋｎｏｗｎｓｔａｔｉｓｔｉｃａｌｐｒｏｐｅ…     

BLOW-UP OF THE SOLUTIONS FOR THE INITIAL-BOUNDARY PROBLEMS OF THE NONLINEAR SCHR?DINGER EQUATIONS

Ｔｈｅｒｅａｒｅｍａｎｙｄｏｃｕｍｅｎｔｓｔｈａｔｄｉｓｃｕｓｓｂｌｏｗ＿ｕｐｏｆｔｈｅｓｏｌｕｔｉｏｎｓｆｏｒｔｈｅｉｎｉｔｉａｌ＿ｂｏｕｎｄａｒｙｖｌｕｅｐｒｏｂｌｅｍｓｏｆｔｈｅｎｏｎｌｉｎｅａｒＳｃｈｒ ｄｉｎｇｅｒｅｑｕａｔｉｏｎｓ,ｓｕｃｈａｓｐａｐｅｒ [1 ] .Ｂｕｔｔｈｅｐａｐｅｒ [1 ]ｈａｓｏｎｅｗｅａｋｐｏｉｎｔ,ｔｈａｔｉｓ,ｉｔｃａｎｎｏｔｕｎｉｔｅｄｉｓｃｕｓｓｉｏｎｆｏｒｂｌｏｗ＿ｕｐｏｆｔｈｅｓｏｌｕｔｉｏｎｓｆｏｒｔｈｅｉｎｉｔｉａｌ＿ｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌ…     

Study on the role of rivulet in rain–wind-induced cable vibration through wind tunnel testing

Rain–wind-induced vibration (RWIV) of stay cables has become a concern in bridge engineering over the past decades. The excitation mechanism of RWIV remains unclear. Many researchers believe that the upper rivulet is crucial to RWIV. However, experimental study on rivulet is challenging and limited. The current study designs and tests a cable model of 160 mm in diameter in an open jet wind tunnel. The upper rivulet movement and cable vibration are simultaneously measured. The importance of the upper rivulet in RWIV is directly demonstrated by alternately controlling the upper and lower rivulets. The characteristics of the upper rivulet movement and the effects of this movement on RWIV are investigated in detail. The experiment shows that the rivulet–cable system is coupled, which causes the cable and upper rivulet to vibrate at different amplitudes under the same wind speed. The upper rivulet harmonic movement changes the wind loading on the cable, causing the harmonic vibration of the cable, which in turn exerts a harmonic inertia force on the rivulet. A large vibration of the coupled system then develops.     

变化外形的水线对斜拉索风雨激振的激发作用

讨论变化外形的水线对斜拉桥拉索风雨激振的激发作用.首先,建立考虑水线外形变化的斜拉桥拉索风雨激振计算模型,并将由采用变化水线外形的模型得到的拉索最大振幅与固定水线外形模型的计算结果及试验实测结果对比,对模型进行验证;在模型得到验证的基础上,进一步讨论拉索和变化水线外形的水线振动稳定性及水线对拉索风雨激振贡献.计算结果表明,在四个典型工况下,考虑水线外形变化的模型得到的拉索计算振幅固定水线外形模型能更好地与试验实测振幅吻合;理论分析发现拉索速度和水线速度的耦合作用对水线运动的激发起到主导作用;水线的加速发散发生在拉索大幅激振之前.没有水线加速发散的时程中,拉索均不发生大幅激振.     

Aerodynamic characteristics of an inclined and yawed circular cylinder with artificial rivulet

Stay cables of cable-stayed bridges often experience vibrations with large amplitudes induced by wind or jointly by both wind and rain. To understand the aerodynamic characteristics of the stay cables and excitation mechanics of rain–wind-induced vibration (RWIV), an inclined and yawed circular cylinder with and without an artificial upper rivulet is studied through a series of wind tunnel tests. The impacts of upper rivulet and axial flow on the aerodynamics of the cylinder are investigated. It is found that for an inclined and yawed cylinder without rivulet there exists a non-zero lift force at large wind angle. Furthermore, the wind pressures and aerodynamic forces acting on both the cylinder and the upper rivulet are obtained, which can be used to develop more rational theoretical models for RWIV of stay cables. Results show that the upper rivulet can both enhance and depress Karman vortex shedding depending on the position of the rivulet. As a result, dramatic variations of the aerodynamic forces acting on the cylinder and the rivulet will occur, which may eventually result in RWIV. Also axial flow may have a noticeable influence on the aerodynamic characteristics of the inclined and yawed cylinder. And the presence of the rivulet can enhance such influence from the axial flow.     

