Support vector machine based aerodynamic analysis of cable stayed bridges

Flutter, a self-excited vibration resulting from the interaction between structural motion and aerodynamic force, is the major aspect in wind resistant design of cable stayed bridges. The critical speed for flutter of a deck section can be evaluated using the flutter derivatives obtained by sectional model testing of the bridge deck in a wind tunnel. Since it is very expensive, time consuming and laborious to conduct wind tunnel tests for all the practical dimensions of deck, the support vector machine (SVM) is applied for predicting the flutter derivatives for any deck size. The wind tunnel experimental data is collected from literature and SVM is trained. Thus predicted flutter derivatives are used for estimation of critical flutter velocity of cable stayed bridges. The effect of each aerodynamic derivative on flutter instability is investigated in this study.     

Sensitivity analysis of bridge flutter with respect to mechanical parameters of the deck

A methodology for carrying out an analytical sensitivity analysis of the flutter phenomenon in long-span bridges is developed. Decks of bridges are generally bluff bodies and therefore the aeroelastic forces under wind action have to be experimentally evaluated in wind tunnels. Such forces depend on the response frequency of the bridge, which is not known until the problem is solved. Consequently, the calculus of the critical wind speed that initiates the flutter instability comprises a complex nonlinear eigenvalue problem. During the design phase, the sensitivity analysis gives very interesting information about the gradient of the flutter speed with respect to the key chosen design variables, moments of inertia of the bridge deck. The presented method is applied to the Great Belt and Vasco da Gama Bridges, as well as to the old Tacoma Bridge.     

Critical and flutter speeds of optical disks

 Critical speeds and aerodynamic flutter instability of various optical disks are experimentally studied in this paper. The two nodal diameter modes of ASMO and CD/DVD disks have the lowest critical speeds at 3800 and 6900 rpm, respectively, where the backward natural frequency vanishes. As the rotational speed increases, aeroelastic disk flutter is observed. Experiments using ASMO disks show that the three nodal diameter mode causes flutter instability at 8750 rpm. At the flutter speed, the vibration amplitude of the flutter mode grows dramatically. The natural frequencies of multiple vibration modes remain almost constant in the post-flutter region, which is called frequency lock-on. CD/DVD disks do not experience flutter up to 14,000 rpm. Received: 5 July 2001/Accepted: 1 November 2001     

动力伞伞翼阵风响应的数值模拟

采用有限体积法求解非定常Euler方程,并通过引入动态网格方法模拟阵风条件,对不同风速下水平和垂直阵风的伞翼气动力响应进行动态模拟与计算,针对动力伞伞翼柔性结构和飞行速度慢的特点,运用动态仿真方法求解阵风响应的附加气动力与力矩。结果表明:遇水平阵风时,伞翼气动力表现为多周期不同幅度的主动颤振运动;遇垂直阵风时,气动力响应基本与阵风速度变化趋势保持一致,最终稳定后气动力相对于阵风加载前变化不大。     

Aeroelastic time response analysis of thin airfoils by transonic code LTRAN2

A computer based numerical procedure is used to perform aeroelastic time response analysis of thin airfoils oscillating with single and two d.o.f.'s in two-dimensional, unsteady, low-frequency, small-disturbance, transonic potential flow. A computational transonic code LTRAN2 based on fully implicit time integration scheme is employed to obtain the aerodynamic forces. Structural equations of motion and the aerodynamic equations are integrated simultaneously by a numerical method. Results are first obtained for a time response example for a flat plate oscillating at M_∞ = 0.7 with (1) a single pitching d.o.f.; (2) a single plunging d.o.f.; and (3) two d.o.f.s—plunging and pitching. A parallel set of results are also obtained based on subsonic aerodynamic theory for comparison. The agreement is good. Results are then obtained for a time response example for a NACA 64A006 airfoil pitching and plunging at M_∞ = 0.85 which was found to give the lowest flutter speed for the case considered. The parameters that result in neutrally stable response agree with those found in a separate flutter analysis. It was found through comparison between flutter results and response analysis that the principle of superposition of airloads is valid for the present example cases. The results also include the effect of altitude on aeroelastic response.     

