In this work, the aerodynamic stability of the Yichang Suspension Bridge over Yangtze River during erection was determined by three dimensional nonlinear flutter analysis, in which the nonlinearities of structural dy...In this work, the aerodynamic stability of the Yichang Suspension Bridge over Yangtze River during erection was determined by three dimensional nonlinear flutter analysis, in which the nonlinearities of structural dynamic characteristics and aeroelastic forces caused by large deformation are fully considered. An interesting result obtained was that the bridge was more stable when the stiffening girders were erected in a non symmetrical manner as opposed to the traditional symmetrical erection schedule. It was also found that the severe decrease in the aerodynamic stability was due to the nonlinear effects. Therefore, the nonlinear factors should be considered accurately in aerodynamic stability analysis of long span suspension bridges during erection.展开更多
The Hopf bifurcations of an airfoil flutter system with a cubic nonlinearity are investigated, with the flow speed as the bifurcation parameter. The center manifold theory and complex normal form method are Used to ob...The Hopf bifurcations of an airfoil flutter system with a cubic nonlinearity are investigated, with the flow speed as the bifurcation parameter. The center manifold theory and complex normal form method are Used to obtain the bifurcation equation. Interestingly, for a certain linear pitching stiffness the Hopf bifurcation is both supercritical and subcritical. It is found, mathematically, this is caused by the fact that one coefficient in the bifurcation equation does not contain the first power of the bifurcation parameter. The solutions of the bifurcation equation are validated by the equivalent linearization method and incremental harmonic balance method.展开更多
The flutter characteristics of an actuator-fin system are investigated with structural nonlinearity and dynamic stiffness of the electric motor. The component mode substitution method is used to establish the nonlinea...The flutter characteristics of an actuator-fin system are investigated with structural nonlinearity and dynamic stiffness of the electric motor. The component mode substitution method is used to establish the nonlinear governing equations in time domain and frequency domain based on the fundamental dynamic equations of the electric motor and decelerator. The existing describing function method and a proposed iterative method are used to obtain the flutter characteristics containing preload freeplay nonlinearity when the control command is zero. A comparison between the results of frequency domain and those of time domain is studied. Simulations are carried out when the control command is not zero and further analysis is conducted when the freeplay angle is changed. The results show that structural nonlinearity and dynamic stiffness have a significant influence on the flutter characteristics. Limit cycle oscillations （LCOs） are observed within linear flutter boundary. The response of the actuator-fin system is related to the initial disturbance. In the nonlinear condition, the amplitude of the control command has an influence on the flutter characteristics.展开更多
Variable stiffness composite laminates(VSCLs)are promising in aerospace engineering due to their designable material properties through changing fiber angles and stacking sequences.Aiming to control the thermal postbu...Variable stiffness composite laminates(VSCLs)are promising in aerospace engineering due to their designable material properties through changing fiber angles and stacking sequences.Aiming to control the thermal postbuckling and nonlinear panel flutter motions of VSCLs,a full-order numerical model is developed based on the linear quadratic regulator(LQR)algorithm in control theory,the classical laminate plate theory(CLPT)considering von Kármán geometrical nonlinearity,and the first-order Piston theory.The critical buckling temperature and the critical aerodynamic pressure of VSCLs are parametrically investigated.The location and shape of piezoelectric actuators for optimal control of the dynamic responses of VSCLs are determined through comparing the norms of feedback control gain(NFCG).Numerical simulations show that the temperature field has a great effect on aeroelastic tailoring of VSCLs;the curvilinear fiber path of VSCLs can significantly affect the optimal location and shape of piezoelectric actuator for flutter suppression;the unstable panel flutter and the thermal postbuckling deflection can be suppressed effectively through optimal design of piezoelectric patches.展开更多
