Aerodynamic admittance functions and buffeting forces for bridges via indicial functions

Buffeting forces on bridge decks are commonly modelled by Sears’ function. However, it is well known that Sears’ function is reliable only for very streamlined bridge deck sections and that a complete model would require a suitable formulation of buffeting forces in time domain. In this paper, self-excited and buffeting loads are modelled by means of indicial functions. Corresponding aerodynamic admittance functions are numerically evaluated for rectangular sections and compared with experimental and analytical results. A complete time-domain model for cross-sections including vertical turbulence is presented. Numerical simulations are performed on a sample rectangular section. Comparison with experimental results and relevant flutter analyses are also discussed.     

桥梁多模态耦合抖振控制方法研究

目前已证实调谐质量阻尼器(TM D)可以有效控制桥梁抖振响应,并已在工程中得到应用。然而,传统桥梁抖振被动控制理论是基于单模态叠加SRSS法,无法考虑多模态参与作用和模态间气动耦合效应,本文基于Scan lan多模态耦合抖振理论和多重调谐质量阻尼器(M TM D)被动控制理论,提出一种桥梁多模态耦合抖振M TM D控制方法,该方法可以考虑多模态参与作用、模态间气动耦合效应和单模态中各模态位移分量的气动耦合,且对各TM D在主梁上的安装位置没有任何限制。本文最后采用时域仿真方法对该方法进行了验证,两者计算结果吻合良好,表明本文所提出的方法的正确性。     

Using a Proper Orthogonal Decomposition representation of the aerodynamic forces for stochastic buffeting prediction

High-performance aircraft often suffer from the consequences of tail buffeting at moderate subsonic Mach numbers and medium to high angles of attack. The impact of the aircraft’s highly unsteady flow field on the tails can result in significant structural fatigue and degraded handling qualities. Various methods have been developed to predict tail buffeting. Stochastic response methods are among frequently used approaches. For such methods the size of the excitation data set can become an issue, especially when the auto- and cross-spectra of all available excitation signals on the configuration are considered. The present paper demonstrates how to modify stochastic tail buffeting prediction methods using Proper Orthogonal Decomposition (POD). The approach is based on the modal decomposition of the aerodynamic buffet excitation data set. It notably reduces the computational effort for structural response and loads prediction with limited losses in accuracy while using all power- and cross-spectra of the reduced dataset. The method was applied to the computational buffeting prediction for a generic configuration with double-delta wing and horizontal tail plane (HTP) over a wide range of angles of attack. It was shown that the POD-modes of the aerodynamic buffet excitation resembled the characteristics of configuration’s complex vortical flow field. The predicted structural response and loads converged well with increasing number of POD-modes. With the presented approach, the computational effort of stochastic tail buffeting prediction has been reduced by orders of magnitude compared to the case with the full aerodynamic buffet excitation data set.     

叶轮机械叶片颤振研究的进展与评述

颤振一类气动弹性稳定性问题是叶轮机械设计者关心的主要问题之一. 本文对叶轮机械叶片颤振模型研究的进展进行了回顾, 包括非定常气动模型、结构模型以及颤振的预测方法等内容. 通过对颤振模型研究的介绍, 讨论了不同方法处理颤振这类气动弹性稳定性问题的优缺点. 提出了关于颤振研究目前的不足和部分难点, 认为流固耦合模型的研究值得进一步重点关注.      

安装固定气动翼板的大跨桥梁抖振分析

建立了安装固定气动翼板的大跨桥梁多模态耦合抖振分析框架，推演了作用在整个桥梁-气动翼板系统上的抖振力和自激力的显式表达式，考虑了多模态耦合效应．基于有限元法，作用在主梁-气动翼板系统上的抖振力转化为节点力，进一步得到作用在整个桥梁上的抖振力并导出了其功率谱密度矩阵；作用在主梁．气动翼板系统上的气弹自激力转化为节点力，并将其表达为气弹刚度矩阵和气弹阻尼矩阵．通过组集得到系统的运动方程，然后运用虚拟激励法在频域计算系统的抖振响应．以某大跨斜拉桥为例进行研究，结果表明：在主梁下方安装-对固定气动翼板后，主梁的扭转角位移、角加速度以及侧向加速度响应能够得到有效控制。     

Aerodynamic equivalence of asymmetric bodies with allowance for nonlinear body shape influence factors and angle of attack

In order to determine the aerodynamic coefficients of asymmetric bodies the principle of aerodynamic equivalence is used. In the gas dynamic function expansions in the asymmetry parameter and the angle of attack both linear and second-order terms are taken into account. This makes it possible to establish theoretically the principle of aerodynamic equivalence with allowance for nonlinear body shape influence factors and angle of attack. A universal structure of the aerodynamic characteristics of asymmetric bodies with an arbitrary cross-sectional shape is obtained. The theoretical conclusions are confirmed by the results of a numerical solution of the three-dimensional gas dynamic problem.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 116–122, November–December, 1993.     