Three dimensional numerical simulations of long-span bridge aerodynamics, using block-iterative coupling and DES

The design of long-span bridges often depends on wind tunnel testing of sectional or full aeroelastic models. Some progress has been made to find a computational alternative to replace these physical tests. In this paper, an innovative computational fluid dynamics (CFD) method is presented, where the fluid-structure interaction (FSI) is solved through a self-developed code combined with an ANSYS-CFX solver. Then an improved CFD method based on block-iterative coupling is also proposed. This method can be readily used for two dimensional (2D) and three dimensional (3D) structure modelling. Detached-Eddy simulation for 3D viscous turbulent incompressible flow is applied to the 3D numerical analysis of bridge deck sections. Firstly, 2D numerical simulations of a thin airfoil demonstrate the accuracy of the present CFD method. Secondly, numerical simulations of a U-shape beam with both 2D and 3D modelling are conducted. The comparisons of aerodynamic force coefficients thus obtained with wind tunnel test results well meet the prediction that 3D CFD simulations are more accurate than 2D CFD simulations. Thirdly, 2D and 3D CFD simulations are performed for two generic bridge deck sections to produce their aerodynamic force coefficients and flutter derivatives. The computed values agree well with the available computational and wind tunnel test results. Once again, this demonstrates the accuracy of the proposed 3D CFD simulations. Finally, the 3D based wake flow vision is captured, which shows another advantage of 3D CFD simulations. All the simulation results demonstrate that the proposed 3D CFD method has good accuracy and significant benefits for aerodynamic analysis and computational FSI studies of long-span bridges and other slender structures.     

Aerodynamic effect on natural frequency and flutter instability in rotating optical disks

 Experimental studies on the aerodynamic coupling effect on natural frequencies and flutter instability of rotating disks are investigated in this paper. The experiments performed using a vacuum chamber and optical disks give two main results. One is that the aerodynamic effect by surrounding air reduces the natural frequencies and critical speeds of the vibration modes in pre-flutter regions. The other is that the natural frequency of the disk rotating at ambient atmospheric pressure is equal to that in vacuum at the flutter onset speed where the disk experiences aero-induced flutter. In post-flutter regions, the aerodynamic coupling between the disk and surrounding air increases the natural frequencies of the disk. Received: 17 June 2002/Accepted: 7 October 2002 The work was supported by Grant No. R11-1997-042-090001-0 of the Center for Information Storage Devices designated by the Korea Science & Engineering Foundation. Paper presented at the 13th Annual Symposium on Information Storage and Processing Systems, Santa Clara, CA, USA, 17–18 June, 2002     

Comparison of numerical techniques for 3D flutter analysis of cable-stayed bridges

This paper presents the results of a comparison study of the numerical techniques of structural and aerodynamic force models developed based on the spline finite strip method with the conventional finite element approach in three-dimensional flutter analysis of cable-stayed bridges. In the new formulation, the bridge girder is modelled by spline finite strips. The mass and stiffness properties of the torsional behaviour of complex bridge girder, which have a significant influence on the wind stability of long-span bridges, are modelled accurately in the formulation. The effects of the spatial variation of the aerodynamic forces can be taken into account in the proposed numerical model by distributing the loads to the finite strips modelling the bridge deck. The numerical example of a 423 m long-span cable-stayed bridge is presented in the comparison study. The accuracy and effectiveness of the proposed finite strip model are compared to the results obtained from the equivalent beam finite element models. The advantages and disadvantages of these different modelling schemes are discussed.     

Aeroelastic tailoring considering uncertainties in material properties

The robustness of aeroelastic design optimization with respect to uncertainties in material and structural properties is studied both numerically and experimentally. The model consists of thin orthotropic composite wings virtually without fuselage. Three different configurations with consistent geometry but varying orientation of the main stiffness axis of the material are investigated. The onset of aeroelastic instability, flutter, is predicted using finite element analysis and the doublet-lattice method for the unsteady aerodynamic forces. The numerical results are experimentally verified in a low-speed wind tunnel. The optimization problem is stated as to increase the critical air speed, above that of the bare wing by massbalancing. It is seen that the design goals are not met in the experiments due to uncertainties in the structural performance of the wings. The uncertainty in structural performance is quantified through numerous dynamic material tests. Once accounting for the uncertainties through a suggested reformulation of the optimization problem, the design goals are met also in practice. The investigation indicates that robust and reliable aeroelastic design optimization is achievable, but careful formulation of the optimization problem is essential.     

