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Stability of a linear oscillator with damping force of the fractional-order derivative

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Science china(Physics,Mechanics & Astronomy) 2010年第2期53卷 345-352页

作者： wang zaihua1,2 & HU HaiYan1 1 institute of vibration engineering research,nanjing univ.rsity of aeronautics and astronautics,nanjing 210016,china 2 institute of Science,PLA univ.rsity of Science and Technology,nanjing 211101,china 1. institute of vibration engineering research Nanjing University of Aeronautics and Astronautics Nanjing 210016 China2. Institute of Science PLA University of Science and Technology Nanjing 211101 China

It begins with the study of damping representation of a linear vibration system of single degree of freedom (SDOF),from the view point of fractional calculus. By using the idea of stability switch,it shows that the linear term involving the fractional-order derivative of an order between 0 and 2 always acts as a damping force,so that the unique equilibrium is asymp-totically stable. Further,based on the idea of stability switch again,the paper proposes a scheme for determining the stable gain region of a linear vibration system under a fractional-order control. It shows that unlike the classical velocity feedback which can adjust the damping force only,a fractional-order feedback can adjust not only the damping force,but also the elastic re-storing force,and in addition,a fractional-order PDα control can either enlarge the stable gain region or narrow the stable gain region. For the dynamic systems described by integer-order derivatives,the asymptotical stability of an equilibrium is guaranteed if all characteristic roots stay in the open left half-plane,while for the systems with fractional-order derivatives,the asymptotical stability of an equilibrium is guaranteed if all characteristic roots stay within a sector in the complex plane. Analysis shows that the proposed method,based on the idea of stability switch,works effectively in the stability analysis of dynamical systems with fractional-order derivatives.

关键词： vibration system fractional-order derivative asymptotical stability stability switch

Morphology and reaction force of toes of geckos freely moving on ceilings and walls

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Science china(Technological Sciences) 2010年第6期53卷 1688-1693页

作者： wang ZhouYi1,2,GU WenHua1,2,WU Qiang1,2,JI AiHong1 & DAI ZhenDong1 1 institute of Bio-inspired Structure and Surface engineering,nanjing univ.rsity of aeronautics and astronautics,nanjing 210016,china 2 College of Mechanical and Electrical engineering,nanjing univ.rsity of aeronautics and astronautics,nanjing 210016,china 1. institute of Bio-inspired Structure and Surface engineering Nanjing University of Aeronautics and Astronautics Nanjing 210016 China2. College of Mechanical and Electrical Engineering Nanjing University of Aeronautics and Astronautics Nanjing 210016 China

The 3-dimensional interactions between toes of a gecko and substrates (ceilings or walls) were measured when it moves on ceilings or walls by using a 3-dimensional force measuring array,and the correspondent morphology of the gecko toes was recorded by a high speed *** study aims to understand the relationship between adhesive and shear forces generated by the toes of the gecko and the locomotion behavior when it walks on walls and *** showed that shear force is along the toe-only 12.6° and 3.1° away from the toe for wall-climbing and ceiling-crawling,respectively while the adhesion is big enough to balance the body weight and *** shear forces generated by the first and the fifth toes are in opposite directions;this redundant force increases the reliability of adhesion and stability of *** support angles of toes are equal approximately for ceiling-crawling and *** study greatly inspires the design of a gecko-like robot.

关键词： reaction force of toe morphometrics ceiling redundant force gecko-like robot

Global view of Hopf bifurcations of a van der Pol oscillator with delayed state feedback

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Science china(Technological Sciences) 2010年第3期53卷 595-607页

作者： ZHANG Li1,wang HuaiLei1 & HU HaiYan1,2 1 MOE Key Lab of Mechanics and Control of Aerospace Structures,nanjing univ.rsity of aeronautics and astronautics,nanjing 210016,china 2 School of Aerospace engineering,Beijing institute of Technology,Beijing 100081,china 1. MOE Key Lab of Mechanics and Control of Aerospace Structures Nanjing University of Aeronautics and Astronautics Nanjing 210016 China2. School of Aerospace Engineering Beijing Institute of Technology Beijing 100081 China

This paper presents both analytical and numerical studies on the global view of Hopf bifurcations of a van der Pol oscillator with delayed state *** on a detailed analysis of the stability switches of the trivial equilibrium of the system,the stability charts are given in a parameter space consisting of the time delay and the feedback *** center manifold reduc-tion and the normal form method are used to study Hopf bifurcations with respect to the time *** gain an insight into the persistence of a Hopf bifurcation as the time delay varies farther away from its critical value,the method of multiple scales is used to obtain the global view of Hopf bifurcations with respect to the time *** the analytical results of Hopf bifurca-tions and global view of those bifurcations are validated via a collocation scheme implemented on *** most important discovery in this paper is the well-structured global view of Hopf bifurcations for the system of concern,showing the generality of the persistence of Hopf bifurcations.

