An accurate singularity-free geometrically exact beam formulation using Euler parameters

Wind-induced nonlinear oscillations of twin-box girder bridges are very sensitive to the aerodynamic shape of the deck (i.e., slot width ratio (SWR) and wind fairing shape) due to the complicated flow characteristics around the bridge deck. This paper presents a fully integrated finite element (FE) model in time domain, involving a nonlinear aerodynamic force model and a bridge FE model, to allow the investigation of nonlinear oscillation behaviors of long-span twin-box girder bridges with various SWRs and wind fairing shapes. The parameters in integrated FE model were firstly identified by using CFD simulation, and then, the proposed model was validated by conducting wind tunnel testing using sectional models and full-bridge aeroelastic models. It demonstrates that the developed integrated model has the capability of simulating the nonlinear flutter behaviors of twin-box girder bridges with various aerodynamic shapes. Furthermore, the prediction results show that the wind fairing shape has significant impact on the degree of freedom participation in coupled oscillation and failure modes, as well as flutter performance of the bridges. In addition, there is an increase in amplitudes of the limit cycle oscillations with the increase in the SWR of the twin-box girder bridges, and the relationships between the bending-torsional coupled oscillation, failure modes, and SWR of the bridges with anti-symmetric wind fairings are opposite to those with symmetric wind fairings.     

Modeling vortex-shedding effects for the stochastic response of tall buildings in non-synoptic winds

This study derives a model for the vortex-induced vibration and the stochastic response of a tall building in strong non-synoptic wind regimes. The vortex-induced stochastic dynamics is obtained by combining turbulent-induced buffeting force, aeroelastic force and vortex-induced force. The governing equations of motion in non-synoptic winds account for the coupled motion with nonlinear aerodynamic damping and non-stationary wind loading. An engineering model, replicating the features of thunderstorm downbursts, is employed to simulate strong non-synoptic winds and non-stationary wind loading. This study also aims to examine the effectiveness of the wavelet-Galerkin (WG) approximation method to numerically solve the vortex-induced stochastic dynamics of a tall building with complex wind loading and coupled equations of motions. In the WG approximation method, the compactly supported Daubechies wavelets are used as orthonormal basis functions for the Galerkin projection, which transforms the time-dependent coupled, nonlinear, non-stationary stochastic dynamic equations into random algebraic equations in the wavelet space. An equivalent single-degree-of-freedom building model and a multi-degree-of-freedom model of the benchmark Commonwealth Advisory Aeronautical Research Council (CAARC) tall building are employed for the formulation and numerical analyses. Preliminary parametric investigations on the vortex-shedding effects and the stochastic dynamics of the two building models in non-synoptic downburst winds are discussed. The proposed WG approximation method proves to be very powerful and promising to approximately solve various cases of stochastic dynamics and the associated equations of motion accounting for vortex shedding effects, complex wind loads, coupling, nonlinearity and non-stationarity.     

Nonlinear aeroelastic stability analysis of wind turbine blade with bending–bending–twist coupling

In this study, the nonlinear aeroelastic stability of wind turbine blade with bending–bending–twist coupling has been investigated for composite thin-walled structure with pretwist angle. The aerodynamic model used here is the differential dynamic stall nonlinear ONERA model. The nonlinear aeroelastic equations are reduced to ordinary equations by Galerkin method, with the aerodynamic force decomposition by strip theory. The nonlinear resulting equations are solved by a time-marching approach, and are linearized by small perturbation about the equilibrium point. The nonlinear aeroelastic stability characteristics are investigated through eigenvalue analysis, nonlinear time domain response, and linearized time domain response.     

基于Huth方法的民机气动弹性改进建模方法

使用高仿真精度和高计算效率的有限元模型进行飞机颤振边界预测具有重要意义．本文提出了基于Huth紧固件柔度计算方法的民机气动弹性模型的改进建模方法，计及了固定前缘的刚度及其与机翼盒段之间的弹性效应，建立了全机气动弹性模型并进行了固有特性和颤振特性分析．分析结果与全机地面共振试验、风洞试验结果的偏差均在±1 %以内，分析时长与现有模型基本保持不变，验证了改进建模方法的有效性．     

Assessment of low-altitude atmospheric turbulence models for aircraft aeroelasticity