The incremental harmonic balance method was extended to analyze the flutter of systems with multiple structural strong nonlinearities. The strongly nonlinear cubic plunging and pitching stiffness terms were considered...The incremental harmonic balance method was extended to analyze the flutter of systems with multiple structural strong nonlinearities. The strongly nonlinear cubic plunging and pitching stiffness terms were considered in the flutter equations of two-dimensional airfoil. First, the equations were transferred into matrix form, then the vibration process was divided into the persistent incremental processes of vibration moments. And the expression of their solutions could be obtained by using a certain amplitude as control parameter in the harmonic balance process, and then the bifurcation, limit cycle flutter phenomena and the number of harmonic terms were analyzed. Finally, numerical results calculated by the Runge-Kutta method were given to verify the results obtained by the proposed procedure. It has been shown that the incremental harmonic method is effective and precise in the analysis of strongly nonlinear flutter with multiple structural nonlinearities.展开更多
In this paper,a framework is established for nonlinear flutter and gust response analyses based on an efficient Reduced Order Model(ROM).The proposed method can be used to solve the aeroelastic response problems of wi...In this paper,a framework is established for nonlinear flutter and gust response analyses based on an efficient Reduced Order Model(ROM).The proposed method can be used to solve the aeroelastic response problems of wings containing geometric nonlinearities.A structural modeling approach presented herein describes the stiffness nonlinearities with a modal formulation.Two orthogonal spanwise modes describe the foreshortening effects of the wing.Dynamic linearization of the ROM under nonlinear equilibrium states is applied to a nonlinear flutter analysis,and the fully nonlinear ROM coupled with the non-planar Unsteady Vortex Lattice Method(UVLM)is applied to gust response analysis.Furthermore,extended Precise Integration Method(PIM)ensures accuracy of the dynamic equation solutions.To demonstrate applicability and accuracy of the method presented,a wind tunnel test is conducted and good agreements between theoretical and test results of nonlinear flutter speed and gust response deflection are reached.The method described in this paper is suitable for predicting the nonlinear flutter speed and calculating the gust responses of a large-aspect-ratio wing in time domain.Meanwhile,the results derived highlight the effects of geometric nonlinearities obviously.展开更多
With the gradual increase in the size and flexibility of composite blades in large wind turbines,problems related toaeroelastic instability and blade vibration are becoming increasingly more important.Given their impa...With the gradual increase in the size and flexibility of composite blades in large wind turbines,problems related toaeroelastic instability and blade vibration are becoming increasingly more important.Given their impact on thelifespan of wind turbines,these subjects have become important topics in turbine blade design.In this article,firstaspects related to the aeroelastic(structural and aerodynamic)modeling of large wind turbine blades are summarized.Then,two main methods for blade vibration control are outlined(passive control and active control),including the case of composite blades.Some improvement schemes are proposed accordingly,with a specialfocus on the industry’s outstanding suppression scheme for stall-induced nonlinear flutter and a new high-frequencymicro-vibration control scheme.Finally,future research directions are indicated based on existingresearch.展开更多
The equation of motion of sandwich beam with pyramidal lattice core in the supersonic flow considering geometric nonlinearity is formulated using Hamilton＇s principle. The piston theory is used to evaluate aerodynami...The equation of motion of sandwich beam with pyramidal lattice core in the supersonic flow considering geometric nonlinearity is formulated using Hamilton＇s principle. The piston theory is used to evaluate aerodynamic pressure. The structural aeroelastic properties are analyzed using frequency- and time-domain methods, and some interesting phenomena are observed. It is noted that the flutter of sandwich beam occurs under the coupling effect of low order modes. The critical flutter aerodynamic pressure of the sandwich beam is higher than that of the isotropic beam with the same weight, length and width. The influence of inclination angle of core truss on flutter characteristic is analyzed.展开更多
