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Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Agrivoltaics is a relatively new term used originally for integrating photovoltaic (PV) systems into the agricultural landscape and expanded to applications such as animal farms, greenhouses, and recreational parks. The dual use of land offers multiple solutions for the renewable energy sector worldwide, provided it can be implemented without negatively impacting agricultural production. However, agrivoltaics represent a relatively new technology, facing challenges including economic viability, vulnerability to wind loads, and interference with growing crops. This paper reviews the recent research on integrating agrivoltaics with farming applications, focusing on challenges, wind impact on agrivoltaics, and economic solutions. The effect of agrivoltaics on temperature control of the lands is a critical factor in managing (1) water and the soil of the land, (2) animal comfort, and (3) greenhouse productivity, positively or negatively. In this review, a contradiction between the different versions of the American Society of Civil Engineers (ASCE) standards and the wind tunnel results is shown. Important factors affecting the wind load, such as damping and mass increase, optimum stow position, and aerodynamic edge modification, are highlighted with emphasis on the significant knowledge gap in the wind load mitigation methods. [ABSTRACT FROM AUTHOR]

Signal complexity analysis based entropy measure has been used to propose a model-free approach towards assessment of flutter critical wind speed and identification of the type of flutter in wind tunnel testing of long span bridges. The approach is based only on the measured output responses from the structure, which accounts for appropriate effects that stem from the non-linearity of the structure and fluid structure interaction. The usefulness of the proposed approach has been demonstrated with dynamic sectional models of two deck cross-sections in wind tunnel. The gain in regularity of responses on approaching the flutter critical wind speed, demonstrated with time history of responses and recurrence quantification plots, has been quantified using sample entropy. Based on the sensitivity of the sample entropy values on the embedding dimension, it has been suggested to adopt embedding dimension in the range of 2 and 5, to obtain a swift estimate of the state of the dynamic system. The proposed approach has shown potential to provide valuable insight about the flutter instability and distinguish between different types of flutter without requiring prior knowledge about the system under consideration. The study offers a promising complementary methodology to the conventional model-based approaches for evaluating flutter critical wind speed. [ABSTRACT FROM AUTHOR]

This study presents a comprehensive investigation on the characteristics of the aerodynamic damping and amplitude-dependent flutter derivatives of a streamlined box girder for various wind angles of attack through a scaled section-model free vibration wind tunnel test. The response characteristics of the section model in vertical, torsional, and vertical–torsional coupled directions are investigated. A piecewise sliding windows fitting method, which is effective, generic, and at the same time provides an accurate estimation of the amplitude-dependent damping ratio, is proposed. The method is applied in three experimental measured examples, and the yielded results match satisfactorily with the measurements, confirming the feasibility and the advantage of the proposed method. Besides, the modal damping ratios of the section model for the considered degrees of freedom at different cases are identified from the method. The evolution of the aerodynamic damping with the wind speed and wind angle of attack and its influence on the generation of stable and unstable limit cycle oscillations and flutter response are discussed. The contribution of vertical and torsional motion to the generation of different flutter types is revealed. The full set of amplitude-dependent flutter derivatives is identified from the experimental modal properties of the different dynamic systems. The accuracy of the flutter derivatives is cross-validated through a free vibration wind tunnel test. [ABSTRACT FROM AUTHOR]

In this paper, the critical wind speed of flutter has been predicted by using two-dimensional computational fluid dynamics (CFD) model side by side with the empirical formula (Selberg's formula, 1961). The deck section of the Great Belt Bridge's main span has been used herein as a reference among other sectional varieties. For each case of the examined sections, the width was changed case by case, while its depth maintained unchanged. Both of the two methods, the semi-empirical using the "CFD" simulation and the empirical formula have been employed to predict the critical wind speed of flutter for a variety of the (width/depth) ratio and the natural frequency ratio (torsional/vertical). The results were obtained from the semi-empirical method and validated by comparison with wind tunnel test for typical section model of the Great Belt Bridge presented in the literature, and also compared with the empirical method. The results were represented graphically for each method and they have indicated the variation of the critical speed in terms of the section dimension and its natural frequencies, and furthermore, the change of the difference between the two methods was represented too. [ABSTRACT FROM AUTHOR]