We investigate the dynamic aeroelastic response of large but slow aircraft in low-altitude atmospheric turbulence. To this end, three turbulence models of increasing fidelity, namely, the one-dimensional von Kármán model, the two-dimensional Kaimal model and full three-dimensional wind fields extracted from large-eddy simulations (LES) are used to simulate ambient turbulence near the ground. Load calculations and flight trajectory predictions are conducted for a representative high-aspect-ratio wing aircraft, using a fully coupled nonlinear flight dynamics/aeroelastic model, when it operates in background atmospheric turbulence generated by the aforementioned models. Comparison of load envelopes and spectral content, on vehicles of varying flexibility, shows strong dependency between the selected turbulence model and aircraft aeroelastic response (e.g. 58% difference in the predicted magnitude of the wing root bending moment between LES and von Kármán models). This is mainly due to the presence of large flow structures at low altitudes that have comparable dimensions to the vehicle, and which despite the relatively small wind speeds within the Earth boundary layer, result in overall high load events for slow-moving vehicles. Results show that one-dimensional models that do not capture those effects provide fairly non-conservative load estimates and are unsuitable for very flexible airframe design.     

On damage detection by continuous dynamic monitoring in wind-excited suspension bridges

The paper discusses the application of dynamic methods for damage detection in the main cables of suspension bridges, using data continuously recorded under wind excitation through permanent monitoring systems and automated operational modal analysis. A continuum model for predicting the vertical aeroelastic response of wind-excited damaged suspension bridges is formulated and presented at first. The model shows that, for a real sample bridge, typical variations of mean wind speed produce variations of natural frequencies, due to aeroelastic effects, that are more significant than those produced by a small damage. A possible solution to this issue, proposed in the paper, consists of removing the dependence on the excitation source by calculating frequency shifts considering frequencies, in reference and damaged states, associated to approximately the same mean wind speed. This task and the necessary estimation of frequency shifts through a statistical analysis of identified natural frequencies outline the need for a continuous dynamic monitoring. The analytical model is finally employed for generating dynamic wind response data that are successively processed by means of an advanced automated modal identification tool. Although based on the simplifications inherently contained in the analytical model, the results show that frequency shifts caused by a relatively small damage can be accurately estimated from response data recorded under wind excitation with a reasonable number of data sets.     

Aeroelastic analysis of large horizontal wind turbine baldes

A nonlinear aeroelastic analysis method for large horizontal wind turbines is described. A vortex wake method and a nonlinear finite element method (FEM) are coupled in the approach. The vortex wake method is used to predict wind turbine aerodynamic loads of a wind turbine, and a three-dimensional (3D) shell model is built for the rotor. Average aerodynamic forces along the azimuth are applied to the structural model, and the nonlinear static aeroelastic behaviors are computed. The wind rotor modes are obtained at the static aeroelastic status by linearizing the coupled equations. The static aeroelastic performance and dynamic aeroelastic responses are calculated for the NH1500 wind turbine. The results show that structural geometrical nonlinearities significantly reduce displacements and vibration amplitudes of the wind turbine blades. Therefore, structural geometrical nonlinearities cannot be neglected both in the static aeroelastic analysis and dynamic aeroelastic analysis.     

Linear and nonlinear aeroelastic analysis frameworks for cable-supported bridges

Based on the general framework of the linear thin airfoil theory, aeroelastic analysis of bridges has evolved over the last few decades in both time and frequency domains. As the bridge span increases, aeroelastic forces exerted on the evolving bridge deck cross-sections exhibit a clear departure from the linearized analysis framework that have been the basis of conventional schemes. This trend and observations of nonlinearity in the bridge aeroelasticity in wind-tunnel experiments have prompted the need for the development of a new general analysis framework attentive to both linear and nonlinear wind-bridge interactions. In this paper, the existing conventional linear and nonlinear analysis frameworks are first systematically reviewed with a focus on the study of the relationships among them. After analyzing the shortcomings of these conventional frameworks, two advanced nonlinear models, i.e., artificial neural network- (ANN-) and Volterra series-based models are introduced. The important parameters of conventional and advanced models are investigated in detail to emphasize the physical significance of these models in the simulation of the wind-bridge interactions. Application examples of the linear and nonlinear schemes are also presented highlighting the aeroelastic effects under smooth/turbulent wind conditions.     