关键词： Hopf bifurcation global view center manifold reduction method of multiple scales collocation scheme

Comparative studies on the structure and adhesion of setae in G. gecko and G. swinhonis

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Science china(Life Sciences) 2007年第6期50卷 831-838页

作者： GUO Ce1, wang WenBo1, YU Min1, DAI ZhenDong1 & SUN JiuRong2 1 institute of Bio-inspired Structure and Surface engineering, nanjing univ.rsity of aeronautics and astronautics, nanjing 210016, china 2 College of Life Science, Peking univ.rsity, Beijing 100871, china 1. institute of Bio-inspired Structure and Surface engineering Nanjing University of Aeronautics and Astronautics Nanjing 210016 China 2. College of Life Science Peking University Beijing 100871 China

Scanning electron microscopy (SEM) and histological techniques were used to observe and study the setae structures of two gecko species (G. gecko and G. swinhonis) and the relationships between these structures and the adhesive forces. The SEM results showed that the setae of these two species were densely distributed in an orderly fashion, and branched with curved tips. The setae of G. gecko had cluster structures, each cluster containing 4-6 setae whose terminal branches curved towards the center of the toes at ~ 10o, the tips of the branches like spatulae and densely arrayed at an interval of less than 0.2―0.3 μm. On the contrary, the branch tips in the setae of G. swinhonis were curled, and the terminal parts of setae curved towards the center of the toes at various angles. Usually the setae of these gecko species branch twice at the top at intervals greater than that of G. gecko. The histological observation found that inside the setae of these two species there were plenty of unevenly distributed contents, such as epithelia, fat cells, pigmental cells and muscle tissue, but no gland cells existed. The results of functional experiments suggested that modifying the structure of gecko’s setae could reduce its adhesive ability dramatically, demonstrating the positive correlation between the structure of the gecko’s setae and its adhesive ability. The above results provide important information in designing bio-mimic setae and bio-gecko robots.

关键词： G. gecko, G. swinhonis, setae, microstructure, adhesion, bionics

Delayed Hopf bifurcation in time-delayed slow-fast systems

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中国科学:技术科学 2010年第2期 212-212页

This paper presents an investigation on the phenomenon of delayed bifurcation in time-delayed slow-fast differential systems. Here the two delayed's have different meanings. The delayed bifurcation means that the bifurcation does not happen immediately at the bifurcation point as the bifurcation parameter passes through some bifurcation point, but at some other point which is above the bifurcation point by an obvious distance. In a time-delayed system, the evolution of the system depends not only on the present state but also on past states. In this paper, the time-delayed slow-fast system is firstly simplified to a slow-fast system without time delay by means of the center manifold reduction, and then the so-called entry-exit function is defined to characterize the delayed bifurcation on the basis of Neishtadt's theory. It shows that delayed Hopf bifurcation exists in time-delayed slow-fast systems, and the theoretical prediction on the exit-point is in good agreement with the numerical calculation, as illustrated in the two illustrative examples.

关键词： time delay delayed bifurcation Hopf bifurcation slow-fast systems exit-point entry-exit function

Stability and Hopf bifurcation of a class of TCP/AQM networks

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Stability and Hopf bifurcation of a class of TCP/AQM network...

Liquid propellant analogy technique in dynamic modeling of launch vehicle

第十二届全国非线性振动暨第九届全国非线性动力学和运动稳定性学术会议

作者： wang zaihua & zheng yuanguang institute of vibration engineering research, nanjing univ.rsity of aeronautics and astronautics, 210016 nanjing, china

In this paper, the local dynamics around the equilibrium of a class of TCP/AQM networks with proportional feedback is investigated, and the effect of the communication delay on the stability is addressed. It is found that the internet system keeps stable if the delay is not large, and it exhibits good performance only for mediate delay in the stable interval, NOT the case as expected: the smaller the better. In addition, a Hopf bifurcation occurs after the equilibrium loses its stability, and the method of multiple scales (MMS) is used to calculate the bifurcated periodic solution, and to determine the direction of the bifurcation, and to determine the stability of the periodic motion resulted from the bifurcation. The method of multiple scales involves easy computation and yields prediction on the bifurcated periodic solution in very good agreement with the numerical results.