Buffet suppression in long-span suspension bridges

We study the aerodynamic control of long-span suspension bridges and seek to raise the critical flutter wind speeds, while simultaneously suppressing buffeting. The control system design study is based on a simple flexible bridge section model that interacts with a constant-velocity air stream. A streamlined bridge deck is assumed and non-steady thin aerofoil theory is used to describe the interactions between the bridge deck and the air stream. Classical turbulence models, first developed in the aircraft industry, are used to model the buffet forces acting on the deck. While a wide variety of control systems is possible, we focus on a compensation scheme that can be implemented using passive mechanical components such as springs, dampers and a rack and pinion mechanism. A single-loop control system is investigated that controls a trailing-edge flap by sensing movements of the bridge deck; several such mechanisms are contemplated. The first finding is that the critical wind speed for flutter can be greatly increased, with good robustness characteristics, through passive feedback control. It is also possible simultaneously to suppress flutter using the same passive mechanical controller by solving a passive mixed H₂/H_∞ control problem. The effect of flexible controller mounting arrangements are considered briefly.     

Active control of supersonic/hypersonic aeroelastic flutter for a two-dimensional airfoil with flap

The flutter, post-flutter and active control of a two-dimensional airfoil with control surface operating in supersonic/hypersonic flight speed regions are investigated in this paper. A three-degree-of-freedom dynamic model is established, in which both the cubic nonlinear structural stiffness and the nonlinear aerodynamic load are accounted for. The third order Piston Theory is employed to derive the aerodynamic loads in the supersonic/hypersonic airflow. Nonlinear flutter happens with a phenomenon of limit...     

Robust control of wind turbines based on fractional nonlinear disturbance observer

In order to assure maximum energy conversion, the angular velocity of the wind turbine rotor tracks a nominal profile depending on the wind speed. However, conventionally, wind flows present non‐differentiable components due to turbulence and gust winds, which affect the wind energy management. Thus, a fast and robust controller is required to induce such nominal regime for maximum energy transfer. A fractional‐order nonlinear disturbance‐observer (FNDOB) is proposed in this paper to cancel the non‐differentiable components of the wind speed, as well as dynamic uncertainties and other aerodynamic disturbances. The proposed FNDOB is based on continuous fractional sliding modes, assuring that disturbances and uncertainties are exactly compensated in finite‐time. A representative simulation study for a variable‐speed wind turbine is presented to show the reliability of the proposed scheme, and a comparative analysis with respect to a conventional linear disturbance observer based control is presented.     

基于CFD系统辨识的气弹分析及GPU并行算法初探

通过求解Euler方程获得运动翼段的非定常流场,并用CUDA语言对流场求解器进行GPU并行计算.使用ARMA(auto-regressive-moving-average)模型对非定常气动力进行辨识,由系统辨识模型得到的结果与全阶CFD计算结果十分吻合.基于降阶气动模型与结构的耦合,计算了具有S型颤振边界的气动弹性标准算例-Isogai Wing的跨音速颤振.本文给出的方法可以在保证气动弹性计算精度的前提下大幅提高计算效率.     

Calculation of critical flutter speeds of an aircraft in subsonic flow

The procedure for calculation of critical flutter speeds of an aircraft in subsonic flow on minicomputer, is displayed in the paper.Problem of vibrational assymmetry, determined during vibrational tests, is solved using decomposition of each mode into inertialy normalised symmetrical and antisyrnmetrical parts. Unsteady aerodynamic loadings are determined by the doublet-lattice method. Modest memory of minicomputer used dictated the choice of the method of optimal elimination for solution of an assymmetric system of complex linear equations.Interpolation of total matrices of generalised aerodynamical forces is done by, in this paper proposed, modified method of natural cubic spline.Flutter eigenvalues are calculated using iterative Laguerre's procedure.     

Aeroelastic tailoring using fiber orientation and topology optimization

This work presents a structural optimization aided design methodology for composite laminated plates subject to fluid-structure interaction. The goal of the optimization procedure is to increase the flutter speed onset through the maximization of natural frequencies related to the vibration modes involved in the phenomenon. The aeroelastic stability analysis is performed using ZAERO software system, which includes ZONA 6 unsteady lifting surface method. The finite element method is applied to solve the structural model equilibrium equations, the eigenvalues sensitivities with respect to design variables are calculated analytically, and sequential linear programming is applied. The maximization is accomplished using two methods; the first method uses an aeroelastic analysis to determine which eigenmode causes the flutter onset, and its eigenvalue is then maximized. In the second method, a forward finite difference method is applied and the flutter speed sensitivities with respect to the eigenvalues are calculated. This sensitivity is used to guide the optimization process. Finally, a topology optimization problem is formulated to reduce the plate mass under a minimum flutter velocity constraint, using density distribution as the design variable.     