Three-phase coupled modelling research on rain–wind induced vibration of stay cable based on lubrication theory

Cables of cable-stayed bridges may vibrate with large amplitude under wind and rain, which is known as rain–wind induced vibration (RWIV). According to the pervious researches, the formations and oscillations of rivulets on stay cable surface play important roles in RWIV. In this paper, four different 2D models are presented based on lubrication theory, and the best way of simulating RWIV through lubrication theory is confirmed by the comparisons of rivulet motions and cable vibration responses between these four models and pervious researches. On this basis, the relations among rivulet motions, cable aerodynamic forces and vibration responses are investigated to reveal the mechanism of RWIV. Numerical simulation results show that when RWIV occurs, the periodic oscillations of rivulets around cable lead to the periodic fluctuations of cable lift and drag, whose frequencies are almost equal and close to cable natural frequency. Under the periodically fluctuant lift and drag, cable vibrates with large amplitude in across-wind and along-wind directions, which may further enhance the circumferential oscillations of rivulets conversely. These confirm the conclusion that the resonance between rivulets and cable oscillation may be one of the main reasons for RWIV.     

Numerical simulation and analysis of the effects of water-film morphological changes on the aerodynamic lift of stay cables

The cables in cable-stayed bridges can vibrate at large amplitudes during rain and windy conditions, a phenomenon known as rain-wind induced vibration (RWIV). Previous studies have demonstrated that the formation and oscillation of rivulets on stay cable surfaces play an important role in RWIV.This paper presents a new numerical method for simulating the evolution of rivulets on stay cable surfaces based on a combination of the gas–liquid two-phase theory and the volume of fluid method (VOF method), which allows for the straightforward determination of the cables’ aerodynamic lift when RWIV occurs. To verify the accuracy of this method and analyze the effects of wind velocity on the water film and the aerodynamic lift around the cable, three cases with different loadings were investigated using the computational fluid dynamics (CFD) software CFX. To verify the method’s accuracy, the aerodynamic lifts calculated from these cases were applied to the cable to obtain its vibrational response. In accordance with the experimental results, the numerical results demonstrated that an upper rivulet with a periodic oscillation was formed at a specific wind speed, causing the aerodynamic lift to change with a similar periodicity. The aerodynamic lift’s frequency was approximately the cable’s natural frequency, and induced large vibrations in the cable. No obvious upper rivulets were formed at sufficiently low wind speeds. The frequency of an aerodynamic lift that was significantly larger than the cable’s natural frequency induced small vibrations in the cable. When the wind speed was sufficiently high, despite the eventual formation of a continuous upper rivulet, the frequencies of the upper rivulet’s oscillation and the aerodynamic lift remained distinct from the natural frequency, and the cable continued to exhibit small-amplitude vibrations. These observations confirmed the conclusion that periodic variations in the water film morphology could lead to periodic changes in the aerodynamic lift that would induce RWIV.     

Rain-wind-induced vibrations of a simple oscillator

In this paper a relatively simple mechanical oscillator which may be used to study rain-wind-induced vibrations of stay cables of cable-stayed bridges is considered. In recent publications, mention is made of vibrations of (inclined) stay cables which are excited by a wind field containing rain drops. The rain drops that hit the cables generate a rivulet on the surface of the cable. The presence of flowing water on the cable changes the cross section of the cable experienced by the wind field. A symmetric flow pattern around the cable with circular cross section may become asymmetric due to the presence of the rivulet and may consequently induce a lift force as a mechanism for vibration. During the motion of the cable the position of rivulet(s) may vary as the motion of the cable induces an additional varying aerodynamic force perpendicular to the direction of the wind field. It seems not too easy to model this phenomenon, several author state that there is no model available yet.The idea to model this problem is to consider a horizontal cylinder supported by springs in such a way that only one degree of freedom, i.e. vertical vibration is possible. We consider a ridge on the surface of the cylinder parallel to the axis of the cylinder. Additionally, let the cylinder with ridge be able to oscillate, with small amplitude, around the axis such that the oscillations are excited by an external force.It may be clear that the small amplitude oscillations of the cylinder and hence of the ridge induce a varying lift and drag force. In this approach it is assumed that the motion of the ridge models the dynamics of the rivulet(s) on the cable. By using a quasi-steady approach to model the aerodynamic forces, one arrives at a non-linear second-order equation displaying three different kinds of excitation mechanisms: self-excitation, parametric excitation and ordinary forcing. The first results of the analysis of the equation of motion show that even in a linear approximation for certain values of the parameters involved, stable periodic motions are possible. In the relevant cases where in linear approximation unstable periodic motions are found, results of an analysis of the non-linear equation are presented.     