A review on the recent advance in nonlinear aeroelasticity of the aircraft is presented in this paper. The nonlinear aeroelastic problems are divided into three types based on different research objects, namely the tw...A review on the recent advance in nonlinear aeroelasticity of the aircraft is presented in this paper. The nonlinear aeroelastic problems are divided into three types based on different research objects, namely the two dimensional airfoil, the wing, and the full aircraft. Different non- linearities encountered in aeroelastic systems are discussed firstly, where the emphases is placed on new nonlinear model to describe tested nonlinear relationship. Research techniques, especially new theoretical methods and aeroelastic flutter control methods are investigated in detail. The route to chaos and the cause of chaotic motion of two-dimensional aeroelastic system are summarized. Var- ious structural modeling methods for the high-aspect-ratio wing with geometric nonlinearity are dis- cussed. Accordingly, aerodynamic modeling approaches have been developed for the aeroelastic modeling of nonlinear high-aspect-ratio wings. Nonlinear aeroelasticity about high-altitude long- endurance （HALE） and fight aircrafts are studied separately. Finally, conclusions and the chal- lenges of the development in nonlinear aeroelasticity are concluded. Nonlinear aeroelastic problems of morphing wing, energy harvesting, and flapping aircrafts are proposed as new directions in the future.展开更多
The wash-out filter （WF） technique is used to control the flutter of a two dimensional airfoil with cubic non-linearity in incompressible flow. Firstly, Hopf bifurcation theory is used to determine the point at whic...The wash-out filter （WF） technique is used to control the flutter of a two dimensional airfoil with cubic non-linearity in incompressible flow. Firstly, Hopf bifurcation theory is used to determine the point at which the nonlinear controller is introduced. The system is then transformed into Jordan canonical form, based on analysis of linearized eigenvalues of the system. Secondly, for the introduced WF controller, the linear control gain is determined according to Hopf bifurcation condition. The sym- bolic computing program of normal form direct method （NFDM） is also used to obtain the normal form of the controlled system. The non-linear control gain can be determined based on the relation of the type of bifurcation and the parameters of the normal form, to transform sub-critical Hopf bifurcation to be su- per-critical one. Lastly, numerical simulations are used to certify the validity of theoretical analysis, in which the amplitude of flutter or limit cycle of the controlled system is reduced greatly, comparing to the original system.展开更多
A constrained adaptive neural network control scheme is proposed for a multi-input and multi-output（MIMO） aeroelastic system in the presence of wind gust,system uncertainties,and input nonlinearities consisting of i...A constrained adaptive neural network control scheme is proposed for a multi-input and multi-output（MIMO） aeroelastic system in the presence of wind gust,system uncertainties,and input nonlinearities consisting of input saturation and dead-zone.In regard to the input nonlinearities,the right inverse function block of the dead-zone is added before the input nonlinearities,which simplifies the input nonlinearities into an equivalent input saturation.To deal with the equivalent input saturation,an auxiliary error system is designed to compensate for the impact of the input saturation.Meanwhile,uncertainties in pitch stiffness,plunge stiffness,and pitch damping are all considered,and radial basis function neural networks（RBFNNs） are applied to approximate the system uncertainties.In combination with the designed auxiliary error system and the backstepping control technique,a constrained adaptive neural network controller is designed,and it is proven that all the signals in the closed-loop system are semi-globally uniformly bounded via the Lyapunov stability analysis method.Finally,extensive digital simulation results demonstrate the effectiveness of the proposed control scheme towards flutter suppression in spite of the integrated effects of wind gust,system uncertainties,and input nonlinearities.展开更多
Based on the piston theory of supersonic flow and the energy method, the flutter motion equations of a two-dimensional wing with cubic stiffness in the pitching direction are established. The aeroelastic system contai...Based on the piston theory of supersonic flow and the energy method, the flutter motion equations of a two-dimensional wing with cubic stiffness in the pitching direction are established. The aeroelastic system contains both structural and aerodynamic nonlinearities. Hopf bifurcation theory is used to analyze the flutter speed of the system. The effects of system parameters on the flutter speed are studied. The 4th order Runge-Kutta method is used to calculate the stable limit cycle responses and chaotic motions of the aeroelastic system. Results show that the number and the stability of equilibrium points of the system vary with the increase of flow speed. Besides the simple limit cycle response of period 1, there are also period-doubling responses and chaotic motions in the flutter system. The route leading to chaos in the aeroelastic model used here is the period-doubling bifurcation. The chaotic motions in the system occur only when the flow speed is higher than the linear divergent speed and the initial condition is very small. Moreover, the flow speed regions in which the system behaves chaos axe very narrow.展开更多
