Stability of periodic motion, bifurcations and chaos of a two-degree-of-freedom vibratory system with symmertical rigid stops

A two-degree-of-freedom system having symmetrically placed rigid stops and subjected to periodic excitation is considered. Such models play an important role in the studies of mechanical systems with clearances or gaps. The period-one double-impact symmetrical motion and its Poincaré map are derived analytically. Stability and local bifurcations of the period-one double-impact symmetrical motion are analyzed by the equation of Poincaré map. The routes from period-one double-impact symmetrical motion to chaos, via pitchfork bifurcations and period-doubling bifurcation, are studied by numerical simulation. Some non-typical routes to chaos, caused by grazing the stops and Hopf bifurcation of period two four-impact motion, are analyzed. Hopf bifurcations of period-one double-impact symmetrical and antisymmetrical motions are shown to exist in the two-degree-of-freedom vibratory system with two-sided stops. Interesting feature like the period-one four-impact symmetrical motion is also found, and its route to chaos is analyzed. It is of special interest to acquire an overall picture of the system dynamics for some extreme values of parameters, especially those which relate to the degenerated case of a single-degree-of-freedom system, and these analyses are presented here.     

Dynamics of a mobile system with an internal acceleration-controlled mass in a resistive medium

The dynamics of a mobile system with a movable internal mass is investigated in this paper. Due to the periodic motion of the internal acceleration-controlled mass as well as the anisotropy of the external resistance, the system can move in a resistive medium. Major attention is given to the steady-state motion and stick-slip effect of the system as a whole. For anisotropic Coulomb's dry friction, in light of the non-smooth factors in both the internal control mode and external resistance, method of averaging is adopted to obtain an approximate expression of the average steady-state velocity when the stick-slip motion is absent. Optimizing the parameters of the internal controlled mass enables one to realize a maximal average steady-state velocity of the system. In view of the stick-slip effect, the steady-state motion of the system is classified into eight types, and the characteristics of each type are analyzed. Stick-slip motion is of our interest and receives extra attention. Two strategies of control are put forward based on the characteristics of stick-slip motion. Making use of these two control strategies, directed motions of the system are possible and the direction of the motion can be simply controlled by modifying the values of internal accelerations. To achieve an always forward motion with higher average steady-state velocity, further optimization is carried out. For anisotropic linear resistance, the approximate expression of average steady-state velocity can be also obtained by the method of averaging. No stick-slip motion may occur in this instance. All the analytical results are numerically simulated in order to verify their correctness.     

Vibrational response of a moving suspension-slider loading system exciting a rotating flexible disk

To investigate the vibrational response of the magnetic read/write head in hard disk drives this paper models a rotating flexible disk excited by a moving suspension-slider system which is considered to be a mass-dashpot-spring loading system, with the initial unstressed transverse runout integrated into the rotating disk dynamic model. The slider motion on the disk surface is driven by the suspension rotating at a constant speed. By subtracting the steady-state deflection component from the instantaneous deflection response of the rotating disk system, the relative vibration transverse deflection of the slider caused by the motion of the suspension-slider loading system is obtained. The effects of the slider initial and final positions, speed of movement, the disk rotational speed, and the disk mode of the initial transverse runout on the maximum amplitude of the relative vibration deflection are analyzed.     

Motion invariants for a charge in a linearly polarized wave field

Six motion integrals for a relativistic charge in the field of a transverse linearly polarized electromagnetic wave propagating with an arbitrary phase velocity u>c were obtained by solving the canonical equations of motion. On the basis of these integrals, the charge trajectory as a function of the wave phase is analyzed in a fixed coordinate system. The coordinates, time, and phase are related by elliptic functions.     

Generalization of a nonlinear friction relation for a dimer sliding on a periodic substrate

An atomic cluster moving along a solid surface can undergo dissipation of its translational energy through a direct mode, involving the coupling of the center-of-mass motion to thermal excitations of the substrate, and an indirect mode, due to damping of the internal motion of the cluster, to which the center-of-mass motion can be coupled as a result of surface potential. Focussing only on the less well understood indirect mode, on the basis of numerical solutions, we present, departures from a recently reported simple relationship between the force and velocity of nonlinear friction. A generalization of the analytic considerations that earlier led to that relationship is carried out and shown to explain the departures satisfactorily. Our generalization treats for the system considered (dimer sliding over a periodic substrate) the complete dependence on several of the key parameters, specifically internal dissipation, natural frequency, substrate corrugation, and length ratio. Further predictions from our generalizations are found to agree with new simulations. The system analyzed is relevant to nanostructures moving over crystal surfaces.     