Parametric studies on relationships between flutter derivatives of slender bridge （Ⅱ）

Based on curve fitting of coefficients of three component forces of the Messina Straits Bridge, and the previously proposed semi-analytical expressions of flutter derivatives of flexible structure, the change of flutter derivatives of slender bridge cross-section with respect to its aerodynamic center, rotational speed and angle variation is studied using a parametric method. The calculated results are compared with the measured ones, and expressions of flutter derivatives of the Messina Straits Bridge are derived. The intrinsic relationships existing in flutter derivatives are validated again. It is shown that the influence of the rotational speed on flutter derivatives is not negligible. Therefore, it provides an additional semi-analytical approach for analyzing flutter derivatives of the bridge with streamlined cross-section to get its aerodynamic information.     

Modeling and analysis of piezoaeroelastic energy harvesters

This work investigates the influence of structural and aerodynamic nonlinearities on the dynamic behavior of a piezoaeroelastic system. The system is composed of a rigid airfoil supported by nonlinear torsional and flexural springs in the pitch and plunge motions, respectively, with a piezoelectric coupling attached to the plunge degree of freedom. The analysis shows that the effect of the electrical load resistance on the flutter speed is negligible in comparison to the effects of the linear spring coefficients. The effects of aerodynamic nonlinearities and nonlinear plunge and pitch spring coefficients on the system’s stability near the bifurcation are determined from the nonlinear normal form. This is useful to characterize the effects of different parameters on the system’s output and ensure that subcritical or “catastrophic” bifurcation does not take place. Numerical solutions of the coupled equations for two different configurations are then performed to determine the effects of varying the load resistance and the nonlinear spring coefficients on the limit-cycle oscillations (LCO) in the pitch and plunge motions, the voltage output and the harvested power.     

Parametric studies on relationships between flutter derivatives of slender bridge (Ⅱ)

Based on curve fitting of coefficients of three component forces of the Messina Straits Bridge, and the previously proposed semi-analytical expressions of flutter deriva-tives of flexible structure, the change of flutter derivatives of slender bridge cross-section with respect to its aerodynamic center, rotational speed and angle variation is studied using a parametric method. The calculated results are compared with the measured ones, and expressions of flutter derivatives of the Messina Straits Bridge are derived. The in-trinsic relationships existing in flutter derivatives are validated again. It is shown that the influence of the rotational speed on flutter derivatives is not negligible. Therefore, it provides an additional semi-analytical approach for analyzing flutter derivatives of the bridge with streamlined cross-section to get its aerodynamic information.     

Linear and Nonlinear Aerodynamic Theory of Interaction between Flexible Long Structure and Wind

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Effects of vertical central stabilizers on nonlinear wind-induced stabilization of a closed-box girder suspension bridge with various aspect ratios

The aerodynamic shape of a closed-box girder plays an important role in the wind-induced stabilization of long-span suspension bridges. The purpose of this study is to investigate the effects of the combination of five aspect ratios and a downward vertical central stabilizer (DVCS) on nonlinear flutter and aerostatic behaviors of a super long-span suspension bridge with closed-box girders. Through conducting a series of wind-tunnel tests and nonlinear finite element analysis, the results show that the nonlinear self-excited forces and the critical wind speed (U_cr) gradually increase as the increase of the aspect ratio (i.e. the width to depth ratios). Furthermore, the application of 20% deck depth DVCS could significantly increase the nonlinear self-excited forces and U_cr for small aspect ratios of 7.9 and 7.1. Particularly, the installation of the DVCS could change the flutter divergence patterns of the bridge from soft flutter to hard flutter, especially for a relatively small aspect ratio. In addition, the aerostatic force coefficients and torsional divergence critical wind speeds of the larger aspect ratio with DVCS are significantly larger than that without DVCS. A relatively small aspect ratio of the bridge has better aerostatic performance than that with a larger aspect ratio.

