Flutter reliability analysis of suspension bridges

A reliability analysis method is proposed in this paper through a combination of the advantages of the response surface method (RSM), finite element method (FEM), first-order reliability method (FORM) and the importance sampling updating method. The method is especially applicable for the reliability evaluation of complex structures of which the limit state surfaces are not known explicitly. After the accuracy and efficiency of the method are demonstrated through numerical examples, the method is used to estimate the flutter reliability of a suspension bridge. The uncertainties such as material properties, geometric parameters, structural damping ratio, flutter derivatives and extreme wind velocity at the bridge site are considered. The example suspension bridge is the Jiang Yin Bridge with a main span length of 1385 m built in China. The results show that the proposed method based on an empirical formula in which the limit state function is explicitly represented as a function of variables overestimates the flutter reliability of suspension bridges. The actual flutter reliability should be more accurately analyzed using the proposed method based on the deterministic finite element method in which the limit state function is implicitly represented as a function of variables. Finally, the most influential random variables on flutter reliability of suspension bridges are identified by using a sensitivity analysis.     

Estimation of torsional-flutter probability in flexible bridges considering randomness in flutter derivatives

Torsional-flutter instability is an aeroelastic phenomenon of interest to the bridge engineer, corresponding to a torsionally unstable vibration regime of the deck driven by wind excitation and appearing beyond a certain critical wind velocity. In this study a method for the derivation of the flutter probability for long-span bridges with bluff decks is proposed.In the first part of this study the deterministic problem is addressed. In contrast with the classical solution method in the frequency domain based on a numerical procedure for assessing the critical wind velocity, a single-mode “closed-form” algorithm for the derivation of the critical velocity was investigated. A polynomial representation of the aeroelastic-loading coefficients (flutter derivatives), necessary for torsional-flutter analysis, was utilized.In the second part an algorithm for estimating the torsional-flutter probability was developed, considering randomness in bridge properties, and flutter derivatives in particular due to their preeminent role in torsional-flutter velocity estimation.Experimental errors in the extraction of flutter derivatives from wind tunnel tests were analyzed. The “closed-form” algorithm, developed in the first part, allowed for a direct numerical solution of the flutter probability in a simple way.The torsional-flutter probability for three simulated bridge models with rectangular closed-box and truss-type girder deck was numerically determined. A set of experimental data, available from the literature, was employed. The simulations enabled the validation of the proposed algorithm.     

Weighting ensemble least-square method for flutter derivatives of bridge decks

In this paper, a reliable but simple identification method, here called the weighting ensemble least-square method (WELS), has been developed to extract all eight flutter derivatives of bridge deck from free vibration records. For every wind speed, free vibration test of section model is generally repeated several times in order to obtain more reliable parameter estimates. In the WELS method, many free vibration records at the same wind speed are regarded as an ensemble. The common mode parameters are then identified simultaneously from the ensemble data. The parameter fit is obtained by a nonlinear least-square method. Weighting factors are proposed to make each experiment record with the same weight in total residual error analysis. The ensemble composed of many records can reduce the effect of the colored noise of few records on the convergence of least-square iteration process. The flutter derivatives of two section models are identified to indicate the reliability and effectiveness of the WELS method.     

Framework for sensitivity and uncertainty quantification in the flutter assessment of bridges

The phenomenon of aerodynamic instability caused by wind is usually a major design criterion for long-span cable-supported bridges. If the wind speed exceeds the critical flutter speed of the bridge, this constitutes an Ultimate Limit State. The prediction of the flutter boundary therefore requires accurate and robust models. The state-of-the-art theory concerning determination of the flutter stability limit is presented. Usually bridge decks are bluff and therefore the aeroelastic forces under wind action have to be experimentally evaluated in wind tunnels or numerically computed through Computational Fluid Dynamics (CFD) simulations. The self-excited forces are modelled using aerodynamic derivatives obtained through CFD forced vibration simulations on a section model. The two-degree-of-freedom flutter limit is computed by solving the Eigenvalue problem.A probabilistic flutter analysis utilizing a meta-modelling technique is used to evaluate the effect of parameter uncertainty. A bridge section is numerically modelled in the CFD simulations. Here flutter derivatives are considered as random variables. A methodology for carrying out sensitivity analysis of the flutter phenomenon is developed. The sensitivity with respect to the uncertainty of flutter derivatives and structural parameters is considered by taking into account the probability distribution of the flutter limit. A significant influence on the flutter limit is found by including uncertainties of the flutter derivatives due to different interpretations of scatter in the CFD simulations. The results indicate that the proposed probabilistic flutter analysis provides extended information concerning the accuracy in the prediction of flutter limits.The final aim is to set up a method to estimate the flutter limit with probabilistic input parameters. Such a tool could be useful for bridge engineers at early design stages. This study shows the difficulties in this regard which have to be overcome but also highlights some interesting and promising results.     

