Vibration analysis of a partially treated multi-layer beam with magnetorheological fluid

Semi-active vibration control based on magnetorheological (MR) materials offers excellent potential for high bandwidth control through rapid variations in the rheological properties of the fluid under varying magnetic field. Such fluids may be conveniently applied to partial or more critical components of a large structure to realize more efficient and compact vibration control mechanism with variable damping. This study investigates the properties and vibration responses of a partially treated multi-layer MR fluid beam. The governing equations of a partially treated multi-layered MR beam are formulated using finite element method and Ritz formulation. The validity of the proposed finite element formulations is demonstrated by comparing the results with those obtained from the Ritz formulation and the experimental measurements. The properties of different configurations of a partially treated MR-fluid beam are evaluated to investigate the influences of the location and length of the MR-fluid for different boundary conditions. The properties in terms of natural frequencies and loss factors corresponding to various modes are evaluated under different magnetic field intensities and compared with those of the fully treated beams. The effect of location of the fluid treatment on deflection mode shapes is also investigated. The forced vibration responses of the various configurations of partially treated MR sandwich beam are also evaluated under harmonic force excitations. The results suggest that the natural frequencies and transverse displacement response of the partially treated MR beams are strongly influenced not only by the intensity of the applied magnetic field, but also by the location and the length of the fluid pocket. The application of partial treatment could also alter the deflection pattern of the beam, particularly the location of the peak deflection.     

共晶键合与减薄技术的压电能量采集器（英）

采用微硅 锆钛酸铅（Si-PZT）悬臂梁结构并在悬臂梁末端附加镍质量块,构成可以工作于低频环境（小于1 000 Hz）的微压电能量采集器,一种利用压电效应将环境振动能转换为电能的器件。利用金薄膜作为中间层的共晶键合技术和PZT研磨减薄技术制备了微压电悬臂梁结构,PZT减薄实验最好结果为减薄至8 m。镍质量块（2 mm2 mm0.6 mm）采用微电铸工艺制备。通过对硅片与块材PZT的共晶键合工艺与PZT减薄技术的研究,制备出总厚度约为71 m的Si-PZT悬臂梁结构,其中硅梁厚约为47 m,PZT梁厚约为24 m。制备的微压电振动能量采集器样品的测试结果表明:在谐振频率为950 Hz,1.0g加速度激励条件下,其交流输出峰值电压可达958 mV。     

Magnetization reversal observed by the deflection of magnetic actuator

A magnetic actuator consisting of a silicon oxide microcantilever and a silicon oxide plate deposited on ferromagnetic multilayer thin films is fabricated using electron beam lithography and electron beam evaporation, and placed in various magnetic fields to observe its flexure. The magnetic actuator is bent by magnetic torque produced by ferromagnetic multilayer thin films under an external magnetic field owing to the fabrication of a highly sensitive microcantilever and the design of elliptic ferromagnetic thin films with high magnetic shape anisotropy. The magnetic actuator is placed in four kinds of magnetic field directions to investigate the diversity of deflections; the angles between the easy axis of the ferromagnetic multilayer thin films and the direction of the external magnetic field are 90°, 70°, 45° and 20°.     

Dynamic analysis of magnetorheological elastomer-based sandwich beam with conductive skins under various boundary conditions

The dynamic analysis of a three-layered symmetric sandwich beam with magnetorheological elastomer (MRE) embedded viscoelastic core and conductive skins subjected to a periodic axial load have been carried out under various boundary conditions. As the skins of the sandwich beam are conductive, magnetic loads are applied to the skins during vibration. Due to the field-dependent shear modulus of MRE material, the stiffness of the MRE embedded sandwich beam can be changed by the application of magnetic fields. Using extended Hamilton’s principle along with generalized Galarkin’s method the governing equation of motion has been derived. The free vibration analysis of the system has been carried out and the results are compared with the published experimental and analytical results which are found to be in good agreement. The parametric instability regions of the sandwich beam have been determined for various boundary conditions. Here, recently developed magnetorheological elastomer based on natural rubber containing iron particles and carbon blacks have been used. The effects of magnetic field, length of MRE patch, core thickness, percentage of iron particles and carbon blacks on the regions of parametric instability for first three modes of vibration have been studied. These results have been compared with the parametric instability regions of the sandwich beam with fully viscoelastic core to show the passive and active vibration reduction of these structures using MRE and magnetic field. Also, the results are compared with those obtained using higher order theory.     

The investigation of high frequency vibration modes of PZT-4 transducers using ESPI techniques with reference beam modulation

In this paper the experimental vibration amplitudes together with the vibration modes of the PZT-4 transducer radiating front face are presented for generation in various media. The studies were carried out using an electronic speckle pattern interferometer (ESPI) with reference beam modulation to give resolution down to 20 Å of surface amplitude. Analogies are drawn between these transducers and the resonant vibration modes of thin plates. The relationship between the surface vibration amplitudes and the radiation beam pattern of the transducers is also presented.     