     

Analytical formulation of 2-D aeroelastic model in weak ground effect

This paper deals with the aeroelastic modeling and analysis of a 2-D oscillating airfoil in ground effect, elastically constrained by linear and torsional springs and immersed in an incompressible potential flow (typical section) at a finite distance from the ground. This work aims to extend Theodorsen theory, valid in an unbounded flow domain, to the case of weak ground effect, i.e., for clearances above half the airfoil chord. The key point is the determination of the aerodynamic loads, first in the frequency domain and then in the time domain, accounting for their dependence on the ground distance. The method of images is exploited in order to comply with the impermeability condition on the ground. The new integral equation in the unknown vortex distribution along the chord and the wake is solved using asymptotic expansions in the perturbation parameter defined as the inverse of the non-dimensional ground clearance of the airfoil. The mathematical model describing the aeroelastic system is transformed from the frequency domain into the time domain and then in a pure differential form using a finite-state aerodynamic approximation (augmented states). The typical section, which the developed theory is applied to, is obtained as a reduced model of a wing box finite element representation, thus allowing comparison with the corresponding aeroelastic analysis carried out by a commercial solver based on a 3-D lifting surface aerodynamic model. Stability (flutter margins) and response of the airfoil both in frequency and time domains are then investigated. In particular, within the developed theory, the solution of the Wagner problem can be directly achieved confirming an asymptotic trend of the aerodynamic coefficients toward the steady-state conditions different from that relative to the unbounded domain case. The dependence of flutter speed and the frequency response functions on ground clearance is highlighted, showing the usefulness of this approach in efficiently and robustly accounting for the presence of the ground when unsteady analysis of elastic lifting surfaces in weak ground effect is required.     

Panel flutter prediction in two dimensional flow with enhanced piston theory

Piston theory may be used in the high Mach number supersonic flow region and/or in very high frequency subsonic or supersonic flow. In this flow model, the pressure at a point on the fluid-solid interface only depends on the downwash at the same point. However the classical piston theory may not be sufficient for some phenomena in aeroelasticity and aeroacoustics (far field prediction). Dowell and Bliss have created an extension of piston theory that allows for higher order effects that take into account the effect the distribution of downwash on pressure at any point. For simple harmonic motion, expansions in reduced frequency, inverse reduced frequency and/or inverse (square of) Mach number have all been created; The effects of higher order terms in these several expansion in creating an enhanced piston theory was illustrated for plunge and pitch motion of an airfoil (discrete system) by Ganji and Dowell. In the present paper, flutter prediction for a flexible panel in two –dimensional flow is investigated using enhanced piston theory. The goal of the present paper is to demonstrate that an enhance version of piston theory can analyze single degree of freedom flutter of a panel as compared to the classical piston theory and quasi-steady aerodynamic models which can only treat coupled mode flutter.     

飞行器跨声速气动弹性数值分析

将流体和结构运动方程分别构造为含子迭代的计算格式,发展了一种紧耦合气动弹性分析方法.其中流体计算的空间离散采用改进的HLLEW(Harten—Lax-van Leer-Einfeldt-Wada)格式. TFI(transfinite inter- polation)方法用于生成随结构变形的自适应多块动网格.利用所发展的方法,对-翼-身-尾气动外形,数值预测了马赫数在0.3-1.3范围内的气动颤振边界.并详细研究了时间步长、子迭代步数、初始流场、耦合方法、疏密网格对颤振计算结果的影响.     

Separated Flow and Buffeting Control

In transonic flow conditions, the shock wave/turbulent boundary layer interaction and the flow separations on the upper wing surfaces of civil aircraft induce flow instabilities, ‘buffet’ and then structural vibrations, ‘buffeting’. Buffeting can greatly affect aerodynamic behavior. The buffeting phenomenon appears when the aircraft's Machnumber or angle of attack increases. This phenomenon limits the aircraft's flight envelope. The objectives of this study are to cancel out or decrease the aerodynamic instabilities (unsteady separation, movement of the shock position) due to this type of flow by using control systems. The following actuators can be used: ‘Vortex Generators’ situated upstream of the shock position, a ‘Bump’ located at the shock position, and a new moving part designed by ONERA, situated on the trailing edge of the wing, the ‘Trailing Edge Deflector’ or TED. It looks like an adjustable ‘Divergent Trailing Edge’. It is an active actuator and can take different deflections or be driven by dynamic movements up to 250 Hz. Tests were performed in transonic 2D flow with models well equipped with unsteady pressure transducers. For high lift coefficients, a selected static position of the ‘Trailing Edge Deflector’ increases the wing's aerodynamic performances and delays the onset of buffet. Furthermore, in 2D flow buffet conditions, the ‘Trailing Edge Deflector’, driven by a closed-loop active control using the measurements of the unsteady wall static pressures, can greatly reduce buffet. The aerodynamic performances are not improved to the same extent by the bump actuator. From our experience, there is no effect on buffet or separated flow because of the incorrect positioning of the bump. All that can be observed is a local improvement on the intensity of the shock wave when the bump is very precisely situated at the shock position. Vortex generators have a great impact on the separated flow. The separated flow instabilities are greatly reduced and buffet is totally controlled even for strong instabilities. The aerodynamic performances of the airfoil are also greatly improved.     

