Chaotic dynamics of simple vibrational systems

This study discusses the development of a technique for analysis of the dynamical regimes of complex mechanical systems consisting of a rotor motor coupled to a system with multi-degrees-of-freedom. To understand the possible qualitatively different dynamical regimes in such systems, a simple mechanical system is considered of the “rotator-oscillator” type with a finite power source. This system has four degrees-of-freedom and is defined in four-dimensional cylindrical phase space with 12 parameters. Near the main resonance the original system is reduced to the Lorenz system with four parameters defined in a three-dimensional Cartesian phase space. This is done with the help of a special change of variables, parameters, and employing an averaging method. Studying the latter system, the existence of one of the chaotic attractors, namely of Lorenz attractor is established. Also established is the Feigenbaum attractor and the alternation. Chaotic limit sets define chaotic behavior of the instantaneous frequency of rotation of the asynchronous motor. The Poincare mappings are presented to show the correspondence of the original 4 dof and averaged 3 dof systems. The qualitative rotational characteristics for different values of the system parameters are obtained. In particular, the system can possess normal Sommerfeld effect, doubled Sommerfeld effect and a so-called scattering of the torque curve. The scattering of the torque curve (which is a known effect in micro-electronics) is likely to be a new effect in mechanics. In contrast to the Sommerfeld effect, when frequency or amplitude jumps occur instantaneously (once the unstable point of the characteristic is reached), the jump to a next stable point may take a certain time, even infinite one. Such chaotic mistuning of the motor frequency would result in random vibrations leading to system wear and damage.     

Comments on nonlinear dynamics of a non-ideal Duffing-Rayleigh oscillator: Numerical and analytical approaches

An analytical and numerical investigation into the dynamic interaction between a cantilever beam with nonlinear damping and stiffness behavior, modeled by the Duffing-Rayleigh equation, and a non-ideal motor that is connected to the end of the beam, is presented. Non-stationary and steady-state responses in the resonance region as well as the passage through resonance behavior when the frequency of the excitation is varied are analyzed. The influences of nonlinear stiffness, nonlinear damping and the extent of the unbalance in the motor are examined. It is found that in this situation so-called Sommerfeld effects may be observed; the increase required by a source operating near the resonance results in a small change in the frequency, but there is a large increase in the amplitude of the resultant vibration and the jump phenomenon occurs.     

A non-ideal portal frame energy harvester controlled using a pendulum

A model of energy harvester based on a simple portal frame structure is presented. The system is considered to be non-ideal system (NIS) due to interaction with the energy source, a DC motor with limited power supply and the system structure. The nonlinearities present in the piezoelectric material are considered in the piezoelectric coupling mathematical model. The system is a bi-stable Duffing oscillator presenting a chaotic behavior. Analyzing the average power variation, and bifurcation diagrams, the value of the control variable that optimizes power or average value that stabilizes the chaotic system in the periodic orbit is determined. The control sensitivity is determined to parametric errors in the damping and stiffness parameters of the portal frame. The proposed passive control technique uses a simple pendulum to tuned to the vibration of the structure to improve the energy harvesting. The results show that with the implementation of the control strategy it is possible to eliminate the need for active or semi active control, usually more complex. The control also provides a way to regulate the energy captured to a desired operating frequency.     

Characteristics of a high frequency ion source used in a low-energy accelerator

This work presents the characteristics of a high frequency ion source operating on a low energy, 150 keV accelerator. The latter is to be used as a neutron generator and its design is based on a theoretical analysis which shows that if the axial potential in an electrostatic electrode system is made to increase with four thirds the power of axial distance, inward electric forces will compensate space charge forces tending to blow up the beam. This results in a simplified acceleration tube much shorter and of higher gradient than the conventional acceleration columns. The ion source itself is an ordinary type using axial extraction of the beam, and its main properties investigated are the beam current and beam quality (or emittance). Dependence of the two on different parameters is investigated in a series of tests.     