Aeroelastic stability analysis of flexible overexpanded rocket nozzle

The aim of this paper is to present a new aeroelastic stability model taking into account the viscous effects for a supersonic nozzle flow in overexpanded regimes. This model is inspired by the Pekkari model which was developed initially for perfect fluid flow. The new model called the “Modified Pekkari Model” (MPM) considers a more realistic wall pressure profile for the case of a free shock separation inside the supersonic nozzle using the free interaction theory of Chapman. To reach this objective, a code for structure computation coupled with aerodynamic excitation effects is developed that allows the analysis of aeroelastic stability for the overexpanded nozzles. The main results are presented in a comparative manner using existing models (Pekkari model and its extended version) and the modified Pekkari model developed in this work.     

Dynamic instability of inclined cables under combined wind flow and support motion

In this paper an inclined nearly taut stay, belonging to a cable-stayed bridge, is considered. It is subject to a prescribed motion at one end, caused by traveling vehicles, and embedded in a wind flow blowing simultaneously with rain. The cable is modeled as a non-planar, nonlinear, one-dimensional continuum, possessing torsional and flexural stiffness. The lower end of the cable is assumed to undergo a vertical sinusoidal motion of given amplitude and frequency. The wind flow is assumed uniform in space and constant in time, acting on the cable along which flows a rain rivulet. The imposed motion is responsible for both external and parametric excitations, while the wind flow produces aeroelastic instability. The relevant equations of motion are discretized via the Galerkin method, by taking one in-plane and one out-of-plane symmetric modes as trial functions. The two resulting second-order, non-homogeneous, time-periodic, ordinary differential equations are coupled and contain quadratic and cubic nonlinearities, both in the displacements and velocities. They are tackled by the Multiple Scale perturbation method, which leads to first-order amplitude-phase modulation equations, governing the slow dynamics of the cable. The wind speed, the amplitude of the support motion and the internal and external frequency detunings are set as control parameters. Numerical path-following techniques provide bifurcation diagrams as functions of the control parameters, able to highlight the interactions between in-plane and out-of-plane motions, as well as the effects of the simultaneous presence of the three sources of excitation.     

Nonlinear aeroelastic reduced order modeling by recurrent neural networks

The paper develops a reduction scheme based on the identification of continuous time recursive neural networks from input–output data obtained through high fidelity simulations of a nonlinear aerodynamic model at hand. The training of network synaptic weights is accomplished either with standard or automatic differentiation integration techniques. Particular emphasis is given to using such a reduced system in the determination of aeroelastic limit cycles. The related solutions are obtained with the adoption of two different approaches: one trivially producing a limit cycle through time marching simulations, and the other solving a periodic boundary value problem through a direct periodic time collocation with unknown period. The presented formulations are verified for a typical section and the BACT wing.     

结构变形对气动力影响的计算分析

本文介绍了笔者在静气动弹性效应的理论与实验研究中的若干进展。静气动弹性研究涉及作用于飞行器的气 力与结构变形的相互作用,是研究飞行器的风洞试验数据和飞行试验数据相关性的一个重要方面。文讨论了在进行静气动弹性分析时对一些总理２的处理并对风洞试验模型及某型导弹进行了计算,结果表明,对于所选算例,结构变形使升力线斜率降低,压心前移。     

Aeroelastic analysis of cantilever plates using Peters’ aerodynamic model,and the influence of choosing beam or plate theories as the structural model

In this paper, the aeroelastic analyses of a rectangular cantilever plate of varying aspect ratio is presented. The classical plate theory has been selected as the structural model. The main point that distinguishes this study from previously reported research is employing Peters’ theory to model aerodynamic effect which is not straightforward. The Peters’ aerodynamic model was originally developed to provide lift and moment, which is only applicable to the structural model based on the beam theories. In this study, using the basic concept of the Peters’ aerodynamic model in addition to utilizing the Fourier series, the pressure distribution is derived, which makes Peters’ model applicable to structural models based on plate theory. This combination provides a much simpler state–space aeroelastic model for plates in comparison to the prevalent panel methods, which could lead to a significant reduction in computational time. In addition, the aeroelastic response of the plate with respect to changes in the structural model from the beam theory to the plate theory is evaluated. By using data from an experiment carried out at Duke University, the theoretical results are evaluated. Furthermore, the differences in structural models obtained from the plate and beam theories can be divided into two distinct parts, which are responsible for differences in bending and torsional behaviors of the structure, separately. This approach enables us to measure the effects of differences of each behavior separately, which could provide with a new insight into the problem. It has been determined that the flutter speeds obtained from the beam and plate aeroelastic models are little affected by the difference in bending behavior, but rather is mainly caused by the difference in torsional frequencies.     