Limit cycle oscillations （LCOs） as well as nonlinear aeroelastic analysis of a 3-DOF aeroelastic airfoil motion with cubic restoring moments in the pitch degree of freedom are investigated. Aeroelastic equations of ...Limit cycle oscillations （LCOs） as well as nonlinear aeroelastic analysis of a 3-DOF aeroelastic airfoil motion with cubic restoring moments in the pitch degree of freedom are investigated. Aeroelastic equations of an airfoil with control surface in an incompressible potential flow are presented in the time domain. The harmonic balance （HB） method is utilized to calculate the LCO frequency and amplitude for the airfoil. Also the semi-analytical method has revealed the presence of stable and unstable limit cycles, along with stability reversal in the neighborhood of a Hopf bifurcation. The system response is determined by nu- merically integrating the governing equations using a standard Runge-Kutta algorithm and the obtained results are compared with the HB method. Also the results by the third order HB （HB3） method for control surface are consistent with the other numerical solution. Finally, by combining the numerical and the HB methods, types of bifiarcation, be it supercritical, subcritical, or diver- gent flutter area are identified.展开更多
The dynamics character of a two degree-of-freedom aeroelastic airfoil with combined freeplay and cubic stiffness nonlinearities in pitch submitted to supersonic and hypersonic flow has been gaining significant attenti...The dynamics character of a two degree-of-freedom aeroelastic airfoil with combined freeplay and cubic stiffness nonlinearities in pitch submitted to supersonic and hypersonic flow has been gaining significant attention. The Poincare mapping method and Floquet theory are adopted to analyse the limit cycle oscillation flutter and chaotic motion of this system. The result shows that the limit cycle oscillation flutter can be accurately predicted by the Floquet multiplier. The phase trajectories of both the pitch and plunge motion are obtained and the results show that the plunge motion is much more complex than the pitch motion. It is also proved that initial conditions have important influences on the dynamics character of the airfoil system. In a certain range of airspeed and with the same system parameters, the stable limit cycle oscillation, chaotic and multi-periodic motions can be detected under different initial conditions. The figure of the Poincare section also approves the previous conclusion.展开更多
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, ...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 C-t = C-t (beta(t), 0). (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. Bohm's.展开更多
文摘In this work, the aerodynamic stability of the Yichang Suspension Bridge over Yangtze River during erection was determined by three dimensional nonlinear flutter analysis, in which the nonlinearities of structural dynamic characteristics and aeroelastic forces caused by large deformation are fully considered. An interesting result obtained was that the bridge was more stable when the stiffening girders were erected in a non symmetrical manner as opposed to the traditional symmetrical erection schedule. It was also found that the severe decrease in the aerodynamic stability was due to the nonlinear effects. Therefore, the nonlinear factors should be considered accurately in aerodynamic stability analysis of long span suspension bridges during erection.
基金Project supported by the National Natural Science Foundation of China (No.10772202)the Doctoral Foundation of Ministry of Education of China (No.20050558032)the Natural Science Foundation of Guangdong Province (Nos.07003680 and 05003295)
文摘The Hopf bifurcations of an airfoil flutter system with a cubic nonlinearity are investigated, with the flow speed as the bifurcation parameter. The center manifold theory and complex normal form method are Used to obtain the bifurcation equation. Interestingly, for a certain linear pitching stiffness the Hopf bifurcation is both supercritical and subcritical. It is found, mathematically, this is caused by the fact that one coefficient in the bifurcation equation does not contain the first power of the bifurcation parameter. The solutions of the bifurcation equation are validated by the equivalent linearization method and incremental harmonic balance method.