THERMALLY INDUCED BENDING VIBRATION OF COMPOSITE SPACECRAFT BOOMS SUBJECTED TO SOLAR HEATING

Thermally induced bending vibration of spacecraft booms modeled as circular thin-walled beams of closed cross section and subjected to thermal radiation is investigated. One assumes that the boom is built up of composite material systems, and in this context, the constituent materials of the beam include nonclassical effects such as anisotropy and transverse shear. In addition, in order to induce beneficial elasticcouplings, a special ply-angle distribution achieved via the usual helically wounding fiber-reinforced technology is implemented. Both the dynamic governing equations involving the temperature effects and the related boundary conditions are obtained via the application of the extended Hamilton principle. The case of the spacecraft boom equipped with a concentrated mass at its free end, fixed at the other end, and exposed to solar radiant heating is studied from both the induced-vibration and stability points of view. The numerical simulations display deflection time history of bending displacements as a function of the fiber orientation of the composite materials, damping factor, and angle of incidence of heat radiation. The obtained results are likely to fill a gap in the specialized literature and to play a good role toward a better understanding of the factors that contribute not only to the occurrence of the thermal flutter instability, but also to its avoidance.     

碰撞阻尼器对机翼／外挂系统颤振半主动抑制分析

本文在碰撞阻尼器引入机翼/外挂系统的基础上,分析了碰撞间隙对机翼/外挂系统颤振速度的影响,建立了半主动抑制颤振模型,用增益调度控制方法对带碰撞阻尼器的机翼/外挂系统进行反馈控制。结果表明,机翼/外挂系统颤振速度大大提高。     

基于嵌入式传感装置的数控机床颤振实时补偿研究

针对数控机床加工时出现的颤振影响工件加工精度的难题,提出了基于嵌入式传感装置对数控机床颤振误差进行实时补偿的一种方法。首先,构建了CAN总线车间机床工作状态信息采集网络,并且采用PIC18F系列微处理器作为智能终端,移植TCP/IP协议,实现了机床各轴加速度数据的采集;然后,将数据打包通过无线网络通信模块将数据上传至上位机,上位机服务器系统通过数据筛选、分析和解包显示相关信息;最后,通过加速度传感器信息和颤振误差补偿模型计算数控机床颤振补偿值。实验结果表明：该嵌入式系统对数控机床加工精度有着良好的改善、可靠性好,并且有效地提高了车间机床的加工效率。     

柔性工件金属切削机床加工中的2 DOF模型

针对细长轴工件车削过程中的颤振抑制问题,提出一种可在状态空间域中分析柔性工件金属切削过程的2 DOF模型。对端面车削操作中细长轴工件的模态解耦效应进行分析,并在状态空间中对该2 DOF模型进行理论分析,得出由切削过程和工件形成的系统特征值解析式。对系统稳定性进行分析,确定无颤振的条件,并通过模型仿真,得到系统固有频率与切削速度的函数关系。在CNC数控车床上对细长轴工件加工进行实际测试。结果表明：对于初始直径为38.2 mm的C45钢制细长轴工件,在相同切削条件下,仿真和实测的频率均收敛到792.8 Hz,且最低切削速度为105 m/min,验证了该模型的有效性。该模型可用于更准确地预测细长轴工件加工的稳定极限,进而有效地预防颤振发生。     

Parametric study on flutter derivatives of bridge decks

The method for identification of flutter derivatives of bridge decks developed by the authors is first briefly described in this paper. To investigate the effects of dynamic parameters of a bridge deck model on the flutter derivatives a test of the sectional Jiangyin Bridge deck's models with different dynamic parameters was carried out in a boundary layer wind tunnel using the present identification method. In both smooth and simulated turbulent flow conditions, a plate model and the sectional deck model of the Jiangyin Bridge were tested to further survey the effects of turbulence on flutter derivatives. The identified results tend to indicate that the effects of parameters of the model and turbulence on the flutter derivatives are negligible.     

Study of Passive Deck-Flaps Flutter Control System on Full Bridge Model. I: Theory

A passive aerodynamic control method for suppression of the wind-induced instabilities of a very long span bridge is presented in this paper. The control system consists of additional control flaps attached to the edges of the bridge deck. Control flap rotations are governed by prestressed springs and additional cables spanned between the control flaps and an auxiliary transverse beam supported by the main cables of the bridge. The rotational movement of the flaps is used to modify the aerodynamic forces acting on the deck and provides aerodynamic forces on the flaps used to stabilize the bridge. A time-domain formulation of self-excited forces for the whole three-dimensional suspension bridge model is obtained through a rational function approximation of the generalized Theodorsen function and implemented in the FEM formulation. This paper lays the theoretical groundwork for the one that follows.