Featured Application: This study provides a simplified approach to the flutter analysis of suspension bridges having two superposed decks. The George Washington Bridge engineering case is analyzed, in consideration of its historical relevance and age. The obtained results are compared with the predictions of simplified formulations available from other sources. We deal with the flutter analysis of the George Washington bridge, in both the single- and double-deck configurations of 1931 and 1962, respectively. The influence of the additional lower deck on the aerodynamic behavior is investigated. To overcome the lack of aerodynamic data, a simplified approach is followed based on Fung's formulation, in which the flutter derivatives are expressed in terms of the real and imaginary parts of the Theodorsen function and of the steady-state aerodynamic coefficients of the deck cross-section. The latter are obtained by Computational Fluid Dynamics simulations conducted in ANSYS FLUENT, whereas the ANSYS Mechanical APDL finite element package is used to perform the flutter analyses. Two different methods for the application of the aeroelastic forces are employed for the double-deck configuration: (i) self-excited forces, based on flutter derivatives related to the whole cross-section, acting on the upper deck; and (ii) self-excited forces, based on flutter derivatives related to the single deck, simultaneously applied to the upper and lower decks. The obtained results are critically compared with theoretical predictions of simple formulas available from the literature; it is suggested that laboratory tests are needed since no experimental results seem to be available. [ABSTRACT FROM AUTHOR]

The significance of long-span bridges being susceptible to wind-induced vibrations and the need for evaluating their aerodynamic performance is the focus of this study. The main emphasis is on experimental methods for assessing the bridges' aerodynamic stability, using sectional model tests with the free vibration technique. The dynamic properties of the model are determined from the measured response, using various system identification methods, including the modified Ibrahim time domain (MITD) and iterative least squares (ILS) for two-degree-of-freedom systems and the logarithmic decrement method (LDM) and the Hilbert transform method (HTM) for single-degree-of-freedom (SDOF) systems. A new dynamic testing setup was designed to facilitate single-degree-of-freedom (heave and pitch) and coupled two-degree-of-freedom (2DOF) motion in a wind tunnel section model. The vertical and torsional stiffnesses of the model were adjusted with elastic springs. A Great Belt Bridge section model was selected for testing due to its streamlined aerodynamic shape. The direct and crossflow derivatives were extracted from the measured response using the system identification methods mentioned. Additionally, analytical studies and numerical computational fluid dynamics simulations were conducted to validate the experimental results. The study found that HTM is most effective in SDOF due to its ability to extract both damping and frequency from the nonlinear response, whereas the MITD method is faster in converging system parameters in 2DOF system tests. The experimental and numerical results are comparable to the flat plate, which confirms the streamlined behavior of the Great Belt section from an aerodynamic perspective. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The clarification of the nonlinear and unsteady aerodynamic characteristics of a quasi-flat plate is of great importance to predict its wind-induced post-flutter behavior. Forced motion wind tunnel tests on a quasi-flat plate sectional model with a width-over-thickness ratio of 62.5:1 are conducted using the synchronous measurement of the dynamic forces and torsional displacements at various initial angles of attack (AoAs), vibration amplitudes and incoming wind speeds. The flutter derivatives related to torsional degree of freedom (DOF) are identified and compared. The nonlinear and unsteady characteristics of self-excited forces (SEFs) in terms of the frequency components and phase lag between the force and motion are quantitatively examined. The wind-induced energy maps of the quasi-flat plate at various initial AoAs are analyzed by introducing the aerodynamic work done by the self-excited lifting moment. A polynomial model is proposed to describe the nonlinear characteristics of the SEFs. It is validated that the flutter derivatives related to the torsional DOF are almost a single-valued function with respect to the reduced frequency, even at large vibration amplitudes. At large initial AoAs and oscillation amplitudes, the high-order frequency components of SEFs are significant, and the nonlinearity of the self-excited lifting moment is stronger than that of the self-excited lift force for torsional motion. This provides a reasonable explanation for the significant amplitude dependence of the flutter derivatives related to the lifting moment. The proposed polynomial nonlinear SEF model can achieve satisfactory accuracy in reproducing the SEFs in both time and frequency domains. [ABSTRACT FROM AUTHOR]

This paper presents a novel parameter identification and uncertainty quantification method for flutter derivatives estimation of bridge decks. The proposed approach is based on free-decay vibration records of a sectional model in wind tunnel tests, which consists of parameter identification by a heuristic optimization algorithm in the sense of weighted least squares and uncertainty quantification by a bootstrap technique. The novel contributions of the method are on three fronts. Firstly, weighting factors associated with vertical and torsional motion in the objective function are determined more reasonably using an iterative procedure rather than preassigned. Secondly, flutter derivatives are identified using a hybrid heuristic and classical optimization method, which integrates a modified artificial bee colony algorithm with the Powell's algorithm. Thirdly, a statistical bootstrap technique is used to quantify the uncertainties of flutter derivatives. The advantages of the proposed method with respect to other methods are faster and more accurate achievement of the global optimum, and refined uncertainty quantification in the identified flutter derivatives. The effectiveness and reliability of the proposed method are validated through noisy data of a numerically simulated thin plate and experimental data of a bridge deck sectional model. [ABSTRACT FROM AUTHOR]