Vibration of L-shaped plates under a deterministic force or moment excitation: a case of statistical energy analysis application

Analytical and closed form solutions are presented in this paper for the vibration response of an L-shaped plate under a point force or a moment excitation. Inter-relationships between wave components of the source and the receiving plates are clearly defined. Explicit expressions are given for the quadratic quantities such as input power, energy flow and kinetic energy distributions of the L-shaped plate. Applications of statistical energy analysis (SEA) formulation in the prediction of the vibration response of finite coupled plate structures under a single deterministic forcing are examined and quantified. It is found that the SEA method can be employed to predict the frequency averaged vibration response and energy flow of coupled plate structures under a deterministic force or moment excitation when the structural system satisfies the following conditions: (1) the coupling loss factors of the coupled subsystems are known; (2) the source location is more than a quarter of the plate bending wavelength away from the source plate edges in the point force excitation case, or is more than a quarter wavelength away from the pair of source plate edges perpendicular to the moment axis in the moment excitation case due to the directional characteristic of moment excitations. SEA overestimates the response of the L-shaped plate when the source location is less than a quarter bending wavelength away from the respective plate edges owing to wave coherence effect at the plate boundary.     

弯管对末端带弹性障板充液管路辐射声能量的影响

基于声固耦合有限元方法建立了末端带弹性障板的充液管路数值模型,重点分析了不同激励下弯管对管口辐射声能量的影响.结果表明:弯管引入的高阶周向模式耦合使结构振动和流体声传播都发生明显改变,以致系统辐射声能量及主要能量贡献源也发生转移,并随激励方式和频率而不同.对本文管路模型,平面波激励下弯管系统在低频的结构辐射声能量明显增...     

Nonlinear resonances of a single-wall carbon nanotube cantilever

The dynamics of an electrostatically actuated carbon nanotube (CNT) cantilever are discussed by theoretical and numerical approaches. Electrostatic and intermolecular forces between the single-walled CNT and a graphene electrode are considered. The CNT cantilever is analyzed by the Euler–Bernoulli beam theory, including its geometric and inertial nonlinearities, and a one-mode projection based on the Galerkin approximation and numerical integration. Static pull-in and pull-out behaviors are adequately represented by an asymmetric two-well potential with the total potential energy consisting of the CNT elastic energy, electrostatic energy, and the Lennard-Jones potential energy. Nonlinear dynamics of the cantilever are simulated under DC and AC voltage excitations and examined in the frequency and time domains. Under AC-only excitation, a superharmonic resonance of order 2 occurs near half of the primary frequency. Under both DC and AC loads, the cantilever exhibits linear and nonlinear primary and secondary resonances depending on the strength of the excitation voltages. In addition, the cantilever has dynamic instabilities such as periodic or chaotic tapping motions, with a variation of excitation frequency at the resonance branches. High electrostatic excitation leads to complex nonlinear responses such as softening, multiple stability changes at saddle nodes, or period-doubling bifurcation points in the primary and secondary resonance branches.     

Nonlinear vibration of a curved beam under uniform base harmonic excitation with quadratic and cubic nonlinearities

This paper presents nonlinear vibration analysis of a curved beam subject to uniform base harmonic excitation with both quadratic and cubic nonlinearities. The Galerkin method is employed to discretize the governing equations. A high-dimensional model that can take nonlinear model coupling into account is derived, and the incremental harmonic balance (IHB) method is employed to obtain the steady-state response of the curved beam. The cases investigated include softening stiffness, hardening stiffness and modal energy transfer. The stability of the periodic solutions for given parameters is determined by the multi-variable Floquet theory using Hsu's method. Particular attention is paid to the anti-symmetric response with and without excitation, as the excitation frequency is close to the first and third natural frequencies of the system. The results obtained with the IHB method compare very well with those obtained via numerical integration.     

Modeling and performance study of a beam microgyroscope

We develop a mathematical model of a microgyroscope whose principal component is a rotating cantilever beam equipped with a proof mass at its end. The microgyroscope undergoes two flexural vibrations that are coupled via base rotation about the microbeam longitudinal axis. The primary vibratory motion is produced in one direction (drive direction) of the microbeam by a pair of DC and AC voltages actuating the proof mass. The microbeam angular rotation induces a secondary vibration in the orthogonal (sense) direction actuated by a second DC voltage. Closed-form solutions are developed for the linearized problem to study the relationship between the base rotation and gyroscopic coupling. The response of the microgyroscope to variations in the DC voltage across the drive and sense electrodes and frequency of excitation are examined and a calibration curve of the gyroscope is obtained analytically.     

