The equations of motion of an insect with flapping wings are derived and then simplified to that of a flying body using the ＂rigid body＂ assumption. On the basis of the simplified equations of motion, the longitudin...The equations of motion of an insect with flapping wings are derived and then simplified to that of a flying body using the ＂rigid body＂ assumption. On the basis of the simplified equations of motion, the longitudinal dynamic flight stability of four insects （hoverfly, cranefly, dronefly and hawkmoth） in hovering flight is studied （the mass of the insects ranging from 11 to 1,648 mg and wingbeat frequency from 26 to 157Hz）. The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are used to solve the equations of motion. The validity of the ＂rigid body＂ assumption is tested and how differences in size and wing kinematics influence the applicability of the ＂rigid body＂ assumption is investigated. The primary findings are： （1） For insects considered in the present study and those with relatively high wingbeat frequency （hoverfly, drone fly and bumblebee）, the ＂rigid body＂ assumption is reasonable, and for those with relatively low wingbeat frequency （cranefly and howkmoth）, the applicability of the ＂rigid body＂ assumption is questionable. （2） The same three natural modes of motion as those reported recently for a bumblebee are identified, i.e., one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. （3） Approximate analytical expressions of the eigenvalues, which give physical insight into the genesis of the natural modes of motion, are derived. The expressions identify the speed derivative Mu （pitching moment produced by unit horizontal speed） as the primary source of the unstable oscillatory mode and the stable fast subsidence mode and Zw （vertical force produced by unit vertical speed） as the primary source of the stable slow subsidence mode.展开更多
Both the asymptotical stability criterion and the bounded stability criterion of the coning motion for wrap around fin(WAF) rockets are proposed through the analy-sis of coning motion equations,which can be easily use...Both the asymptotical stability criterion and the bounded stability criterion of the coning motion for wrap around fin(WAF) rockets are proposed through the analy-sis of coning motion equations,which can be easily used to determine the exis-tence of the coning motion during the rocket design. The correctness of the crite-rions is verified by mathematical simulation examples of a WAF rocket with differ-ent setting angles. It is also found that the setting angle of WAF has great effects on the rolling moment and side moment of the rocket.展开更多
In this study, the intrinsic mechanism of aerodynamic effects on the motion stability of a high-speed maglev system was investigated. The concept of a critical speed for maglev vehicles considering the aerodynamic eff...In this study, the intrinsic mechanism of aerodynamic effects on the motion stability of a high-speed maglev system was investigated. The concept of a critical speed for maglev vehicles considering the aerodynamic effect is proposed. The study was carried out based on a single magnetic suspension system, which is convenient for proposing relevant concepts and obtaining explicit expressions. This study shows that the motion stability of the suspension system is closely related to the vehicle speed when aerodynamic effects are considered. With increases of the vehicle speed, the stability behavior of the system changes. At a certain vehicle speed,the stability of the system reaches a critical state, followed by instability. The speed corresponding to the critical state is the critical speed. Analysis reveals that when the system reaches the critical state, it takes two forms, with two critical speeds, and thus two expressions for the critical speed are obtained. The conditions of the existence of the critical speed were determined, and the effects of the control parameters and the lift coefficient on the critical speed were analyzed by numerical analysis. The results show that the first critical speed appears when the aerodynamic force is upward,and the second critical speed appears when the aerodynamic force is downward. Moreover, both critical speeds decrease with the increase of the lift coefficient.展开更多
In this paper, analytical and numerical studies are carried out on the full annular rub motions of a nonlinear Jeffcott rotor. Transition sets of the synchronous full annular rub are given with the help of averaging m...In this paper, analytical and numerical studies are carried out on the full annular rub motions of a nonlinear Jeffcott rotor. Transition sets of the synchronous full annular rub are given with the help of averaging method and constraint bifurcation theory to discuss the effects of system parameters on jump phenomena. Routh-Hurwitz criteria are employed to analyze the stability of synchronous full annular rub solution and determine the boundaries of static and Hopf bifurcations. Finally, the response and onset condition of reverse dry whip are investigated numerically, and at the same time, the influences of rotor parameters and rotation speed on the characteristics of the rotor response are investigated.展开更多