An adaptive beam model and dynamic characteristics of magnetorheological materials

Magnetorheological (MR) materials show variations in their rheological properties when subjected to varying magnetic fields. They have quick time response, in the order of milliseconds, and thus are potentially applicable to structures and devices when a tunable system response is required. When incorporated into an adaptive structural system, they can yield higher variations in the dynamic response of the structure. This study presents a detailed analysis of dynamic characteristics of adaptive beam based on MR materials. The relationship between the magnetic field and the complex shear modulus of MR materials in the pre-yield regime is researched using oscillatory rheometry techniques. A structural dynamic modelling approach is discussed and vibration characteristics of MR adaptive structures are predicted for different magnetic field levels. In addition to the model predictions, actual MR adaptive beam is fabricated and tested. Both studies illustrate the vibration minimization capabilities of the MR adaptive beam at different magnetic field levels.     

Nonlinear vibration of a double-walled carbon nanotube embedded in a polymer matrix

In the current work, the nonlinear vibration of an embedded double-walled carbon nanotube (DWCNT) aroused by nonlinear van der Waals (vdW) interaction forces from both surrounding medium and adjacent tubes is studied. Using both Euler–Bernoulli and Timoshenko beam models, the relation between deflection amplitudes and resonant frequencies of the DWCNT is derived through harmonic balance method. It is found that the nonlinear vdW forces from the surrounding medium result in noncoaxial vibration of the embedded DWCNT. The noncoaxial vibration includes both uni-directional and bi-directional vibration modes. It is found that the surrounding matrix has more prominent effect on the uni-directional vibration in comparison to the bi-directional vibration. The axial load effect on the vibrational behavior of the embedded DWCNT is also discussed. Due to the influence of the surrounding polymer, the prediction on the resonant frequencies of embedded CNTs is quite different from that for free-standing CNTs. A softening behavior for the deflection amplitude-resonant frequency relation is observed for the first time in the bi-directional vibration of the embedded DWCNT, which can only be obtained using the Timoshenko beam theory.     

A distributed-mass approach for dynamic analysis of Timoshenko plane frames

The dynamic stiffness method is the exact method for the dynamic analysis of plane frames using the continuous-coordinate system to consider the effect of mass distribution in beam elements. The dynamic stiffness method may create some null modes where the joints of beam element have null deformation. Unlike the Bernoulli–Euler frames, adding an interior node at the middle of the beam elements cannot normalize all the null modes of flexural vibration in the Timoshenko frames. The floating interior-node scheme is proposed to eliminate the null modes of flexural vibration in the Timoshenko frames. Orthogonal properties of vibration modes in Timoshenko plane frames are theoretically derived, through which the equations of motion in beam elements can be transformed into the decoupled equations of motion in terms of mode amplitudes.     

VIBRATION-BASED DIAGNOSTICS OF FATIGUE DAMAGE OF BEAM-LIKE STRUCTURES

The analytical investigation of vibration of damaged structures is a complicated problem. This problem may be simplified if a structure can be represented in the form of a beam with corresponding boundary and loading conditions. In this connection, free vibrations of an elastic cantilever Bernoulli-Euler beam with a closing edge transverse crack is considered in the present work as a model of a structure with a fatigue crack. The modelling of bending vibrations of a beam with a closing crack is realized based on the solutions for an intact beam and for a beam with an open crack. The algorithm of consecutive (cycle-by-cycle) calculation of beam mode shapes amplitudes is presented. It is shown that at the instant of crack opening and closing, the growth of the so-called concomitant mode shapes which differ from the initially given mode shape takes place. Moreover, each of the half-cycles is characterized by a non-recurrent set of amplitudes of concomitant modes of vibration and these amplitudes are heavily dependent on the crack depth.The vibration characteristics of damage based on the estimation of non-linear distortions of the displacement, acceleration and strain waves of a cracked beam are investigated, and the comparative evaluation of their sensitivity is carried out.     

CYCIAE-100轴向注入线设计及中心区束流匹配

采用包含空间电荷效应的束流光学计算软件TRANSOPTR对CYCIAE-100回旋加速器轴向注入线进行设计,在综合考虑空间布局、元件选择、真空度、空间电荷效应、轴向磁场和造价等问题后,最终确定了轴向注入线的聚焦结构。将数值跟踪获得的真实磁场下螺旋偏转板传的输矩阵编写到TRANSOPTR程序中,从而实现了从离子源出口至偏转板出口的束流光学匹配。介绍了CYCIAE-100回旋加速器轴向注入线的设计思想、布局结构和束流光学计算结果,并给出了主要元件的设计结果。在确定中心区结构和对中轨道后,采用多粒子轨道跟踪的方法进行中心区束流匹配的研究,通过对数值模拟的结果进行椭圆拟合并结合解析公式计算得到注入点处匹配矩阵,为注入线的设计提供拟合条件。     

Crack detection in single-crystalline silicon wafers using impact testing

This paper presents acoustic measurements obtained by mechanically exciting vibratory modes in single-crystalline silicon wafers with hairline periphery cracks of different type and location. The data presented shows a dependence of natural frequencies, peak amplitudes and damping levels of four audio vibration modes in the frequency range up to 1000 Hz on crack type and crack location. Data from defective wafers exhibit lower natural frequencies, higher damping levels, and lower peak amplitudes. The results suggest an impact test method may be useful for solar cell crack detection and quality control.     

