Synchronization Analysis of Coupled Noncoherent Oscillators

We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the R?ssler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators.     

松弛型基因随机振子的同步和聚类

松弛型基因随机振子是三类基因振子(光滑振子、松弛振子和随机振子)中的一种.具有相抑制耦合细胞通信的这种类基因振子的同步与聚类是一个有趣且令人关注的问题.这里,数值模拟显示出振子之间的相差分布能够展示出单峰、双峰或多峰分布,但依赖于噪声强度和细胞密度.而且,数值地发现存在细胞数目的一个阈值,当细胞数目超过此阈值时,对于任意的噪声强度相差分布函数的峰值性几乎保持不变.这些结果表明抑制耦合的松弛型随机振子具有不同于普通耦合的光滑或松弛振子的同步与聚类机制.     

In-Nozzle Measurements of a Turbulent Opposed Jet Using PIV

Turbulent opposed jet burners are an excellent test case for combustion research and model development due to the burners’ compactness, relative simplicity, and the good optical access they provide. The flow-field in the flame region depends strongly on the turbulence generation inside the nozzles, so that realistic flow simulations can only be achieved if the flow inside the nozzles is represented correctly, which must be verified by comparison to suitable experimental data. This paper presents detailed particle image velocimetry (PIV) measurements of the flow issuing from the turbulence generating plates (TGP) inside a glass nozzle. The resulting data is analyzed in terms of first and second moments, time-series, frequency spectra and phase averages. The measurements show how individual high velocity jets emerging from the TGP interact and recirculation zones are formed behind the solid parts of the TGP. Vortex shedding is observed in the jet’s shear layer were high levels of turbulent kinetic energy are generated. Time series measurements revealed periodic pulsations of the individual jets and implied a coupling between adjacent jets. The peak frequencies were found to be a function of the Reynolds-number.     

Homoclinic Twist Bifurcation in a System of Two Coupled Oscillators

We analyse the dynamics of two identical Josephson junctions coupled through a purely capacitive load in the neighborhood of a degenerate symmetric homoclinic orbit. A bifurcation function is obtained applying Lin's version of the Lyapunov–Schmidt reduction. We locate in parameter space the region of existence of n-periodic orbits, and we prove the existence of n-homoclinic orbits and bounded nonperiodic orbits. A singular limit of the bifurcation function yields a one-dimensional mapping which is analyzed. Numerical computations of nonsymmetric homoclinic orbits have been performed, and we show the relevance of these computations by comparing the results with the analysis.     

Approximate Solution of a Class of Nonlinear Oscillators in Resonance with a Periodic Excitation

This paper deals with the most important characteristics of a generalized Van der Pol–Duffing oscillator in resonance with a periodic excitation. We use an asymptotic perturbation method based on Fourier expansion and time rescaling and demonstrate through a second order perturbation analysis the existence of one or two limit cycles. Moreover, we identify a sufficient condition to obtain a doubly periodic motion, when a second low frequency appears, in addition to the forcing frequency. Comparison with the solution obtained by the numerical integration confirms the validity of our analysis.     

Transition of Energy to a Nonlinear Localized Mode in a Highly Asymmetric System of Two Oscillators

Redistribution of energy in a highly asymmetric system consisting ofcoupled linear and highly nonlinear damped oscillators isinvestigated. Special attention is paid to the excitation of a nonlinearnormal mode while the energy is initially stored in other modes of thesystem. The transition proceeds via the mechanism of subharmonicresonance which is possible because of the strong nonlinearity of thesystem. The conditions of the energy transition to NNM being effectiveare revealed and guidelines to design such a systems are formulatedin detail.     

Dynamical Order in Systems of Coupled Noisy Oscillators

We investigate a dynamical order induced by coupling and/or noise in systems of coupled oscillators. The dynamical order is referred to a one-dimensional topological structure of the global attractor of the system in the context of random skew-product flows. We show that if the coupling is sufficiently strong, then the system exhibits one dimensional dynamics regardless of the strength of noise. If the coupling is weak, then it is shown numerically that the system also exhibits one dimensional dynamics provided the noise is sufficiently strong. We also show that for any coupling and any noise, the system has a unique rotation number and hence all the oscillators tend to oscillate with the same frequency eventually (frequency locking). Dedicated to Professor Pavol Brunovsky on the occasion of his 70th birthday.     