Synchronization in a chain of nearest neighbors coupled oscillators with fixed ends

We investigate a system of coupled phase oscillators with nearest neighbors coupling in a chain with fixed ends. We find that the system synchronizes to a common value of the time-averaged frequency, which depends on the initial phases of the oscillators at the ends of the chain. This time-averaged frequency decays as the coupling strength increases. Near the transition to the frozen state, the time-averaged frequency has a power law behavior as a function of the coupling strength, with synchronized time-averaged frequency equal to zero. Associated with this power law, there is an increase in phases of each oscillator with 2pi jumps with a scaling law of the elapsed time between jumps. During the interval between the full frequency synchronization and the transition to the frozen state, the maximum Lyapunov exponent indicates quasiperiodicity. Time series analysis of the oscillators frequency shows this quasiperiodicity, as the coupling strength increases.     

带有分数阶阻尼的压电能量采集系统相干共振

研究了含分数阶阻尼的双稳态能量采集系统的相干共振. 建立了带有分数阶阻尼的轴向受压梁压电能量采集系统动力学模型. 对于分数阶方程, 采用Euler-Maruyama-Leipnik方法进行求解, 计算了不同阻尼阶数下的能量采集系统的信噪比、响应均值、跃迁数目等统计物理量. 结果表明: 此压电能量采集系统在随机激励下可以实现相干共振, 阻尼阶数对相干共振的临界噪声强度和相干共振幅值有很大影响. 关键词： 分数阶阻尼 随机激励 能量采集系统 相干共振     

金属材料次表面缺陷成像检测系统及其应用

介绍了一种基于光热光偏转检测技术的原理,可以检测金属材料次表面缺陷空间分布的激光热波探测系统.该系统具有结构紧凑,调试简便,运行稳定,测试结果可靠的特点,它用半导体激光作泵浦光源和探测光源,采用电源调制的方式对泵浦光束进行调制,有频率稳定、噪音小的优点,同时系统可以用低压直流电源供电,为仪器化和便携化研究创造了条件.利用该系统对金属铝片次表面不同深度的凹槽作了检测,得到了与实际样品一致的检测结果.     

Damping as a result of piezoelectric energy harvesting

Systems that harvest or scavenge energy from their environments are of considerable interest for use in remote power supplies. A class of such systems exploits the motion or deformation associated with vibration, converting the mechanical energy to electrical, and storing it for later use; some of these systems use piezoelectric materials for the direct conversion of strain energy to electrical energy. The removal of mechanical energy from a vibrating structure necessarily results in damping. This research addresses the damping associated with a piezoelectric energy harvesting system that consists of a full-bridge rectifier, a filter capacitor, a switching DC–DC step-down converter, and a battery. Under conditions of harmonic forcing, the effective modal loss factor depends on: (1) the electromechanical coupling coefficient of the piezoelectric system; and (2) the ratio of the rectifier output voltage during operation to its maximum open-circuit value. When the DC–DC converter is maximizing power flow to the battery, this voltage ratio is very nearly 1/2, and the loss factor depends only on the coupling coefficient. Experiments on a base-driven piezoelectric cantilever, having a system coupling coefficient of 26%, yielded an effective loss factor for the fundamental vibration mode of 2.2%, in excellent agreement with theory.     

Nonlinear vibration control and energy harvesting of a beam using a nonlinear energy sink and a piezoelectric device

This paper presents an optimal design for a system comprising a nonlinear energy sink (NES) and a piezoelectric-based vibration energy harvester attached to a free–free beam under shock excitation. The energy harvester is used for scavenging vibration energy dissipated by the NES. Grounded and ungrounded configurations are examined and the systems parameters are optimized globally to both maximize the dissipated energy by the NES and increase the harvested energy by piezoelectric element. A satisfactory amount of energy has been harvested as electric power in both configurations. The realization of nonlinear vibration control through one-way irreversible nonlinear energy pumping and optimizing the system parameters result in acquiring up to 78 percent dissipation of the grounded system energy.     