基金National Natural Science Foundation of China(90716006, 10902006)Research Fund for the Doctoral Program of Higher Education of China (20091102110015)
文摘The flutter characteristics of an actuator-fin system are investigated with structural nonlinearity and dynamic stiffness of the electric motor. The component mode substitution method is used to establish the nonlinear governing equations in time domain and frequency domain based on the fundamental dynamic equations of the electric motor and decelerator. The existing describing function method and a proposed iterative method are used to obtain the flutter characteristics containing preload freeplay nonlinearity when the control command is zero. A comparison between the results of frequency domain and those of time domain is studied. Simulations are carried out when the control command is not zero and further analysis is conducted when the freeplay angle is changed. The results show that structural nonlinearity and dynamic stiffness have a significant influence on the flutter characteristics. Limit cycle oscillations （LCOs） are observed within linear flutter boundary. The response of the actuator-fin system is related to the initial disturbance. In the nonlinear condition, the amplitude of the control command has an influence on the flutter characteristics.
基金Project(JCYJ20190808175801656)supported by the Science and Technology Innovation Commission of Shenzhen,ChinaProject(2021M691427)supported by Postdoctoral Science Foundation of ChinaProject(9680086)supported by the City University of Hong Kong,China。
文摘Variable stiffness composite laminates(VSCLs)are promising in aerospace engineering due to their designable material properties through changing fiber angles and stacking sequences.Aiming to control the thermal postbuckling and nonlinear panel flutter motions of VSCLs,a full-order numerical model is developed based on the linear quadratic regulator(LQR)algorithm in control theory,the classical laminate plate theory(CLPT)considering von Kármán geometrical nonlinearity,and the first-order Piston theory.The critical buckling temperature and the critical aerodynamic pressure of VSCLs are parametrically investigated.The location and shape of piezoelectric actuators for optimal control of the dynamic responses of VSCLs are determined through comparing the norms of feedback control gain(NFCG).Numerical simulations show that the temperature field has a great effect on aeroelastic tailoring of VSCLs;the curvilinear fiber path of VSCLs can significantly affect the optimal location and shape of piezoelectric actuator for flutter suppression;the unstable panel flutter and the thermal postbuckling deflection can be suppressed effectively through optimal design of piezoelectric patches.
基金Project supported by the Ph. D. Programs Foundation of Ministry of Education of China (No.20050558032) the Natural Science Foundation of Guangdong Province of China (No.05003295) the Foundation of Sun Yat-sen University Advanced Research Center (No.06M8) the Young Teacher Scientific Research Foundation of Sun Sat-sen University (No.1131011)
文摘The incremental harmonic balance method was extended to analyze the flutter of systems with multiple structural strong nonlinearities. The strongly nonlinear cubic plunging and pitching stiffness terms were considered in the flutter equations of two-dimensional airfoil. First, the equations were transferred into matrix form, then the vibration process was divided into the persistent incremental processes of vibration moments. And the expression of their solutions could be obtained by using a certain amplitude as control parameter in the harmonic balance process, and then the bifurcation, limit cycle flutter phenomena and the number of harmonic terms were analyzed. Finally, numerical results calculated by the Runge-Kutta method were given to verify the results obtained by the proposed procedure. It has been shown that the incremental harmonic method is effective and precise in the analysis of strongly nonlinear flutter with multiple structural nonlinearities.
基金supported by the National Key Research and Development Program of China(No.2016YFB 0200703).
文摘In this paper,a framework is established for nonlinear flutter and gust response analyses based on an efficient Reduced Order Model(ROM).The proposed method can be used to solve the aeroelastic response problems of wings containing geometric nonlinearities.A structural modeling approach presented herein describes the stiffness nonlinearities with a modal formulation.Two orthogonal spanwise modes describe the foreshortening effects of the wing.Dynamic linearization of the ROM under nonlinear equilibrium states is applied to a nonlinear flutter analysis,and the fully nonlinear ROM coupled with the non-planar Unsteady Vortex Lattice Method(UVLM)is applied to gust response analysis.Furthermore,extended Precise Integration Method(PIM)ensures accuracy of the dynamic equation solutions.To demonstrate applicability and accuracy of the method presented,a wind tunnel test is conducted and good agreements between theoretical and test results of nonlinear flutter speed and gust response deflection are reached.The method described in this paper is suitable for predicting the nonlinear flutter speed and calculating the gust responses of a large-aspect-ratio wing in time domain.Meanwhile,the results derived highlight the effects of geometric nonlinearities obviously.