3/4-Fractional Superdiffusion in a System of Harmonic Oscillators Perturbed by a Conservative Noise

We consider a harmonic chain perturbed by an energy conserving noise and show that after a space-time rescaling the energy-energy correlation function is given by the solution of a skew-fractional heat equation with exponent 3/4.     

Multi-Body Analysis of a Tiltrotor Configuration

The paper describes the aeroelastic analysis of a tiltrotor configuration. The 1/5 scale wind tunnel semispan model of the V-22 tiltrotor aircraft is considered. The analysis is performed by means of a multi-body code, based on an original formulation. The differential equilibrium problem is stated in terms of first-order differential equations. The equilibrium equations of every rigid body are written together with the definitions of the momenta. The bodies are connected by kinematic constraints applied in the form of Lagrangian multipliers. Deformable components are mainly modelled by means of beam elements based on an original finite volume formulation. Multi-disciplinary problems can be solved by adding user-defined differential equations. In the presented analysis, the equations related to the control of the swash-plate of the model are considered. Advantages of a multi-body aeroelastic code over existing comprehensive rotorcraft codes include the exact modelling of the kinematics of the hub, the detailed modelling of the flexibility of critical hub components, and the possibility to simulate steady flight conditions as well as wind-up and maneuvers. The simulations described in the paper include (1) the analysis of the aeroelastic stability, with particular regard to the proprotor/pylon instability that is peculiar to tiltrotors, (2) the determination of the dynamic behavior of the system and of the loads due to typical maneuvers, with particular regard to the conversion from helicopter to airplane mode, and (3) the stress evaluation in critical components, such as the pitch links and the conversion downstop spring.     

Synchronization and chimera state in a mechanical system

Nonlinear Dynamics - Synchronization phenomenon appears in several natural systems being associated with physical, chemical and biological processes. In brief, synchronization may be understood as...     

Free Vibration in a Class of Self-Excited Oscillators with 1:3 Internal Resonance

Free vibration of a two degree of freedom weakly nonlinear oscillator is investigated. The type of nonlinearity considered is symmetric, it involves displacement as well as velocity terms and gives rise to self-excited oscillations in many engineering applications. After presenting the equations of motion in a general form, a perturbation methodology is applied for the case of 1:3 internal resonance. This yields a set of four slow-flow nonlinear equations, governing the amplitudes and phases of approximate motions of the system. It is then shown that these equations possess three distinct types of solutions, corresponding to trivial, single-mode and mixed-mode response of the system. The stability analysis of all these solutions is also performed. Next, numerical results are presented by applying this analysis to a specific practical example. Response diagrams are obtained for various combinations of the system parameters, in an effort to provide a complete picture of the dynamics and understand the transition from conditions of 1:3 internal resonance to non-resonant response. Emphasis is placed on identifying the effect of the linear damping, the frequency detuning and the stiffness nonlinearity parameters. Finally, the predictions of the approximate analysis are confirmed and extended further by direct integration of the averaged equations. This reveals the existence of other regular and irregular motions and illustrates the transition from phase-locked to drift response, which takes place through a Hopf bifurcation and a homoclinic explosion of the averaged equations.     

Theoretical and Experimental Study of Multimodal Targeted Energy Transfer in a System of Coupled Oscillators

The purpose of this study is the theoretical and experimental investigation of targeted energy transfers from a two-degree-of-freedom primary structure to a nonlinear energy sink (NES). It is demonstrated that an NES can resonate with and extract energy from both modes of the primary structure. By facilitating these energy transfers, notably through excitation of appropriate periodic and quasi-periodic orbits, one can promote dissipation of a major portion of externally induced energy in the nonlinear attachment.     

Detection of Homoclinic Bifurcations in Resonance Zones of Forced Oscillators

We study homoclinic behaviour in resonance zones of nonconservative,forced oscillators represented as one-parameter families of periodicperturbations of planar Hamiltonian systems. We use a Melnikov-typetechnique and obtain a simple condition under which separatrixsplittings with exponentially small upper bounds may occur. Todemonstrate our theory, we give two examples for Duffing-typeoscillators and compare the theoretical results with numericalsimulations. In these examples, homoclinic behaviour that was notreported in early work is detected.     