基金The project supported by the National Natural Science Foundation of China(10232010 and 10472008)
文摘The equations of motion of an insect with flapping wings are derived and then simplified to that of a flying body using the ＂rigid body＂ assumption. On the basis of the simplified equations of motion, the longitudinal dynamic flight stability of four insects （hoverfly, cranefly, dronefly and hawkmoth） in hovering flight is studied （the mass of the insects ranging from 11 to 1,648 mg and wingbeat frequency from 26 to 157Hz）. The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are used to solve the equations of motion. The validity of the ＂rigid body＂ assumption is tested and how differences in size and wing kinematics influence the applicability of the ＂rigid body＂ assumption is investigated. The primary findings are： （1） For insects considered in the present study and those with relatively high wingbeat frequency （hoverfly, drone fly and bumblebee）, the ＂rigid body＂ assumption is reasonable, and for those with relatively low wingbeat frequency （cranefly and howkmoth）, the applicability of the ＂rigid body＂ assumption is questionable. （2） The same three natural modes of motion as those reported recently for a bumblebee are identified, i.e., one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. （3） Approximate analytical expressions of the eigenvalues, which give physical insight into the genesis of the natural modes of motion, are derived. The expressions identify the speed derivative Mu （pitching moment produced by unit horizontal speed） as the primary source of the unstable oscillatory mode and the stable fast subsidence mode and Zw （vertical force produced by unit vertical speed） as the primary source of the stable slow subsidence mode.
文摘Both the asymptotical stability criterion and the bounded stability criterion of the coning motion for wrap around fin(WAF) rockets are proposed through the analy-sis of coning motion equations,which can be easily used to determine the exis-tence of the coning motion during the rocket design. The correctness of the crite-rions is verified by mathematical simulation examples of a WAF rocket with differ-ent setting angles. It is also found that the setting angle of WAF has great effects on the rolling moment and side moment of the rocket.
基金supported by the National Key Research and Development Program of China(Grant 2016YFB1200602)the National Natural Science Foundation of China (Grants 11672306, 51490673)+2 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant XDB22020101)the National Basic Research Program (973 Program) of China (Grant 2014CB046801)the State Key Laboratory of Hydraulic Engineering Simulation and Safety (Tianjin University)
文摘In this study, the intrinsic mechanism of aerodynamic effects on the motion stability of a high-speed maglev system was investigated. The concept of a critical speed for maglev vehicles considering the aerodynamic effect is proposed. The study was carried out based on a single magnetic suspension system, which is convenient for proposing relevant concepts and obtaining explicit expressions. This study shows that the motion stability of the suspension system is closely related to the vehicle speed when aerodynamic effects are considered. With increases of the vehicle speed, the stability behavior of the system changes. At a certain vehicle speed,the stability of the system reaches a critical state, followed by instability. The speed corresponding to the critical state is the critical speed. Analysis reveals that when the system reaches the critical state, it takes two forms, with two critical speeds, and thus two expressions for the critical speed are obtained. The conditions of the existence of the critical speed were determined, and the effects of the control parameters and the lift coefficient on the critical speed were analyzed by numerical analysis. The results show that the first critical speed appears when the aerodynamic force is upward,and the second critical speed appears when the aerodynamic force is downward. Moreover, both critical speeds decrease with the increase of the lift coefficient.
基金supported by the National Natural Science Foundation of China (Grant No. 10632040)
文摘In this paper, analytical and numerical studies are carried out on the full annular rub motions of a nonlinear Jeffcott rotor. Transition sets of the synchronous full annular rub are given with the help of averaging method and constraint bifurcation theory to discuss the effects of system parameters on jump phenomena. Routh-Hurwitz criteria are employed to analyze the stability of synchronous full annular rub solution and determine the boundaries of static and Hopf bifurcations. Finally, the response and onset condition of reverse dry whip are investigated numerically, and at the same time, the influences of rotor parameters and rotation speed on the characteristics of the rotor response are investigated.