Quantitative evaluation of space charge effects of laser-cooled three-dimensional ion system on a secular motion period scale

In this paper,we introduce a method of quantitatively evaluating and controlling the space charge effect of a lasercooled three-dimensional(3 D) ion system in a linear Paul trap.The relationship among cooling efficiency,ion quantity,and trapping strength is analyzed quantitatively,and the dynamic space distribution and temporal evolution of the 3 D ion system on a secular motion period time scale in the cooling process are obtained.The ion number influences the eigen-micromotion feature of the ion system.When trapping parameter q is ~ 0.3,relatively ideal cooling efficiency and equilibrium temperature can be obtained.The decrease of axial electrostatic potential is helpful in reducing the micromotion heating effect and the degradation in the total energy.Within a single secular motion period under different cooling conditions,ions transform from the cloud state(each ion disperses throughout the envelope of the ion system) to the liquid state(each ion is concentrated at a specific location in the ion system) and then to the crystal state(each ion is subjected to a fixed motion track).These results are conducive to long-term storage and precise control,motion effect suppression,high-efficiency cooling,and increasing the precision of spectroscopy for a 3 D ion system.     

Analysis of a compliantly suspended acoustic velocity sensor

The dynamics of a compliantly suspended acoustic velocity sensor having a spherical geometry are analyzed using theory and experiment. The analysis starts with a review of the motion associated with an unconstrained solid sphere when subjected to an acoustic plane wave in an unbounded inviscid fluid medium. The theory is then modified to account for the inclusion of an inertial sensor and an external suspension system. Accordingly, the open-circuit receiving response of a geophone-based and accelerometer-based device is derived. Density variations associated with the sphere and the surrounding fluid medium are assessed along with the effects fluid viscosity. Wave effects in the sphere and the suspension system are also analyzed.     

Sound generated by a vortex convected past an elastic sheet

We study the motion and sound generated when a line vortex is convected in a uniform low-Mach flow parallel to a thin elastic sheet. The linearized sheet motion is analyzed under conditions where the unforced sheet (in the absence of the line vortex) is stationary. The vortex passage above the sheet excites a resonance mode of motion, where the sheet oscillates at its least stable eigenmode. The sources of sound in the acoustic problem include the sheet velocity and fluid vorticity. It is shown that the release of trailing-edge vortices, resulting from the satisfaction of the Kutta condition, has two opposite effects on sound radiation: while trailing-edge vortices act to reduce the pressure fluctuations occurring owing to the direct interaction of the line vortex with the unperturbed sheet, they extend and amplify the acoustic signal produced by the motion of the sheet. The sheet motion radiates higher sound levels as the system approaches its critical conditions for instability, where the effect of resonance becomes more pronounced. It is argued that the present theory describes the essential mechanism by which sound is generated as a turbulent eddy is convected in a mean flow past a thin elastic airfoil.     

Dynamical behaviors of a plate activated by an induction motor

Dynamics and chaotification of a system consisting of an induction motor activating a mobile plate (with variable contents) fixed to a spring are studied. The dynamical model of the device is presented and the electromechanical equations are formulated. The oscillations of the plate are analyzed through variations of the following reliable control parameters: phase voltage supply of the motor, frequency of the external source and mass of the plate. The dynamics of the system near the fundamental resonance region presents jump phenomenon. Mapping of the control parameters planes in terms of types of motion reveals period-n motion, quasi-periodicity and chaos. Anti-control of chaos of the induction motor is also obtained using the field-oriented control associated to the time delay feedback control.     

Unified properties of a weakly interacting Fermi gas in a weak magnetic field

When the orbital motion and the spin motion of particles were considered simultaneously, the thermodynamic potential function of a weakly interacting Fermi gas in a weak magnetic field was derived using the thermodynamics method. Based on the derived expression, the analytical expressions of energy, heat capacity, chemical potential, susceptibility and stability conditions of the system were given, and the effects of the interparticle interactions as well as the magnetic field on the properties of the system were analyzed. It was shown that the magnetic field always causes energy and stability to decrease, while the chemical potential of the system to increase. The repulsive (attractive) interactions always increase (decrease) energy and stability, but decrease (increase) the chemical potential and paramagnetism. The repulsive (attractive) interactions decrease (increase) heat capacity of the system at high temperatures but increase (decrease) it at low temperatures.     

Hamilton–Jacobi and Symplectic Analysis of a Particle Constrained on a Circle

Hamilton-Jacobi and modified Faddeev-Jackiw methods were applied to investigate the motion of a particle moving on a circle. The results of both methods were found to be equivalent with those of Dirac's formalism. Besides, the importance of the Lagrange multipliers was analyzed and the action of the second-class constrained system was given.     