A Method for Obtaining Approximate Analytic Periods for a Class of Nonlinear Oscillators

This paper deals with nonlinear oscillations of conservative single-degree-of-freedom systems with odd nonlinearity. By combining the linearization of the governing equation with the method of harmonic balance, we establish two approximate analytic formulas for the period. These two formulas are valid for small as well as large amplitudes of oscillation. Three examples are used to illustrate that the proposed formulas can give very satisfactory approximate results. Sommario. Questo lavoro tratta il problema delle oscillazioni nonlineari di sistemi conservativi ad un grado di libertà con nonlinearità simmetriche. Combinando opportunamente la tecnica di linearizzazione dellequazione del moto con il metodo del bilancio armonico si perviene a due formule analitiche approssimate per il periodo. Le formule ottenute sono valide sia per piccole che per grandi ampiezze di oscillazione. Si utilizzano tre esempi classici di oscillatori nonlineari per illustrate lefficacia del metodo nel produrre risultati approssimati soddisfacenti.     

The Description of Localized Normal Modes in a Chain of Nonlinear Coupled Oscillators Using Complex Variables

We present an asymptotic approach to the analysis of coupled nonlinearoscillators with asymmetric nonlinearity based on the complexrepresentation of the dynamic equations. The ideas of the approach arefirst developed for the case of the system with two degrees of freedom.Special attention is paid to the study of localized normal modes in achain of weakly coupled nonlinear oscillators. We discuss also certainpeculiarities of the localization of excitations in the case of strongcoupling between the oscillators.     

Hopf Bifurcation in Symmetric Networks of Coupled Oscillators with Hysteresis

The standard approach to study symmetric Hopf bifurcation phenomenon is based on the usage of the equivariant singularity theory developed by M. Golubitsky et?al. In this paper, we present the equivariant degree theory based method which is complementary to the equivariant singularity approach. Our method allows systematic study of symmetric Hopf bifurcation problems in non-smooth/non-generic equivariant settings. The exposition is focused on a network of eight identical van der Pol oscillators with hysteresis memory, which are coupled in a cube-like configuration leading to S ₄-equivariance. The hysteresis memory is the source of non-smoothness and of the presence of an infinite dimensional phase space without local linear structure. Symmetric properties and multiplicity of bifurcating branches of periodic solutions are discussed in the context showing a direct link between the physical properties and the equivariant topology underlying this problem.     

Modeling the Interaction of a Vortex Pair with the Ground

The results of a numerical investigation of the interaction between an aircraft vortex wake (vortex pair) and the ground during the takeoff and landing phases are presented. The calculations were performed within the framework of the time-dependent two-dimensional Reynolds-averaged Navier-Stokes equations using the Spalart-Shur turbulence model generalizing the turbulent viscosity transport model of Spalart and Allmaras to the case of the flows with curved streamlines and rotation. Similar calculations were carried out on the basis of the original Spalart-Allmaras model and the k- model of Menter. Some new qualitative and quantitative data on the distinctive features of the phenomenon under consideration are obtained.     

Interaction of Two-Dimensional Trailing Vortex Pair with a Shear Layer

The basic laws governing the interaction of a two-dimensional vortex pair with a shear layer of constant thickness are considered. The main idea of the study is to develop and adapt a simplified representation of a hydrodynamic flow based on a point-vortex model simulating the actual interaction of full-scale vortex patterns over the ground surface. It is shown that vortices with vorticity opposite in sign to the shear layer may stop or even ricochet from this layer, while the other vortex may penetrate through the layer. Numerical results are presented as plots and analyzed     

Oscillators with a power-form restoring force and fractional derivative damping: Application of averaging

In this paper free oscillators with a power-form restoring force and with a fractional derivative damping term are considered. An analytical approach based on the averaging method is adjusted to derive analytical expressions for the amplitude and phase of oscillations. Effects of the fractional-order derivative on the amplitude and frequency of oscillations are discussed in several examples, including a generalized van der Pol oscillator, purely nonlinear oscillators and a linear oscillator.     

金属往复滑动摩擦噪声源的识别

对金属往复滑动摩擦噪声进行了声学和动力学测量 ,通过对声压级和加速度进行时间历程波形分析、功率谱分析 ,确认摩擦噪声是由参加相对滑动的摩擦副的 1个或 2个部件的振动辐射所产生 ,摩擦噪声的声源体为参加摩擦运动的振动部件