Aerodynamic flutter instability could lead to the catastrophic collapse of flexible long-span bridges and needs to be prevented. This study investigated the variability of eight experimentally measured flutter derivatives (FDs) for a commonly used a Pasco–Kennewick (PK) section girder using a free vibration technique in a wind tunnel, which provided some new insights into the identification of FDs and supplemented the reliability analysis for buffeting and flutter performance. The aerodynamic uncertainties in terms of the dispersion of flutter coefficients were studied and two implications behind the extraction of FDs were discussed. The statistical and probabilistic behaviors of FDs at different reduced wind speeds were examined before generating sufficient independent random samples using the Monte Carlo (MC) approach. The intercorrelations between experimental FDs quantified by correlation coefficients were also examined and were employed to randomly sample the correlated FDs. The probabilistic flutter solutions in terms of critical wind speed propagated from the FDs uncertainties were studied utilizing step-by-step analysis, which resulted in several multimodal probability distributions of flutter onset. In addition, the role played by each FD on the variation of critical wind speed was discussed. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Flutter derivatives identified from transient (free-decay) vibrations might not be suitable for the analysis of bridge flutter. The application of transient flutter derivatives in the flutter analysis relies on two assumptions: (1) transient flutter derivatives and steady-state flutter derivatives are equivalent and (2) aeroelastic effects are superposable. Both assumptions are challenged in this article. It is shown through transient vibration tests that (1) the aeroelastic-coupling between heaving and rotational motions may switch from one pattern to another as the wind speed varies and (2) some of the transient flutter derivatives may be time-varying. The former implies that the predicted flutter type based on transient flutter derivatives may not be unconditionally consistent with the experimentally observed flutter type; the latter implies the transient flutter derivatives may be physically different from the steady-state flutter derivatives. These two issues undermine the basic assumptions of the flutter analysis of bridges. A possible corollary to this study is that if free vibration is used to predict bridge flutter, we should resort to the steady-state (flutter state) vibration instead of the transient vibration of the sectional model. A revision to the aeroelastic force model is proposed to facilitate the discussion. [ABSTRACT FROM AUTHOR]

To analyze the effects of a central stabilizer on the flutter performance at large angles of attack, this study takes the ideal plate as a section of a bridge deck. The aerodynamic characteristics of stationary cross sections are examined using computational fluid dynamics simulations, and the flutter derivatives are extracted by forced vibration. The critical flutter speed of a target bridge is then calculated, and the aerodynamic mechanism of the central stabilizer is discussed from the work done by aerodynamic forces’ perspective. The results show that use of a central stabilizer with lower heights favors flutter stability at smaller angles of attack by improving the participation level of heaving motion, but the stability of the systematic heaving motion will decrease if the stabilizer is too high, leading to galloping. At larger angles of attack, where the movement of a big vortex causes the occurrence of torsional flutter, the stabilizer can hinder the movement of the vortex if they are on the same side, and the critical flutter speed increases with the increase in stabilizer height. [ABSTRACT FROM AUTHOR]

Bridges are an important component of transportation. Flutter is a self-excited, large amplitude vibration, which may lead to collapse of bridges. It must be understood and avoided. This paper takes the Jianghai Channel Bridge, which is a significant part of the Hong Kong-Zhuhai-Macao Bridge, as an example to investigate the flutter of the bridge deck. Firstly, aerodynamic force models for flutter of bridges were introduced. Then, wind tunnel tests of the bridge deck during the construction and the operation stages, under different wind attack angles and wind velocities, were carried out using a high frequency base balance (HFBB) system and laser displacement sensors. From the tests, the static aerodynamic forces and flutter derivatives of the bridge deck were observed. Correspondingly, the critical flutter wind speeds of the bridge deck were determined based on the derivatives, and they are compared with the directly measured flutter speeds. Results show that the observed derivatives are reasonable and applicable. Furthermore, the critical wind speeds in the operation stage is smaller than those in the construction stage. Besides, the flutter instabilities of the bridge in the construction and the operation stages are good. This study helps guarantee the design and the construction of the Jianghai Channel Bridge, and advances the understanding of flutter of long afterbody bridge decks. [ABSTRACT FROM AUTHOR]

