Galloping of iced quad-conductors bundles based on curved beam theory

Galloping refers to wind-induced, low-frequency, large-amplitude oscillations that have been more frequently observed for a bundle conductor than for a single conductor. In the present work two different models are built to investigate the galloping of a bundle conductor: (1) a finite curved beam element method and (2) a hybrid model based on curved beam element theory. The finite curved beam element model is effective in dealing with the spacers between the bundled conductors and the joint between the conductors and spacers that can be simulated as a rigid joint or a hinge. Furthermore, the finite curved beam element model can be used to deal with large deformation. The hybrid model invokes the small deformation hypothesis and has a high computational efficiency. A hybrid model based on conventional cable element theory is also programmed to be compared with the aforementioned models based on curved beam element theory. Numerical examples are presented to assess the accuracy of the different models in predicting the equilibrium conductor position, natural frequencies and galloping amplitude. The results show that the curved beam element models, involving more degrees of freedom and coupling of translational and torsional motion, are more accurate at simulating the static and dynamic characters of an iced quad-conductor bundle. The use of hinges, rather than rigid connections, reduces the structural response amplitudes of a galloping conductor bundle.     

Nonlinear vibration of iced cable under wind excitation using three-degree-of-freedom model

High-voltage transmission line possesses a typical suspended cable structure that produces ice in harsh weather. Moreover, transversely galloping will be excited due to the irregular structure resulting from the alternation of lift force and drag force. In this paper, the nonlinear dynamics and internal resonance of an iced cable under wind excitation are investigated.Considering the excitation caused by pulsed wind and the movement of the support, the nonlinear governing equations of motion of the iced cable are established using a three-degree-of-freedom model based on Hamilton's principle. By the Galerkin method, the partial differential equations are then discretized into ordinary differential equations. The method of multiple scales is then used to obtain the averaged equations of the iced cable, and the principal parametric resonance-1/2 subharmonic resonance and the 2:1 internal resonance are considered. The numerical simulations are performed to investigate the dynamic response of the iced cable. It is found that there exist periodic, multi-periodic, and chaotic motions of the iced cable subjected to wind excitation.     

Galloping of bundled power line conductors

This paper describes an experimental and analytical study of the galloping of a two-dimensional section model of a two-conductor bundle in which ice-accreted conductors are replaced by two identical square prisms, with both vertical and torsional movements allowed but the horizontal one blocked, in a uniform wind tunnel flow. Emphasis is placed on elucidating the vital role played by the aerodynamic coupling in the stability of bundled conductors. It is shown that, apart from galloping type flutter, two other types of instability, namely, torsional and classical type flutter, can also occur for bundled conductors. In particular, it is shown that the aerodynamic coupling can cause violent classical type flutter to occur when the resonant condition is approached.     

The optimization of mechanical dampers to control self-excited galloping oscillations

The use of mechanical dampers for the control of the self-excited galloping of transmission lines is considered. Two particular dampers, an in-span damper and a resilient mounting, are studied, two mass representations being used. For both dampers it is possible to produce an optimum damper either by maximizing the negative damping excitation that the damped system can withstand, or by choosing the smaller logarithmic decrement of oscillation of the system to be as large as possible in the absence of excitation. These two procedures do not produce the same damper parameters. Simple analytical expressions are produced for the optimum parameters, and these are shown to agree well with numerically optimized parameters. For the in-span damper, either method of optimization gives a damper for a much wider range of ratios of the damper to conductor masses than is predicted by earlier work. For the resilient mounting the optimization based on damping gives very similar behaviour to that of the in-span damper. When aerodynamic excitation is considered for the resilient mounting, a clear optimum exists only for a small range of mass ratios. Results from a representation of the conductor by a stretched string are used to define the range of mass ratios over which the two-mass damper idealizations may be used to define damper properties.     

Differential System＇s Nonlinear Behaviour of Real Nonlinear Dynamical Systems

Chaos attractor behaviour is usually preserved if the four basic arithmetic operations, i.e. addition, subtraction, multiplication, division, or their compound, are applied. First-order differential systems of one-dimensional real discrete dynamical systems and nonautonomous real continuous-time dynamical systems are also dynamical systems and their Lyapunov exponents are kept, if they are twice differentiable. These two conclusions are shown here by the definitions of dynamical system and Lyapunov exponent. Numerical simulations support our analytical results. The conclusions can apply to higher order differential systems if their corresponding order differentials exist.     