Numerical investigation of the coupled interaction between an unsteady aerodynamic flow field and a water film coating on a circular cylinder

Rain–wind induced vibration is an aeroelastic phenomenon that occurs on the inclined cables of cable-stayed bridges and arises due to the interaction between the unsteady wind loading and the formation of water rivulets on the cable surface. A new numerical method has been developed at the University of Strathclyde to simulate the influence of the external flow field on the rivulet dynamics and vice versa. The approach is to couple a Discrete Vortex Method solver to determine the external flow field and unsteady aerodynamic loading, and a pseudo-spectral solver based on lubrication theory to model the evolution and growth of the water rivulets on the cable surface under external loading. Results of this coupled model are presented, to provide detailed information on the development of water rivulets and their interaction with the aerodynamic field. In particular, the effect of the initial water film thickness and the angle of attack in plane on the resulting rivulets are investigated. The results are consistent with previous full scale and experimental observations with rivulets forming on the upper surface of the cable only in configurations where rain–wind induced vibration has been observed. Additionally, the thickness of the lower rivulet is found to be self-limiting in all configurations. The results demonstrate that the model can be used to enhance the understanding of the underlying physical mechanisms of rain–wind-induced vibration.     

长单索结构的多参数流固耦合分析

介绍了长索结构在风场中的流固耦合振动,总结已有的流固耦合基本理论,着重介绍弱耦合问题的具体分析过程.以100m长索在不同拉索倾角和风向角的多参数流固耦合风振为例,应用ANSYS-CFX软件分别在层流模型和湍流模型风场中进行数值分析,得出与力学概念分析基本一致的结果.     

A numerical and experimental hybrid approach for the investigation of aerodynamic forces on stay cables suffering from rain-wind induced vibration

The aerodynamic forces on a stay cable under a rain-wind induced vibration (RWIV) are difficult to measure directly in a wind tunnel test. This paper presents a hybrid approach that combines an experiment with computational fluid dynamics (CFD) for the investigation on aerodynamic forces of a stay cable under a RWIV. The stay cable and flow field were considered as two substructures of the system. The oscillation of the stay cable was first measured by using a wind tunnel test of a RWIV under an artificial rainfall condition. The oscillation of the cable was treated as a previously known moving boundary condition and applied to the flow field. Only the flow field with the known moving cable boundary was then numerically simulated by using a CFD method (such as Fluent 6.3). The transient aerodynamic forces of the stay cable with a predetermined cable oscillation were obtained from numerical calculations. The characteristics of the aerodynamic forces in the time domain and frequency domain were then analysed for various cases. To verify the feasibility and accuracy of the proposed hybrid approach, the transient aerodynamic forces were applied to a single-degree-of-freedom model (SDOF) of the stay cable to calculate the RWIV of the cable. A comparison was performed between the oscillation responses of the stay cable obtained from the calculated (SDOF model) and experimental results, and the results indicate that the hybrid approach accurately simulates the transient aerodynamic forces of the stay cable. The equivalent damping ratios induced by the aerodynamic forces were obtained for various wind speeds. Furthermore, a nonlinear model of the aerodynamic force is proposed based on the calculation results, and the coefficients in the model were identified by a nonlinear least-squares technique.     

Theoretical and experimental studies on the aerodynamic instability of a two-dimensional circular cylinder with a moving attachment

Rain–wind induced vibration of cables in cable-stayed bridges is a worldwide problem of great concern. The effect of the motion of water rivulets on the instability of stay cables has been recognized as one of the mechanisms of this complex phenomenon. In order to investigate how the motion of rivulets affects the unstable vibration of cables without considering the effects of axial flow and axial vortex, a real three-dimensional cable was modeled as a two-dimensional circular cylinder, around which an attachment representing the rivulet can move. This could also be regarded as a new kind of two-dimensional 2-dof dynamic system. This paper studies the aerodynamic instability of the system theoretically and experimentally. Equations governing the motions of the cylinder and the attachment are first established. The Lyapunov stability criterion is applied to the equations of motion to derive the criterion for the unstable balance angle of the attachment. Moreover, a new two-dimensional 2-dof cable model system with a movable attachment is designed and tested in a wind tunnel. Parametric studies are carried out to investigate the effects of major factors such as wind speed, frequency and damping of the dynamic system on the unstable balance angle of the rivulet attachment. Theoretical and experimental results match well. These results may be valuable in elucidating the mechanism of rain–wind induced vibration of stay cables.