A novel system decoupling approach (SDA) that enables three degree-of-freedom (3-DOF) bridge flutter analysis is proposed in this study to simultaneously investigate the relationships between modal parameters and 18 flutter derivatives. Based on the incentivefeedback mechanisms, the aerodynamic coupled system is conveniently decoupled in an iterative solution. Based on the SDA, it is unnecessary to simultaneously calculate all multiple frequencies for determining modal parameters and eventually quantifying critical flutter wind velocity. The efficacy and accuracy of the SDA is verified using a numerical example of thin flat plate. The coupling effects among three DOFs and influence of 18 flutter derivatives on flutter performance are quantified using the newly proposed method. The flutter mechanisms of thin flat plate and bluff deck section of the Akashi Kaikyo Suspension Bridge are numerically examined, and both difference and common grounds for two typical flutter phenomena are summarized. The results by the SDA show good agreement with those by the commonly used complex eigen-value analysis (CEVA). For the Akashi Kaikyo Bridge with bluff deck section, the analytical results of 2-DOF coupled flutter are coincident with the 3-DOF case and the experimental observations. This study provides significant insights into the flutter characteristics of 3-DOF bridges and explores the roles played by various parameters in modifying bridge deck aerodynamics and the evolution of modal coupling with increasing wind velocity. The simplified formulation that only concerns A* 1; A* 2; A* 3;H* 3 is presented, by which acceptable accuracy of flutter parameters can also be achieved for torsional modal branch. It is validated using a thin flat plate and the Akashi Kaikyo Bridge with bluff deck. [ABSTRACT FROM AUTHOR]

In this work the practical applicability of a 2D URANS approach adopting a block structured mesh and Menter’s SST k-ω turbulence model in fluid-structure interaction (FSI) problems is studied using as a test case a ratio B/H = 4 rectangular cylinder. The vortex-induced vibration (VIV) and torsional flutter phenomena are analyzed based on the computation of the out-of-phase and in-phase components of the forced frequency component of lift and moment coefficients when the section is forced to periodically oscillate both in heave and pitch degrees of freedom. Also the flutter derivatives are evaluated numerically from the same forced oscillation simulations. A good general agreement has been found with both experimental and numerical data reported in the literature. This highlights the benefits of this relatively simple and straightforward approach. These methods, once their feasibility has been checked, are ready to use in parametric design of bridge deck sections and, at a later stage, in the shape optimization of deck girders considering aeroelastic constraints. [ABSTRACT FROM AUTHOR]

For long bridges with bluff deck sections, the influence of lateral wind loads on flutter performance needs to be carefully investigated. In this paper, an advanced three-degree-of-freedom (3-DOF) analytical framework considering lateral aeroelastic effects is developed to refine bridge flutter analysis. This approach uses high-order nonlinear equations to determine twin critical flutter parameters, i.e., velocity and frequency. An optimization model to determine the critical flutter parameters is developed. A practical diagrammatical technique is proposed to solve this problem, which is an improvement over the traditional optimization techniques. The intuitiveness and effectiveness of the diagrammatical technique is fully verified using a numerical example. The optimization model and diagrammatical technique are applied to the 3-DOF flutter analyses of two bridges with bluff deck sections. It is revealed that the flutter derivatives , , , , and () play an insignificant role in flutter performance of both bridges. If , the () will be paralyzed, and the influence of only the conventional eight flutter derivatives, those related to the heaving and torsional motions, can be considered. On the other hand, if (), , , and will also lose efficacies. These novel findings are first presented, which can be steadily proved by the explicit expression of the optimization model. This study presents a valuable insight into the flutter characteristics of both bridges and explores the roles in the flutter onset played by various parameters. Further, even with bluff deck sections of both bridges, the analytical results of 2-DOF vertical-torsional coupled flutter for the Akashi Kaikyo Bridge and the 1-DOF torsional flutter for the Suramadu Bridge are coincident with the experimental observations. Thus, the effectiveness of analytical framework is again verified. [ABSTRACT FROM AUTHOR]