Nonlinear dynamics of galloping-based piezoaeroelastic energy harvesters

The normal form is proposed as a tool to analyze the performance and reliability of galloping-based piezoaeroelastic energy harvesters. Two different harvesting systems are considered. The first system consists of a tip mass prismatic structure (isosceles 30° or square cross-section geometry) attached to a multilayered cantilever beam. The only source of nonlinearity in this system is the aerodynamic nonlinearity. The second system consists of an equilateral triangle cross-section bar attached to two cantilever beams. This system is designed to have structural and aerodynamic nonlinearities. The coupled governing equations for the structure’s transverse displacement and the generated voltage are derived and analyzed for both systems. The effects of the electrical load resistance and the type of harvester on the onset speed of galloping are quantified. The results show that the onset speed of galloping is strongly affected by the load resistance for both types of harvesters. The normal form of the dynamic system near the onset of galloping (Hopf bifurcation) is then derived. Based on the nonlinear normal form, it is demonstrated that smaller levels of generated voltage or power are obtained for higher absolute values of the effective nonlinearity. For the first harvesting system, the results show a supercritical Hopf bifurcation for both isosceles 30° or square cross-section geometries. The nonlinear normal form shows that the isosceles triangle section (30°) is more efficient than the square section. For the second harvesting system, the normal form is used to identify the values of the nonlinear torsional spring which changes the harvester’s instability. It is demonstrated that this critical value of the nonlinear torsional spring depends strongly on the load resistance.     

Enhanced conductivity in ionic conductor-insulator composites: numerical models in two and three dimensions

We describe a two-dimensional (2D) and a three-dimensional (3D) percolation model for ionic conductor-insulator composites such as copper(I) bromide-titanium dioxide (CuBr-TiO₂) or lithium iodide-alumina (LiI-Al₂O₃). These composites present an enhanced conductivity closely related to the insulator concentration. This effect is explained by the formation of highly conducting space charge regions near the phase boundaries which are represented by good conductor bonds. Our numerical model takes into account grain size and correlation effects. The dimension has a leading role for the conduction properties. In the 2D case, the good conductor bonds do not percolate, whatever the insulator concentration, and the maximum conductivity of the composite samples is of the same order as that of the ionic conductor grains. The behavior of the system is very different in the 3D case where, for a large domain of composition, the good conductors percolate through the regions between the conductor grains. For the CuBr-TiO₂ composites the conductivity versus composition curve is bell-shaped. Conversely, in the LiI-Al₂O₃ system, a linear relation between the conductivity and the insulator volume fraction is obtained in the experiments. Our model gives a plausible interpretation of the conductivity in both systems. Received 10 April 2001     

Galloping of rectangular prisms in a smooth and in a turbulent flow

Galloping of rectangular prisms ranging from 0·2 to 1·0, approximately, in thickness ratio has been investigated experimentally in a smooth and in a turbulent flow. Attention was focused on galloping instability which builds up spontaneously from rest and is referred to as soft galloping. A close relationship between the onset of soft galloping and the peak characteristic of the steady drag coefficient was observed. Some other experiments to shed light on the mechanism of the onset of soft galloping of a rectangular prism are also reported.     

Magnetic guiding of cold neutral atoms using a V-shaped current-carrying conductor

A new scheme to magnetically guide cold, neutral atoms using a V-shaped current-carrying conductor is proposed. The spatial distributions of the magnetic fields, potentials and forces generated by the V-shaped current-carrying conductor are calculated, and the relationship between the magnetic field and the parameters of the V-shaped current-carrying conductor are analyzed in detail. Our study shows that the V-shaped current-carrying conductor proposed here can be used to guide cold atoms in the weak-field-seeking state, and to construct various atom-optical elements, such as atomic funnel, atomic beam-splitter and atom interferometer and so on, and even to realize a single-mode atomic waveguiding under certain conditions. Received 17 November 2000 and Received in final form 26 May 2001     

On dynamics analysis of a new chaotic attractor

In this Letter, a new chaotic system is discussed. Some basic dynamical properties, such as Lyapunov exponents, Poincaré mapping, fractal dimension, bifurcation diagram, continuous spectrum and chaotic dynamical behaviors of the new chaotic system are studied, either numerically or analytically. The obtained results show clearly that the system discussed in this Letter is a new chaotic system and deserves a further detailed investigation.     

Symmetry-breaking in local Lyapunov exponents

Integrable dynamical systems, namely those having as many independent conserved quantities as freedoms, have all Lyapunov exponents equal to zero. Locally, the instantaneous or finite time Lyapunov exponents are nonzero, but owing to a symmetry, their global averages vanish. When the system becomes nonintegrable, this symmetry is broken. A parallel to this phenomenon occurs in mappings which derive from quasiperiodic Schr?dinger problems in 1-dimension. For values of the energy such that the eigenstate is extended, the Lyapunov exponent is zero, while if the eigenstate is localized, the Lyapunov exponent becomes negative. This occurs by a breaking of the quasiperiodic symmetry of local Lyapunov exponents, and corresponds to a breaking of a symmetry of the wavefunction in extended and critical states. Received 25 October 2001 / Received in final form 8 December 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: r.ramaswamy@mail.jnu.ac.in     

A novel three-dimensional autonomous chaotic system generating two, three and four-scroll attractors

In this Letter a novel three-dimensional autonomous chaotic system is proposed. Of particular interest is that this novel system can generate two, three and four-scroll chaotic attractors with variation of a single parameter. By applying either analytical or numerical methods, basic properties of the system, such as dynamical behaviors (time history and phase diagrams), Poincaré mapping, bifurcation diagram and Lyapunov exponents are investigated to observe chaotic motions. The obtained results clearly show that this is a new chaotic system which deserves further detailed investigation.     

