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Interaction of aeroelastic forces and turbulence at flutter onset wind speed
Abstract
The investigation of the self-feeding forces impact on the structural displacements in turbulent wind is presented. This impact is dealt with as a ratio of the displacement variances with and without the self-feeding forces, and a formula is proposed for this ratio on a 2DOF section-model. The paper also presents a method to determine the softness of the flutter that affects significantly the impact of the self-feeding forces over the buffeting forces. This method highlights the influence of the flutter derivatives on how the structural parameters affect the softness.
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This paper presents a simplified analytical formulation, including closed-form algebraic expressions, for determining the critical flutter velocity of cable supported bridges. The formulae have been developed from the fundamental aeroelastic equations by introducing two assumptions: (1) Flutter derivatives may be approximated by expressions providing a frequency-independent description of self-excited forces. (2) The critical frequency is on the torsional branch of the solution and may be approximated by an uncoupled system of equations. The formulae have been tested for two typical cross sections, for a wide range of hypothetical structural configurations and the structural configurations of some well-known bridges. The numerical results produced by the formulae have been compared with results obtained by complex eigenvalue analysis, and it is concluded that the formulae give satisfactory results for all the cases considered. It is well known that multimodal effects may reduce the stability limits of an aeroelastic system. Hence, multimodal effects have been carefully studied to provide new insight into when a bimodal approach is sufficient, and when a more comprehensive multimodal approach is needed.
Literature on turbulence is very wide, providing several models for the power spectral density function of the single-point turbulence components, for the two-point coherence function of the same turbulence component and for the single-point coherence function of different turbulence components. On the other hand, no suitable and simple model seems to be available for representing the two-point coherence function of different turbulence components, in particular of the longitudinal and vertical turbulence components, which would be useful for modelling buffeting actions on bridges. The Proper Orthogonal Decomposition provides efficient tools to formulate a new model of the turbulence field based on principal components. Furthermore, it suggests physical principles and defines mathematical rules to establish an appropriate model of the two-point coherence function of the longitudinal and vertical components, completing the statistical model of turbulence. Embedded in a Monte Carlo framework, this new representation can be used to simulate multi-dimensional and multi-variate random turbulence fields.
Better understanding of the bimodal coupled bridge flutter involving fundamental vertical bending and torsional modes offers valuable insight into multimode coupled flutter, which has primarily been the major concern in the design of long span bridges. This paper presents a new framework that provides closed-form expressions for estimating modal characteristics of bimodal coupled bridge systems and for estimating the onset of flutter. Though not intended as a replacement for complex eigenvalue analysis, it provides important physical insight into the role of self-excited forces in modifying bridge dynamics and the evolution of intermodal coupling with increasing wind velocity. The accuracy and effectiveness of this framework are demonstrated through flutter analysis of a cable-stayed bridge. Based on this analysis scheme, the role of bridge structural and aerodynamic characteristics on flutter, which helps to better tailor the structural systems and deck sections for superior flutter performance, is emphasized. Accordingly, guidance on the selection of critical structural modes and the role of different force components in multimode coupled flutter are delineated. The potential significance of the consid- eration of intermodal coupling in predicting torsional flutter is highlighted. Finally, clear insight concerning the role of drag force to bridge flutter is presented.
During the last decades, several studies on suspension bridges under wind actions have been developed in civil engineering and many techniques have been used to approach this structural problem both in time and frequency domain. In this paper, four types of time domain techniques to evaluate the response and the stability of a long span suspension bridge are implemented: nonaeroelastic, steady, quasi steady, modified quasi steady. These techniques are compared considering both nonturbulent and turbulent flow wind modelling. The results show consistent differences both in the amplitude of the response and in the value of critical wind velocity.
The response of suspension bridges to wind excitation is studied by means of numerical simulations with a specifically developed finite element program implementing full structural nonlinearities. A pure time-domain load model, linearized around the average configuration, is considered. The self-excited effects are included through the indicial function formulation, whereas the buffeting is considered according to the quasi-steady model. The response under turbulent wind, both fully and partially correlated, is evaluated through a Monte Carlo approach. A simplified structural model is considered, where only two cross-sections are modeled. This allows a high reduction of the number of degrees of freedom (DoFs) but maintains many characteristics of the true bridge, precluded to the classical 2-DoF sectional-model (e.g. considering more than two modes, including structural nonlinearities, introducing along-span wind coherence). The case studies of a long-span suspension bridge and a light suspension footbridge are analyzed. It is observed that structural nonlinearities deemphasize the presence of a critical flutter wind velocity, as they limit the oscillation amplitudes. On the other hand, fully correlated flow may produce an important underestimation of the structural response.
The dynamic response analysis of structures subjected to a stochastic wind field is carried out in the time domain by a step-by-step integration approach. The loading is represented by simulated time histories of the aerodynamic force. The auto-regressive and moving average (ARMA) recursive models are utilized to simulate time series of wind loads. Depending on the system dynamic characteristics, the time-integration schemes require that the time increment should not exceed a prescribed value. This study focuses on the development of ARMA representation based procedures to simulate realizations of wind loading with small time increments required by the time-integration schemes. A three-stage-matching method and a scheme which combines ARMA and digital interpolation filters are presented to efficiently generate correlated time histories of wind loads at the prescribed time increments.