• Wind and Structures
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• v.2 no.1
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• pp.41-49
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• 1999

The flutter of a bridge is induced by self-excited force factors such as lift, drag and aerodynamic moment. These factors are associated with flutter derivatives in the analysis of wind engineering. The flutter derivatives are the function of structure configuration, wind velocity and response circular frequency. Therefore, the governing equations for the interaction between the wind and dynamic response of the structure are complicated and highly nonlinear. Herein, a numerical algorithm through graphical technique for the solution of wind at flutter is presented. It provides a concise approach to the solution of wind velocity at flutter.

• Wind and Structures
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• v.27 no.6
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• pp.381-397
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• 2018

Nonlinear behavior in fluid-structure interaction (FSI) of bridge decks becomes increasingly significant for modern bridges with increasing spans, larger flexibility and new aerodynamic deck configurations. Better understanding of the nonlinear aeroelasticity of bridge decks and further development of reduced-order nonlinear models for the aeroelastic forces become necessary. In this paper, the amplitude-dependent and neutral angle dependent nonlinearities of the motion-induced loads are further highlighted by series of computational fluid dynamics (CFD) simulations. An effort has been made to investigate a semi-analytical time-domain model of the nonlinear motion induced loads on the deck, which enables nonlinear time domain simulations of the aeroelastic responses of the bridge deck. First, the computational schemes used here are validated through theoretically well-known cases. Then, static aerodynamic coefficients of the Great Belt East Bridge (GBEB) cross section are evaluated at various angles of attack, leading to the so-called nonlinear backbone curves. Flutter derivatives of the bridge are identified by CFD simulations using forced harmonic motion of the cross-section with various frequencies. By varying the amplitude of the forced motion, it is observed that the identified flutter derivatives are amplitude-dependent, especially for $A^*_2$ and $H^*_2$ parameters. Another nonlinear feature is observed from the change of hysteresis loop (between angle of attack and lift/moment) when the neutral angles of the cross-section are changed. Based on the CFD results, a semi-analytical time-domain model for describing the nonlinear motion-induced loads is proposed and calibrated. This model is based on accounting for the delay effect with respect to the nonlinear backbone curve and is established in the state-space form. Reasonable agreement between the results from the semi-analytical model and CFD demonstrates the potential application of the proposed model for nonlinear aeroelastic analysis of bridge decks.

• Journal of the Korean Society for Aviation and Aeronautics
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• v.21 no.4
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• pp.47-52
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• 2013

In this paper, limit cycle flutter induced by Hopf bifurcation is studied with nonlinear system analysis approach and observed for the critical slowing down phenomenon. Considering an attractor of the dynamics of a system, when a small perturbation is applied to the system, the dynamics converge toward the attractor at some rate. The critical slowing down means that this recovery rate approaches zero as a parameter of the system varies and the size of the basin of attraction shrinks to nil. Consequently, in the pre-bifurcation regime, the recovery rates decrease as the system approaches the bifurcation. This phenomenon is one of the features used to forecast bifurcation before they actually occur. Therefore, studying the critical slowing down for limit cycle flutter behavior would have potential applicability for forecasting those types of flutter. Herein, modeling and nonlinear system analysis of the 2D airfoil with torsional nonlinearity have been discussed, followed by observation of the critical slowing down phenomenon.

• Journal of the Korean Society for Aviation and Aeronautics
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• v.18 no.1
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• pp.27-32
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• 2010

In this study, transonic flutter response characteristics have been studied for the AGARD 445.6 wing considering various turbulent models and several angle of attacks. The developed fluid-structure coupled analysis system is applied for flutter computations combining computational structural dynamics(CSD), finite element method(FEM) and computational fluid dynamics(CFD) in the time domain. The flutter boundaries of AGARD 445.6 wing are verified using developed computational system. For the nonlinear unsteady aerodynamics in high transonic flow region, DES turbulent model using the structured grid system have been applied for the wing model. Characteristics of flutter responses have been investigated for various angle of attack conditions. Also, it is typically shown that the current computation approach can yield realistic and practical results for aircraft design and test engineers.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.5
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• pp.496-502
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• 2008

In this study, supersonic and hypersonic flutter characteristics have been analyzed for the various typical section shapes of missile fin configurations. Nonlinear flutter analyses are conducted considering the effect of moving shock waves. Computational fluid dynamic method is applied to accurately predict unsteady aerodynamic loads due to structural motions for the solution of aeroelastic governing equations. Commonly used typical section shapes of supersonic and hypersonic launch vehicles are considered in the present numerical study. Detailed flutter responses for four different typical section models are presented and the flutter characteristics are physically investigated.