大功率YAG激光-MAG复合热源的光谱诊断与分析

大功率YAG激光-MAG复合热源具有广泛的工业应用前景,其等离子体状态的诊断对于指导复合热源发展方向、优化复合参数具有重要意义。通过建立的中空探针光谱扫描系统,采用荷兰Avaspec-FT-2快速数字光谱仪,横向扫描焊接电弧等离子体,采集YAG激光-MAG复合等离子体不同空间位置的光谱;通过计算得到其特定辐射谱段的空间分布,对比激光复合前后等离子体辐射的变化;并结合高速摄像照片,探讨其耦合机理。进一步选取特定谱线(FeⅠ),采用Boltzmann图法对复合热源等离子体的空间电子温度进行计算;研究结果表明,YAG激光-MAG电弧复合后,等离子能量更靠近熔池,集中作用于焊接试板,其能量作用区域展宽;在电弧中心区造成电子温度上升。     

BEPCⅡ Positron Source

BEPCⅡ— an upgrade project of the Beijing Electron Positron Collider (BEPC) is a factory type of e^＋e^－ collider. The fundamental requirements for its injector linac are the beam energy of 1.89GeV for on-energy injection and a 40mA positron beam current at the linac end with a low beam emittance of 1.6μm and a low energy spread of ±0.5% so as to guarantee a higher injection rate (≥50mA/min) to the storage ring. Since the positron flux is proportional to the primary electron beam power on the target, we will increase the electron gun current from 4A to 10A by using a new electron gun system and increase the primary electron energy from 120MeV to 240MeV. The positron source itself is an extremely important system for producing more positrons, including a positron converter target chamber, a 12kA flux modulator, the 7m focusing module with DC power supplies and the support. The new positron production linac from the electron gun to the positron source has been installed into the tunnel. In what follows, we will emphasize the positron source design, manufacture and tests.     

High-Power Modulated Intense Relativistic Electron Sources with Applications to RF Generation and Controlled Thermonuclear Fusion

Recent advances in the physics and technology of the modulated intense relativistic electron beams (IREB's) are reviewed in this paper. Bunched dense electron beams can be used to construct high-power RF sources, which may critically affect future progress in fusion technology. In this paper a system is described in which electrical energy can be converted from a single pulse of relatively long duration into a series of subpulses of short duration (nanosecond and subnanosecond) and of high power (~1010 W). This electrical system consists of an IREB propagating through passive structures. The mutual interaction between the electron beam and one passive structure modifies the IREB so that power compression and beam modulation occur. When the modified IREB interacts with the next passive structure, the kinetic energy of the electrons is converted into electrical energy or RF energy. The beam current modulation depends on the injected IREB and the structure parameters. A 100-percent modulation of the current has been achieved. A single-beam source may be used for exciting radiation in a frequency range of 60 MHz to 10 GHz. In the frequency range of 60-750 MHz a modulated beam with power ~1010 W has already been achieved. IREB modulation at a frequency of ~3 GHz was performed and RF energy was extracted from the bunched beam with power output of 5 × 108 W.     

The control of near-field optics: imposing direction through coupling with off-resonant laser light

The well-known spatially distributed form of the near field, associated with a dipolar source, is usually unsuitable for effecting the excitation of a location-specific detector in the vicinity. It is of interest, therefore, to identify a means of producing a much more greatly directed character to such a near field, imposing features that are more commonly associated with longer-range, wave-zone electromagnetic propagation. In this paper, it is shown that nonlinear optical coupling with off-resonant, throughput laser light can achieve this effect. Based on a quantum electrodynamical analysis it is shown that two mechanisms contribute; one requires both the source and detector to be irradiated by the throughput radiation, the other can operate with the source alone irradiated. The analysis leads to results identifying the dependence of each mechanism on the relative directions of the laser beam and the source–detector displacement. Contour maps of the ensuing near field, at the source emission frequency, exhibit a directionality that grows with the off-resonant beam intensity. The phenomenon affords a means of achieving optical control over the near-field distribution.     

Design of a Large Orbit Gyrotron with a Permanent Magnet System

The paper presents results of numerical analysis and outlines the computer-aided design of a novel high-harmonic gyrotron with a beam of electrons gyrating along axis-encircling trajectories. The electron beam is formed by a novel electron-optical system (EOS) based on an electron gun of diode type with thermionic cathode and gradual reversal of the magnetic field. The results of numerical simulations predict satisfactory performance of the EOS and appropriate beam quality parameters. The tube design allows one to install different cavities optimized for excitation of TE_4,1 mode at the fourth harmonic of the cyclotron frequency or TE_3,1 mode at the third one. The target parameters of the device are: frequency about 112 GHz; output power near 1 kW and efficiency of several percent.