Capillary oscillations and Tonks-Frenkel instability of a liquid layer of finite thickness

A dispersion relation is derived and analyzed for the spectrum of capillary motion at a charged flat surface of viscous liquid covering a solid substrate with a layer of finite thickness. It is shown that for waves whose wavelengths are comparable with the layer thickness, viscous damping at the solid bottom begins to play an important role. The spectrum of capillary liquid motion established in this system has high and low wave number limits. The damping rates of the capillary liquid motion with wave lengths comparable with the layer thickness are increased considerably and the Tonks-Frenkel instability growth rates are reduced compared with those for a liquid of infinite depth. Zh. Tekh. Fiz. 67, 27–33 (August 1997)     

Thermocapillary motion of a drop near a plane interface between liquids

The thermocapillary motion of a liquid drop immersed into another liquid near an infinite plane interface between two liquids is theoretically analyzed. The motion is considered under the conditions of a constant temperature gradient normal to the interface at infinity and small Reynolds and Peclet numbers. The problem is solved in bispherical coordinates. The analysis takes into consideration the thermal conductivity of the liquids and the thermocapillary motion of the liquids due to a nonuniform temperature distribution over the plane interface.     

Sensitivity to initial conditions and lyapunov exponent of a quasiperiodic system

The dynamics of a quasiperiodic map is analyzed both in the presence and in the absence of weak noise. It is shown that, in the presence of weak noise, a strange chaotic attractor with a negative Lyapunov exponent and sensitive dependence of trajectories on the initial conditions can exist in the system. This means that the types of motion of a fluctuating system cannot be classified only by the sign of the leading Lyapunov exponent.     

The Energy of a Dynamical Wave-Emitting System in General Relativity

The problem of energy and its localization in general relativity is critically re-examined. The Tolman energy integral for the Eddington spinning rod is analyzed in detail and evaluated apart from a single term. It is shown that a higher order iteration is required to find its value. Details of techniques to solve mathematically challenging problems of motion with powerful computing resources are provided. The next phase of following a system from static to dynamic to final quasi-static state is described.     

Validity of the quantum regression theorem for resonance fluorescence in a photonic crystal

Correlation functions of a driven two‐level system embedded in a photonic crystal are analyzed. The spectral density of the photonic bands near a gap makes this system non‐Markovian. The equations of motion for two‐time correlations are derived by two different methods, the quantum regression theorem and the fluctuation dissipation theorem, and found to be the same.     

Dynamics of a charged test particle in a hard rod fluid

The motion of a charged hard rod, accelerated by a constant and uniform external field, in a fluid of mechanically identical neutral particles is studied. The system, initially at rest, is excited through collisions with the accelerated particle. A class of initial configurations is found for which recollisions between the charged rod and the excitation caused by it (a moving particle) never occur. The evolution of the velocity distribution of the test particle is analyzed in this case. The possibility of obtaining from microscopic dynamics a kinetic equation is discussed. The dependence of the current on the external field is shown to agree with that predicted by the Boltzmann equation.     

一类非线性相对转动系统的组合谐波分岔行为研究

针对一类具有非线性刚度、非线性阻尼的非线性相对转动系统, 应用耗散系统的拉格朗日原理建立在组合谐波激励作用下非线性相对转动系统的动力学方程. 构造李雅普诺夫函数, 分析相对转动系统的稳定性, 研究自治系统的分岔特性. 应用多尺度法求解相对转动系统的非自治系统在组合激励作用下的分岔响应方程. 最后采用数值仿真方法, 通过分岔图、时域波形、相平面图、Poincaré截面图等研究外扰激励、系统阻尼、 非线性刚度对相对转动系统经历倍周期分岔进入混沌运动的影响. 关键词： 相对转动 组合激励 分岔 混沌     

Block-wise motion detection using compressive imaging system

A block-wise motion detection strategy based on compressive imaging, also referred to as feature-specific imaging (FSI), is described in this work. A mixture of Gaussian distributions is used to model the background in a scene. Motion is detected in individual object blocks using feature measurements. Gabor, Hadamard binary and random binary features are studied. Performance of motion detection methods using pixel-wise measurements is analyzed and serves as a baseline for comparison with motion detection techniques based on compressive imaging. ROC (Receiver Operation Characteristic) curves and AUC (Area Under Curve) metrics are used to quantify the algorithm performance. Because a FSI system yields a larger measurement SNR(Signal-to-Noise Ratio) than a traditional system, motion detection methods based on the FSI system have better performance. We show that motion detection algorithms using Hadamard and random binary features in a FSI system yields AUC values of 0.978 and 0.969 respectively. The pixel-based methods are only able to achieve a lower AUC value of 0.627.