• Journal of the Korea Institute of Military Science and Technology
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• v.5 no.4
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• pp.81-87
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• 2002

In this paper, the transonic aeroelastic behavior of the generic fighter model is investigated in the time domain. The simulation of flutter flight test using forced harmonic motion of control surfaces including inertial coupling effects is conducted at the various conditions. The nonlinear aerodynamic effects are considered using a transonic small disturbance equation. A modal model obtained by a free vibration analysis is used for the structural model. The relations between the computed flutter boundary and the simulation results of the responses using the harmonic motions of control surfaces at various conditions are investigated.

• Wind and Structures
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• v.28 no.3
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• pp.171-180
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• 2019

This paper presents a restart iterative approach for time-domain flutter analysis of long-span bridges using the commercial FE package ANSYS. This approach utilizes the recursive formats of impulse-response-function expressions for bridge's aeroelastic forces. Nonlinear dynamic equilibrium equations are iteratively solved by using the restart technique in ANSYS, which enable the equilibrium state of system to get back to last moment absolutely during iterations. The condition for the onset of flutter instability becomes that, at a certain wind velocity, the amplitude of vibration is invariant with time. A long-span suspension bridge was taken as a numerical example to verify the applicability and accuracy of the proposed method by comparing calculated results with wind tunnel tests. The proposed method enables the bridge designers and engineering practitioners to carry out time-domain flutter analysis of bridges in commercial FE package ANSYS.

• International Journal of Aeronautical and Space Sciences
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• v.7 no.1
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• pp.99-105
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• 2006

In this study, nonlinear static and dynamic aeroelastic analyses for a high-aspect-ratio wing have been performed. To achieve these aims, the transonic small disturbance (TSD) theory for the aerodynamic analysis and the large deflection beam theory considering a geometrical nonlinearity for the structural analysis are applied, respectively. For the coupling between fluid and structure, the transformation of a displacement from the structural mesh to the aerodynamic grid is performed by a shape function which is used for the finite element and the inverse transformation of force by work equivalent load method. To validate the current method, the present analysis results of a high-aspect-ratio wing are compared with the experimental results. Static deformations in the vertical and torsional directions caused by an angle of attack and gravity loading are compared with experimental results. Also, static and dynamic aeroelastic characteristics are investigated. The comparisons of the flutter speed and frequency between a linear and nonlinear analysis are presented.

• Journal of the Korea Institute of Military Science and Technology
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• v.11 no.4
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• pp.159-165
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• 2008

The purpose of this paper is to study the impact of concentrated nonlinearities, freeplays, on the aeroelastic behaviors of single- and double-folded control fins. The nonlinearities may cause limit cycle oscillation(LCO) below the linear flutter boundary. The effects of nonlinear hinges on LCO characteristics of the fins are examined as flight condition changes. Nonlinear time-domain flutter analyses are performed, using ZAERO. The results show that the aeroelastic stability boundaries of double-folded fin(DF) are higher than those of the single-folded fin(SF) and the lower hinge freeplay impact more critically on the stability than the upper hinge freeplay of the DF.

• Composites Research
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• v.13 no.5
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• pp.50-59
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• 2000

In this paper, two methods to suppress flutter of the composite panel are examined. First, in the active control method, a controller based on the linear optimal control theory is designed and control input voltage is applied on the actuators and a PZT is used as actuator. Second, a new technique, passive suppression scheme, is suggested for suppression of the nonlinear panel flutter. In the passive suppression scheme, a shunt circuit which consists of inductor-resistor is used to increase damping of the system and as a result the flutter can be attenuated. A passive damping technology, which is believed to be more robust suppression system in practical operation, requires very little or no electrical power and additional apparatuses such as sensor system and controller are not needed. To achieve the great actuating force/damping effect, the optimal shape and location of the actuators are determined by using genetic algorithms. The governing equations are derived by using extended Hamilton's principle. They are based on the nonlinear von Karman strain-displacement relationship for the panel structure and quasi-steady first-order piston theory for the supersonic airflow. The discretized finite element equations are obtained by using 4-node conforming plate element. A modal reduction is performed to the finite element equations in order to suppress the panel flutter effectively and nonlinear-coupled modal equations are obtained. Numerical suppression results, which are based on the reduced nonlinear modal equations, are presented in time domain by using Newmark nonlinear time integration method.