Computational visualization of unsteady flow around vehicles using high performance computing

One of the largest-scale unstructured Large Eddy Simulation (LES) of flow around a full-scale road vehicle is conducted on the Earth Simulator in Japan. The main objective of our study is to look into the validity of LES for the assessment of vehicle aerodynamics, especially in the context of its possibility for unsteady or transient aerodynamic forces. Firstly, the aerodynamic LES proposed is quantitatively validated on the ASMO simplified model by comparing the mean pressure distributions on the vehicle surface with those obtained by a conventional Reynolds-Averaged Navier-Stokes simulation (RANS) or a wind tunnel measurement. Then, the method is applied to the full-scale vehicle with complicated geometry to qualitatively investigate the capability of capturing organized flow structures around the vehicle. Finally, unsteady aerodynamic forces acting on the vehicle in transient yawing angle change are estimated and relationship between the flow structures and the transient aerodynamic forces is mentioned. As a result, it is demonstrated that LES will be a powerful tool for the vehicle aerodynamic assessment in the foreseeable future, because it can provide precious aerodynamic data which conventional wind tunnel tests or RANS simulations are difficult to provide.     

基于数值计算的高速列车气动阻力风洞试验缩比模型选取方法

为给高速列车气动阻力风洞试验模型选取提供更多的参考依据,通过计算流体力学(Computational Fluid Dynamics,CFD)方法,研究不同比例的高速列车缩比模型对气动阻力风洞试验结果的影响.首先,计算得到开口式风洞测试段的静压系数分布曲线,为高速列车气动阻力测量试验模型的长度选择以及摆放位置提供依据;其次,通过数值计算得到全尺寸模型列车在明线运行时,以及不同比例的模型列车在风洞中运行工况下的气动阻力信息,并从阻塞效应和雷诺数的变化,以及风洞试验段内静压分布的影响这3个方面对列车模型的气动阻力结果进行分析,得到在所研究风洞中较合理的列车缩比模型比例选取范围.这种以CFD为基础进行数值仿真,选取风洞试验中列车模型比例及试验测试位置的方法,为在地面交通工具风洞中进行高速列车模型气动阻力试验的缩比模型选取提供一定依据.     

基于复模态方法的二维夹层壁板颤振分析

本文研究二维夹层壁板在一侧受超音速气动力的情况下的颤振现象.利用复模态方法和伽辽金方法分析颤振临界马赫数以及夹芯粘性阻尼对颤振的影响.结果发现考虑前四阶模态时,由于一二阶频率重合而使振动能量积聚发生颤振.考虑中间层的粘弹性时,发现随着粘性阻尼的增加,颤振临界马赫数和临界颤振频率均呈现先降低后升高的现象,其原因是粘弹性一方面降低系统固有频率使得临界马赫数降低,另一方面又使能量耗散使得临界马赫数升高,在这两种作用的影响下出现了上述复杂的现象.本文的研究结果有利于颤振抑制时的设计优化.     

Robust nonlinear control strategy to maximize energy capture in a variable speed wind turbine with an internal induction generator

This paper proposes a control strategy to maximize the wind energy captured in a variable speed wind turbine,with an internal induction generator,at low to medium wind speeds.The proposed strategy cont...     

Evolution of long-span bridge response to wind-numerical simulation and discussion

Flutter and buffeting are two important phenomena of long-span bridges susceptible to wind actions. When the wind velocity increases to the bridge flutter velocity, an initial or self-excited multi-frequency vibration in laminar flow becomes single-frequency flutter instability. Similarly, in turbulent flow, the multi-frequency buffeting vibration develops into a single-frequency dominated divergent vibration that can also be interpreted as flutter instability. Even though this transition from buffeting to flutter was observed in wind tunnel tests, the mechanism of transition from multi-frequency type of buffeting to single-frequency type of flutter has not been well demonstrated numerically. Some existent explanations on the occurrence of flutter are very generic and even somewhat confusing. An attempt to reinvestigate numerically the transition of these two phenomena was made in the present study. The established procedure demonstrates numerically how a pre-flutter multi-frequency free vibration and a multi-frequency buffeting vibration merge into a single-frequency dominated flutter at the flutter critical wind velocity. It is concluded that the modal coupling effect forces all modes to vibrate mainly in a frequency close to the oscillation frequency of the critical flutter mode. The oscillation frequency of each mode itself does not merge to that of the critical mode. As a result, some confusing concepts in flutter vibrations are clarified and the mechanisms of the vibration transition process are better understood. Numerical analyses of the Humen suspension bridge with a main span of 888 m were conducted to facilitate the discussions.