应用波分复用改善像束传像系统像质的研究

本文通过分析空间波分复用系统中包散元件的色散平均效应,用线扩散传递函数研究了像束传像性质,由光学成像的本征理论用像束成像信息量分析了波分复用改善像束传像像质的机制,并从实验上验证了上述分析结论.     

基于遗传算法的四旋翼无人机系统参数辨识

建立准确地系统模型是实现四旋翼无人机的自动飞行控制的基础,为此提出了一种遗传算法,并将其应用于四旋翼无人机系统参数辨识当中。首先,根据四旋翼受力分析建立了小角度下的线性系统模型;然后,将遗传算法应用于线性模型未知参数的辨识中;最后,分别对比了滚转、俯仰和偏航方向的加速度值与实际测量值。实验结果表明在悬停状态或小角度飞行状态下,该辨识方法能够建立比较精确的系统模型。     

Synchronization analysis of singular hybrid coupled networks

In this Letter, singular hybrid coupled systems are introduced to describe complex networks with a special class of constraints. The synchronization problem of singular hybrid coupled systems with time-varying nonlinear perturbation is investigated. A sufficient condition for global synchronization is derived based on the Lyapunov stability theory. The singular system is regular and impulse free. Finally, a numerical example is provided to illustrate the effectiveness of the proposal conditions.     

Adaptive modified function projective synchronization between hyperchaotic Lorenz system and hyperchaotic Lu system with uncertain parameters

This Letter investigates modified function projective synchronization between hyperchaotic Lorenz system and hyperchaotic Lu system using adaptive method. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two hyperchaotic systems modified function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.     

A three-scroll chaotic attractor

This Letter introduces a new chaotic member to the three-dimensional smooth autonomous quadratic system family, which derived from the classical Lorenz system but exhibits a three-scroll chaotic attractor. Interestingly, the two other scrolls are symmetry related with respect to the z-axis as for the Lorenz attractor, but the third scroll of this three-scroll chaotic attractor is around the z-axis. Some basic dynamical properties, such as Lyapunov exponents, fractal dimension, Poincaré map and chaotic dynamical behaviors of the new chaotic system are investigated, either numerically or analytically. The obtained results clearly show this is a new chaotic system and deserves further detailed investigation.     

A novel 3D autonomous system with different multilayer chaotic attractors

This Letter proposes a novel three-dimensional autonomous system which has complex chaotic dynamics behaviors and gives analysis of novel system. More importantly, the novel system can generate three-layer chaotic attractor, four-layer chaotic attractor, five-layer chaotic attractor, multilayer chaotic attractor by choosing different parameters and initial condition. We analyze the new system by means of phase portraits, Lyapunov exponent spectrum, fractional dimension, bifurcation diagram and Poincaré maps of the system. The three-dimensional autonomous system is totally different from the well-known systems in previous work. The new multilayer chaotic attractors are also worth causing attention.     

Electronic properties of quasiperiodic Fibonacci chain including second-neighbor hopping in the tight-binding model

We present an exact real-space renormalization group (RSRG) scheme for the electronic Green's functions of one-dimensional tight-binding systems having both nearest-neighbor and next-nearest-neighbor hopping integrals, and determine the electronic density of states for the quasiperiodic Fibonacci chain. This RSRG method also gives the Lyapunov exponents for the eigenstates. The Lyapunov exponents and the analysis of the flow pattern of hopping integrals under renormalization provide information about the nature of the eigenstates. Next we develop a transfer matrix formalism for this generalized tight-binding system, which enables us to determine the wave function amplitudes. Interestingly, we observe that like the nearest-neighbor tight-binding Fibonacci chain, the present generalized tight-binding system also have critical eigenstates, Cantor-set energy spectrum and highly fragmented density of states. It indicates that these exotic physical properties are really the characteristics of the underlying quasiperiodic structure. Received 5 April 1999     

A Hyperchaotic Attractor with Multiple Positive Lyapunov Exponents

There are many hyperchaotic systems, but few systems can generate hyperchaotic attractors with more than three PLEs （positive Lyapunov exponents）. A new hyperchaotic system, constructed by adding an approximate time-delay state feedback to a five-dimensional hyperchaotic system, is presented. With the increasing number of phase-shift units used in this system, the number of PLEs also steadily increases. Hyperchaotic attractors with 25 PLEs can be generated by this system with 32 phase-shift units. The sum of the PLEs will reach the maximum value when 23 phase-shift units are used. A simple electronic circuit, consisting of 16 operational amplifiers and two analogy multipliers, is presented for confirming hyperchaos of order 5, i.e., with 5 PLEs.