基金supported by the Natural Science Foundation of Shandong Provincial of China(Grant Number ZR2022ME093)the Natural Science Foundation of China(Grant Number 51675315).
文摘With the gradual increase in the size and flexibility of composite blades in large wind turbines,problems related toaeroelastic instability and blade vibration are becoming increasingly more important.Given their impact on thelifespan of wind turbines,these subjects have become important topics in turbine blade design.In this article,firstaspects related to the aeroelastic(structural and aerodynamic)modeling of large wind turbine blades are summarized.Then,two main methods for blade vibration control are outlined(passive control and active control),including the case of composite blades.Some improvement schemes are proposed accordingly,with a specialfocus on the industry’s outstanding suppression scheme for stall-induced nonlinear flutter and a new high-frequencymicro-vibration control scheme.Finally,future research directions are indicated based on existingresearch.
基金Project supported by the National Natural Science Foundation of China(Nos.11572007 and 11172084)
文摘The equation of motion of sandwich beam with pyramidal lattice core in the supersonic flow considering geometric nonlinearity is formulated using Hamilton＇s principle. The piston theory is used to evaluate aerodynamic pressure. The structural aeroelastic properties are analyzed using frequency- and time-domain methods, and some interesting phenomena are observed. It is noted that the flutter of sandwich beam occurs under the coupling effect of low order modes. The critical flutter aerodynamic pressure of the sandwich beam is higher than that of the isotropic beam with the same weight, length and width. The influence of inclination angle of core truss on flutter characteristic is analyzed.
基金the financial support of the National Natural Science Foundation of China (Nos.91116019 and 91216102)
文摘A review on the recent advance in nonlinear aeroelasticity of the aircraft is presented in this paper. The nonlinear aeroelastic problems are divided into three types based on different research objects, namely the two dimensional airfoil, the wing, and the full aircraft. Different non- linearities encountered in aeroelastic systems are discussed firstly, where the emphases is placed on new nonlinear model to describe tested nonlinear relationship. Research techniques, especially new theoretical methods and aeroelastic flutter control methods are investigated in detail. The route to chaos and the cause of chaotic motion of two-dimensional aeroelastic system are summarized. Var- ious structural modeling methods for the high-aspect-ratio wing with geometric nonlinearity are dis- cussed. Accordingly, aerodynamic modeling approaches have been developed for the aeroelastic modeling of nonlinear high-aspect-ratio wings. Nonlinear aeroelasticity about high-altitude long- endurance （HALE） and fight aircrafts are studied separately. Finally, conclusions and the chal- lenges of the development in nonlinear aeroelasticity are concluded. Nonlinear aeroelastic problems of morphing wing, energy harvesting, and flapping aircrafts are proposed as new directions in the future.
文摘The wash-out filter （WF） technique is used to control the flutter of a two dimensional airfoil with cubic non-linearity in incompressible flow. Firstly, Hopf bifurcation theory is used to determine the point at which the nonlinear controller is introduced. The system is then transformed into Jordan canonical form, based on analysis of linearized eigenvalues of the system. Secondly, for the introduced WF controller, the linear control gain is determined according to Hopf bifurcation condition. The sym- bolic computing program of normal form direct method （NFDM） is also used to obtain the normal form of the controlled system. The non-linear control gain can be determined based on the relation of the type of bifurcation and the parameters of the normal form, to transform sub-critical Hopf bifurcation to be su- per-critical one. Lastly, numerical simulations are used to certify the validity of theoretical analysis, in which the amplitude of flutter or limit cycle of the controlled system is reduced greatly, comparing to the original system.