Reduced order nonlinear aeroelasticity of swept composite wings using compressible indicial unsteady aerodynamics

Nonlinear dynamic aeroelasticity of composite wings in compressible flows is investigated. To provide a reasonable model for the problem, the composite wing is modeled as a thin walled beam (TWB) with circumferentially asymmetric stiffness layup configuration. The structural model considers nonlinear strain displacement relations and a number of non-classical effects, such as transverse shear and warping inhibition. Geometrically nonlinear terms of up to third order are retained in the formulation. Unsteady aerodynamic loads are calculated according to a compressible model, described by indicial function approximations in the time domain. The aeroelastic system of equations is augmented by the differential equations governing the aerodynamics lag states to derive the final explicit form of the coupled fluid-structure equations of motion. The final nonlinear governing aeroelastic system of equations is solved using the eigenvectors of the linear structural equations of motion to approximate the spatial variation of the corresponding degrees of freedom in the Ritz solution method. Direct time integrations of the nonlinear equations of motion representing the full aeroelastic system are conducted using the well-known Runge–Kutta method. A comprehensive insight is provided over the effect of parameters such as the lamination fiber angle and the sweep angle on the stability margins and the limit cycle oscillation behavior of the system. Integration of the interpolation method employed for the evaluation of compressible indicial functions at any Mach number in the subsonic compressible range to the derivation process of the third order nonlinear aeroelastic system of equations based on TWB theory is done for the first time. Results show that flutter speeds obtained by the incompressible unsteady aerodynamics are not conservative and as the backward sweep angle of the wing is increased, post-flutter aeroelastic response of the wing becomes more well-behaved.     

Entropy generation of radial rotation convective channels

The exchange of heat between two fluids is established by radial rotating pipe or a channel. The hotter fluid flows through the pipe, while the cold fluid is ambient air. Total length of pipe is made up of multiple sections of different shape and position in relation to the common axis of rotation. In such heat exchanger the hydraulic and thermal irreversibility of the hotter and colder fluid occur. Therefore, the total entropy generated within the radial rotating pipe consists of the total entropy of hotter and colder fluid, taking into account all the hydraulic and thermal irreversibility of both fluids. Finding a mathematical model of the total generated entropy is based on coupled mathematical expressions that combine hydraulic and thermal effects of both fluids with the complex geometry of the radial rotating pipe. Mathematical model follows the each section of the pipe and establishes the function between the sections, so the total generated entropy is different from section to section of the pipe. In one section of the pipe thermal irreversibility may dominate over the hydraulic irreversibility, while in another section of the pipe the situation may be reverse. In this paper, continuous analytic functions that connect sections of pipe in geometric meaning are associated with functions that describe the thermo-hydraulic effects of hotter and colder fluid. In this way, the total generated entropy of the radial rotating pipe is a continuous analytic function of any complex geometry of the rotating pipe. The above method of establishing a relationship between the continuous function of entropy with the complex geometry of the rotating pipe enables indirect monitoring of unnecessary hydraulic and thermal losses of both fluids. Therefore, continuous analytic functions of generated entropy enable analysis of hydraulic and thermal irreversibility of individual sections of pipe, as well as the possibility of improving the thermal–hydraulic performance of the rotating pipe consisting of n sections. Analytical modeling enabled establishing of a mathematical model of the total generated entropy in a radial rotating pipe, while the generated entropy of models with radial rotating pipe were determined by experimental testing, with comparisons of the achieved results.     