Limit cycle oscillations of two-dimensional panels in low subsonic flow

Limit cycle oscillations of a two-dimensional panel in low subsonic flow have been studied theoretically and experimentally. The panel is clamped at its leading edge and free at its trailing edge. A structural non-linearity arises in both the bending stiffness and the mass inertia. Two-dimensional incompressible (linear) vortex lattice aerodynamic theory and a corresponding reduced order aerodynamic model were used to calculate the linear flutter boundary and also the limit cycle oscillations (that occur beyond the linear flutter boundary).     

An analytical and experimental investigation into limit-cycle oscillations of an aeroelastic system

We perform an analytical and experimental investigation into the dynamics of an aeroelastic system consisting of a plunging and pitching rigid airfoil supported by a linear spring in the plunge degree of freedom and a nonlinear spring in the pitch degree of freedom. The experimental results show that the onset of flutter takes place at a speed smaller than the one predicted by a quasi-steady aerodynamic approximation. On the other hand, the unsteady representation of the aerodynamic loads accurately predicts the experimental value. The linear analysis details the difference in both formulation and provides an explanation for this difference. Nonlinear analysis is then performed to identify the nonlinear coefficients of the pitch spring. The normal form of the Hopf bifurcation is then derived to characterize the type of instability. It is demonstrated that the instability of the considered aeroelastic system is supercritical as observed in the experiments.     

Modeling and validation of hitch loading effects on tractor yaw dynamics

This paper develops a yaw dynamic model for a farm tractor with a hitched implement, which can be used to understand the effect of tractor handling characteristics for design applications and for new automated steering control systems. Dynamic equations which use a tire-like model to capture the characteristics of the implement are found to adequately describe the tractor implement yaw dynamics. This model is termed the “3-wheeled” Bicycle Model since it uses an additional wheel (from the traditional bicycle model used to capture lateral dynamics of passenger vehicles) to account for the implement forces. The model only includes effects of lateral forces as it neglects differential longitudinal or draft forces between inner and outer sides of the vehicle. Experiments are taken to verify the hitch model using a three-dimensional force dynamometer. This data shows the implement forces are indeed proportional to lateral velocity and that differential draft forces can be neglected as derived in the “3-wheeled” Bicycle Model. Steady state and dynamic steering data are used for implements at varying depths and speeds to quantify the variation in the hitch loading. The dynamic data is used to form empirical transfer function estimates (ETFEs) of the implements and depths in order to determine the coefficients used in the “3-wheeled” Bicycle Model. Changes in a single parameter, called the hitch cornering stiffness, can capture the various implement configurations. Finally, a model that includes front wheel drive forces is derived. Experiments are taken which provide a preliminary look into the effect of four-wheel drive traction forces, and show a difference with two-wheel versus four-wheel drive, on the yaw dynamics of a tractor with the hitched implement.     

Unsteady aerodynamic reduced-order modeling of an aeroelastic wing using arbitrary mode shapes

Computational fluid dynamics (CFD) based unsteady aerodynamic reduced-order model (ROM) can offer significant improvements to the efficiency of transonic aeroelastic analysis. To construct a ROM based on mode shapes, one run of CFD solver is needed to compute aerodynamic responses corresponding to mode excitations. When mode shapes change with structure, another run of the CFD solver is required to construct the new ROM. The typically large computational cost associated with repeated runs of the CFD solver impedes the application of existing unsteady aerodynamic reduced-order modeling methods to transonic aeroelastic design optimization and aeroelastic uncertainty analysis. This paper demonstrates a method that can replace the CFD solver used in the process of existing unsteady aerodynamic reduced-order modeling. It can produce aerodynamic responses corresponding to mode excitations for arbitrary mode shapes within a few seconds. Computational cost can be reduced by two orders of magnitude using the mode excitations and the corresponding aerodynamic responses computed by the method to construct the ROMs used for flutter analyses in aeroelastic design optimization or aeroelastic uncertainty analysis in transonic regime compared with the existing unsteady aerodynamic reduced-order modeling methods. Results show that the method can accurately produce the aerodynamic responses corresponding to the mode excitations and predict the flutter characteristics of AGARD 445.6 wings root-attached in three different ways.