基金supported by the National Natural Science Foundation of China(Nos.61473307 and 61304120)the Aeronautical Science Foundation of China(No. 20155896026)
文摘A constrained adaptive neural network control scheme is proposed for a multi-input and multi-output（MIMO） aeroelastic system in the presence of wind gust,system uncertainties,and input nonlinearities consisting of input saturation and dead-zone.In regard to the input nonlinearities,the right inverse function block of the dead-zone is added before the input nonlinearities,which simplifies the input nonlinearities into an equivalent input saturation.To deal with the equivalent input saturation,an auxiliary error system is designed to compensate for the impact of the input saturation.Meanwhile,uncertainties in pitch stiffness,plunge stiffness,and pitch damping are all considered,and radial basis function neural networks（RBFNNs） are applied to approximate the system uncertainties.In combination with the designed auxiliary error system and the backstepping control technique,a constrained adaptive neural network controller is designed,and it is proven that all the signals in the closed-loop system are semi-globally uniformly bounded via the Lyapunov stability analysis method.Finally,extensive digital simulation results demonstrate the effectiveness of the proposed control scheme towards flutter suppression in spite of the integrated effects of wind gust,system uncertainties,and input nonlinearities.
基金supported by the National Natural Science Foundation of China and China Academy of Engineering Physics(No. 10576024).
文摘Based on the piston theory of supersonic flow and the energy method, the flutter motion equations of a two-dimensional wing with cubic stiffness in the pitching direction are established. The aeroelastic system contains both structural and aerodynamic nonlinearities. Hopf bifurcation theory is used to analyze the flutter speed of the system. The effects of system parameters on the flutter speed are studied. The 4th order Runge-Kutta method is used to calculate the stable limit cycle responses and chaotic motions of the aeroelastic system. Results show that the number and the stability of equilibrium points of the system vary with the increase of flow speed. Besides the simple limit cycle response of period 1, there are also period-doubling responses and chaotic motions in the flutter system. The route leading to chaos in the aeroelastic model used here is the period-doubling bifurcation. The chaotic motions in the system occur only when the flow speed is higher than the linear divergent speed and the initial condition is very small. Moreover, the flow speed regions in which the system behaves chaos axe very narrow.
文摘Limit cycle oscillations （LCOs） as well as nonlinear aeroelastic analysis of a 3-DOF aeroelastic airfoil motion with cubic restoring moments in the pitch degree of freedom are investigated. Aeroelastic equations of an airfoil with control surface in an incompressible potential flow are presented in the time domain. The harmonic balance （HB） method is utilized to calculate the LCO frequency and amplitude for the airfoil. Also the semi-analytical method has revealed the presence of stable and unstable limit cycles, along with stability reversal in the neighborhood of a Hopf bifurcation. The system response is determined by nu- merically integrating the governing equations using a standard Runge-Kutta algorithm and the obtained results are compared with the HB method. Also the results by the third order HB （HB3） method for control surface are consistent with the other numerical solution. Finally, by combining the numerical and the HB methods, types of bifiarcation, be it supercritical, subcritical, or diver- gent flutter area are identified.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10872141)the Research Fund for the Doctoral Program of Higher Education (Grant No. 20060056005)the National Basic Research Program of China (GrantNo. 007CB714000)
文摘The dynamics character of a two degree-of-freedom aeroelastic airfoil with combined freeplay and cubic stiffness nonlinearities in pitch submitted to supersonic and hypersonic flow has been gaining significant attention. The Poincare mapping method and Floquet theory are adopted to analyse the limit cycle oscillation flutter and chaotic motion of this system. The result shows that the limit cycle oscillation flutter can be accurately predicted by the Floquet multiplier. The phase trajectories of both the pitch and plunge motion are obtained and the results show that the plunge motion is much more complex than the pitch motion. It is also proved that initial conditions have important influences on the dynamics character of the airfoil system. In a certain range of airspeed and with the same system parameters, the stable limit cycle oscillation, chaotic and multi-periodic motions can be detected under different initial conditions. The figure of the Poincare section also approves the previous conclusion.
文摘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 C-t = C-t (beta(t), 0). (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. Bohm's.