For a slender long-span bridge, the global aeroelastic and aerodynamic phenomena, such as flutter stability and buffeting response, induced by wind turbulence significantly affect the safety and lifetime performance of the bridge. To investigate these phenomena, a wind tunnel experimental technique with bridge section models is typically required to identify some critical aerodynamic coefficients, such as flutter derivatives, which are dependent on the specific profile (shape) of a bridge cross section and the functions of reduced frequencies. Obviously, this practice is based on the assumption that the shape of the cross section of a long-span bridge does not vary over time. Such an assumption may not remain valid when the stochastic traffic on the bridge is considered, because of the simple fact that the presence of vehicles changes the profile of the bridge cross section. The current study aims to provide some insights through experimental assessment of traffic impacts on flutter derivatives of the modified bridge cross section because of the presence of traffic. A bridge section model with scaled vehicle models distributed on the bridge deck is tested in the wind tunnel following the simulated stochastic traffic flow. Several scenarios are tested to provide insights on the variations of the flutter derivatives over different sections along the bridge and at different time instants for the same location. In addition, some extreme situations, such as under evacuation or serious congestion, are also studied. [ABSTRACT FROM AUTHOR]

In this paper, the covariance-driven stochastic subspace identification technique (SSI-COV) was presented to extract the flutter derivatives of bridge decks from the buffeting test results. An advantage of this method is that it considers the buffeting forces and responses as inputs rather than as noises. Numerical simulations and wind tunnel tests of a streamlined thin plate model conducted under smooth flows by the free decay and the buffeting tests were used to validate the applicability of the SSI-COV method. Then, the wind tunnel tests of a two-edge girder blunt type of industrial-ring-road (IRR) bridge deck were conducted under smooth and turbulence flows. The flutter derivatives of the thin plate model identified by the SSI-COV technique agree well with those obtained theoretically. The results obtained for the thin plate and the IRR bridge deck are used to validate the reliability and applicability of the SSI-COV technique to various wind tunnel tests and conditions of wind flows. The results also show that for the blunt-type IRR bridge deck, the turbulence wind will delay the onset of flutter, compared with the smooth wind. [ABSTRACT FROM AUTHOR]

Flutter derivatives are essential for flutter analysis of long-span bridges, and they are generally identified from the vibration testing data of a sectional model suspended in a wind tunnel. Making use of the forced vibration testing data of three sectional models, namely, a thin-plate model, a nearly streamlined model, and a bluff-body model, a comparative study was made to identify the flutter derivatives of each model by using a time-domain method and a frequency-domain method. It was shown that all the flutter derivatives of the thin-plate model identified with the frequency-domain method and time-domain method, respectively, agree very well. Moreover, some of the flutter derivatives of each of the other two models identified with the two methods deviate to some extent. More precisely, the frequency-domain method usually results in smooth curves of the flutter derivatives. The formulation of time-domain method makes the identification results of flutter derivatives relatively sensitive to the signal phase lag between vibration state vector and aerodynamic forces and also prone to be disturbed by noise and nonlinearity. [ABSTRACT FROM AUTHOR]

In light of the characteristics of the interactions between flexible structure and wind in three directions, and based on the rational mechanical section-model of structure, a new aerodynamic force model is accepted, i. e. the coefficients of three component forces are the functions of the instantaneous attack angle and rotational speed Ci = Ci(β(t), Θ), (i = D, L, M). So, a new method to formulate the linear and nonlinear aerodynamic items of wind and structure interacting has been put forward in accordance with “strip theory” and modified “quasi-static theory”, and then the linear and nonlinear coupled theory of super-slender structure for civil engineering analyzing are converged in one model. For the linear aerodynamic-force parts, the semi-analytical expressions of the items so-called “flutter derivatives” corresponding to the one in the classic equations have been given here, and so have the nonlinear parts. The study of the stability of nonlinear aerodynamic-coupled torsional vibration of the old Tacoma bridge shows that the form and results of the nonlinear control equation in rotational direction are in agreement with that of V. F. Böhm's. [ABSTRACT FROM AUTHOR]

In light of the characteristics of the interactions between flexible structure and wind in three directions, and based on the rational mechanical section-model of structure, a new aerodynamic force model is accepted, i. e. the coefficients of three component forces are the functions of the instantaneous attack angle and rotational speed Ci=Ci(β(t),ϑ), (i=D, L, M.). So, a new method to formulate the linear and nonlinear aerodynamic items of wind and structure interacting has been put forward in accordance with “strip theory” and modified “quasi-static theory”, and then the linear and nonlinear coupled theory of super-slender structure for civil engineering analyzing are converged in one model. For the linear aerodynamic-force parts, the semi-analytical expressions of the items so-called “flutter derivatives” corresponding to the one in the classic equations have been given here, and so have the nonlinear parts. The study of the stability of nonlinear aerodynamic-coupled torsional vibration of the old Tacoma bridge shows that the form and results of the nonlinear control equation in rotational direction are in agreement with that of V. F. Böhm's. [ABSTRACT FROM AUTHOR]