Study of techniques for obtaining continuous models from 2D discrete reduced‐order state‐space CFD models

The application of unsteady computational fluid dynamics (CFD) codes to aeroelastic calculations leads to a large number of degrees of freedom making them computationally expensive. Reduced‐order models (ROMs) have therefore been developed; an ROM is a system of equations which is able to reproduce the solutions of the full set of equations with reasonable accuracy, but which is of lower order. ROMs have been the focus of research in various engineering situations, but it is only relatively recently that such techniques have begun to be introduced into CFD. In order for the reduced systems to be generally applicable to aeroelastic calculations, it is necessary to have continuous time models that can be put into discrete form for different time steps. While some engineering reduction schemes can produce time‐continuous models directly, the majority of methods reported in CFD initially produce discrete time or discrete frequency models. Such models are restricted in their applicability and in order to overcome this situation, a continuous time ROM must be extracted from the discrete time system. This process can most simply be achieved by inverting the transformation from continuous to discrete time that was initially used to discretize the CFD scheme. However an alternative method reported in literature is based on continuous time sampling, even when this is not used for the initial discretization of the CFD code. This paper focuses on one particular method for ROM generation, eigensystem realization algorithm (ERA), that has been used in the CFD field. This is implemented to produce a discrete time ROM from a standard CFD code, that can be used to investigate methods for obtaining continuous ROMs and the limitations of the resulting models. Copyright © 2006 John Wiley & Sons, Ltd.     

Analysis of self-excited forces for a box-girder bridge deck through unsteady RANS simulations

This paper presents the results of two-dimensional numerical simulations of the flow field around a trapezoidal box-girder bridge section with later cantilevers, experiencing small-amplitude heaving or pitching harmonic oscillations. Unsteady Reynolds-averaged Navier–Stokes equations are solved in conjunction with an eddy-viscosity and an explicit algebraic Reynolds stress model. Flutter derivatives are determined and compared with wind tunnel results, showing fairly good agreement. The degree of sharpness of the deck lower edges is found to play a key role in the aeroelastic behavior of the profile. In particular, the bridge section fully behaves as a bluff body and is prone to low-reduced-wind-speed torsional galloping in the case of perfectly sharp edges. By contrast, the presence of a small radius of curvature in the section lower corners changes the nature of the instability to coupled flutter and significantly postpones the stability threshold, in line with a quasi-streamlined body behavior. Moreover, a wide sensitivity study is carried out, investigating the influence on the self-excited forces of the amplitude of oscillation, mean angle of attack and Reynolds number. In particular, the numerical simulations for the geometry with smooth lower edges highlight the regime transition occurring when the Reynolds number is varied, with significant effects on the flutter derivatives. Finally, the numerical flow visualizations provide a physical explanation of some phenomena observed in the wind tunnel experiments.     

高超声速风洞短时气动力智能辨识算法研究

风洞测力试验是高超声速飞行器研发的重要环节,随着这项技术的发展,试验模型的大尺度化成为高超声速风洞试验的趋势.在几百毫秒的有效测试时间内,大尺度测力系统刚度减弱等问题会严重导致气动力辨识精度变差,试验模型大尺度化对短时脉冲燃烧风洞精确气动力辨识带来了挑战.对此本文提出了一种新的基于传统信号处理结合深度学习的智能气动力辨...     

Passive aeroelastic control of a suspension bridge during erection

This study presents a system based on passively controlled leading- and trailing-edge flaps that is designed to suppress wind-induced instabilities such as flutter and torsional divergence. The utility of the approach is demonstrated on a three-dimensional bridge model. Particular emphasis is placed on the early stages of the deck erection process when the bridge is particularly vulnerable to flutter. The flaps are activated by the deck's movements though passive phase-compensating mechanisms comprising of springs, dampers and inerters. It is demonstrated that optimised compensator parameters, and optimum hinge locations, result in a substantially improved deck aerodynamic performance. Particular importance is given to ensuring that the controlled system has good closed-loop ‘robustness’ properties, or in other words, that the controlled system has a high tolerance to parameter variations and uncertainties in the system dynamics. The practical use of a nonlinear optimisation algorithm with a FE bridge aeroelastic model, which includes the flap dynamics, necessitates the use of reduced-order models. A novel model reduction procedure that is based on the retention of dominant poles is introduced into the aeroelastic modelling framework. Multimodal interactions are observed at the various erection stages and conclusions are drawn with regard to the contributions of various modes of vibration to aeroelastic instabilities. The main advantage of this approach lies on the passive system's simplicity and its ability to simultaneously increase the flutter and torsional divergence boundaries. The Humber Bridge in the U.K. is chosen as a study example for numerical simulations.