关键词： stability Hopf bifurcation Congestion control TCP/AQM networks

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Science china(Technological Sciences) 2010年第8期53卷 2102-2110页

作者： PAN ZhongWen 1,2 ,XING YuFeng 1 ,ZHU LiWen 2 ,DONG Kai 2 &SUN Mu 2 1Solid Mechanics research Center,Beijing univ.rsity of aeronautics and astronautics,Beijing 100191,china 2 Beijing astronautics Systems engineering institute,Beijing 100076,china 1. Solid Mechanics research Center Beijing University of Aeronautics and Astronautics Beijing 100191 China2. Beijing Astronautics Systems Engineering Institute Beijing 100076 China

The coupling effects among lateral mode,longitudinal mode and torsional mode of a launch vehicle cannot be taken into account in traditional dynamic analysis using lateral beam model and longitudinal spring-mass model *** deal with the problem,propellant analogy methods based on beam model are proposed and coupled mass-matrix of liquid propellant is constructed through additional mass in the present *** an integrated model of launch vehicle for free vibration analysis is established,by which research on the interactions between longitudinal and lateral modes,longitudinal and torsional modes of the launch vehicle can be *** examples for tandem tanks validate the present method and its necessity.

关键词： dynamic characteristics coupled mass integrative modeling propellant analogy

vibrations in High Speed Milling of Thin-walled Components

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武汉理工大学学报 2006年第S3期28卷 824-827页

作者： wang Tongyue~(1,2) HE Ning~2 LI Liang~2 (1.Departrnent of Mechanical engineering,Huaiyin institute of Techunology,Huaian 223001,china, 2.College of Mechanical & electrical engineering,nanjing univ.rsity of aeronautics and astronautics,nanjing 210016,china) Department of Mechanical engineering Huaiyin Institute of TechnologyHuaian 223001China College of Mechanical & electrical engineering Nanjing University of Aeronautics and AstronauticsNanjing 210016China College of Mechanical & electrical engineering Nanjing University of Aeronautics and AstronauticsNanjing 210016China

Thin-walled structures have been widely used in the aerospace *** dynamic interaction between the milling cutter and thin-walled workpiece can easily lead to *** paper investigates the vibration caused during milling the thin-walled workpiece on the NC machining center,presents a theoretical milling vibration model of thin-walled *** model was verified by using milling experiments and numerical *** valuable conclusions are derived,this will be references to scientific research and guides to the vibration-free milling of thin-walled structures at different cutting speeds.

关键词： thin-walled components vibration simulation cutting parameters

Formation control for networked spacecraft in deep space:with or without communication delays and with switching topology

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Science china(Information Sciences) 2011年第3期54卷 469-481页

作者： wang Nan 1,2, ZHANG TianWu 2 & XU JieQiong 1 1 School of Aeronautic Science and engineering, Beijing univ.rsity of aeronautics and astronautics, Beijing 100191, china 2 Department of Computer Science and engineering, Henan institute of engineering, zhengzhou 451191, china 1. School of Aeronautic Science and engineering Beijing University of Aeronautics and Astronautics Beijing 100191 China2. Department of Computer Science and Engineering Henan Institute of Engineering Zhengzhou 451191 China

In this paper, several formation controllers are developed with constant and variable connected communication topology for six-degree-of-freedom (6-DOF) networked spacecraft flying in deep space with constant and time-varying communication delays considered. In the control algorithm, any explicit leader does not exist in the formation team and it is required that each spacecraft communicate only with its neighbors and therefore the required communication loads of the whole formation is greatly reduced. The proposed control strategies allow that each spacecraft can track its desired position and attitude and simultaneously the whole group moves to the desired formation and obtain its desired relative attitudes with its neighbors. Simulation results demonstrate the effectiveness of the proposed controllers.

关键词： deep space graph theory formation control communication topology delays