基于螺线盘聚焦径向电子束的理论分析与仿真研究

对径向电子束在浸没式聚焦条件下的传输特性进行了理论分析,得到了束流传输过程中轴向扩张幅值与外加引导磁场强度之间的解析表达式。阐述了螺线盘在空间中任意一点产生磁场的理论,给出了通以相反方向电流的螺线盘之间磁场的分布规律。设计了一种基于螺线盘聚焦径向电子束的引导磁场系统,并对电子束的传输特性进行了仿真研究,结果表明径向电子束能够在设计的引导磁场系统下实现束流的稳定传输。     

Micromagnetic calculation of magnetostatic oscillation modes of an orthogonally magnetized disk of yttrium iron garnet

The absorption spectrum of a normally magnetized disk of yttrium iron garnet, which is associated with resonances of magnetostatic oscillation modes excited by a homogeneous high-frequency magnetic field, has been investigated using a numerical analysis of the micromagnetic model developed for ferromagnetic objects. The distribution of magnetization oscillation amplitudes over the disk surface area has been obtained for the first four modes. A good agreement between the results of the micromagnetic simulation and the data of analytical calculations for special cases has proved the reliability and efficiency of the proposed approach in numerical experiments on the study of the magnetization dynamics in objects with different geometries and shapes, including multilayer magnetic film structures.     

半导体硅熔体的有效(磁)黏度

用钕铁硼(NdFeB)永磁材料构建"魔环"结构的永磁体,向直拉硅生长的熔体所在空间引入磁场,采用回转振荡法测量不同磁场强度下硅熔体的有效黏度(磁黏度).在温度一定时,测得的磁黏度随着磁场强度的增加而增加,二者呈抛物线关系.熔硅温度升高,磁场影响加剧.1490—1610℃温度区间内,磁黏度有异常变化.当引入磁场强度为0068T时,熔硅有效黏度比原黏度增加2—3个数量级,证明引入磁场是硅单晶大直径生长时,抑制熔硅热对流的有效手段. 关键词： 硅熔体 有效(磁)黏度 魔环永磁体 回转振荡法     

FDTD Simulation of Electromagnetic Wave Transformation in a Dynamic Magnetized Plasma

Finite-Difference Time-Domain (FDTD) algorithms are applied to study the transformation of a pre-existing electromagnetic plane wave by prescribed time variation of a cold magnetoplasma with a magnetic field along the propagation direction. A one-dimensional FDTD code is used to verify the results obtained earlier using analytical approximations based on (a) WKB method for slow switching of the plasma medium and (b) Green's function technique for rapid switching of the plasma medium. A novel successive reduction method has been developed and applied to obtain the amplitudes and the frequencies of the new modes generated by the switching of the medium.     

ASYMPTOTIC APPROACH FOR NON-LINEAR PERIODICAL VIBRATIONS OF CONTINUOUS STRUCTURES

An asymptotic approach for determining periodic solutions of non-linear vibration problems of continuous structures (such as rods, beams, plates, etc.) is proposed. Starting with the well-known perturbation technique, the independent displacement and frequency is expanded in a power series of a natural small parameter. It leads to infinite systems of interconnected non-linear algebraic equations governing the relationships between modes, amplitudes and frequencies. A non-trivial asymptotic technique, based on the introduction of an artificial small parameter is used to solve the equations. An advantage of the procedure is the possibility to take into account a number of vibration modes. As examples, free longitudinal vibrations of a rod and lateral vibrations of a beam under cubically non-linear restoring force are considered. Resonance interactions between different modes are investigated and asymptotic formulae for corresponding backbone curves are derived.     

Effect of Longitudinal Magnetic Field on Vibration Characteristics of Single-Walled Carbon Nanotubes in a Viscoelastic Medium

The effect of longitudinal magnetic field on vibration response of a sing-walled carbon nanotube (SWCNT) embedded in viscoelastic medium is investigated. Based on nonlocal Euler-Bernoulli beam theory, Maxwell’s relations, and Kelvin viscoelastic foundation model, the governing equations of motion for vibration analysis are established. The complex natural frequencies and corresponding mode shapes in closed form for the embedded SWCNT with arbitrary boundary conditions are obtained using transfer function method (TFM). The new analytical expressions for the complex natural frequencies are also derived for certain typical boundary conditions and Kelvin-Voigt model. Numerical results from the model are presented to show the effects of nonlocal parameter, viscoelastic parameter, boundary conditions, aspect ratio, and strength of the magnetic field on vibration characteristics for the embedded SWCNT in longitudinal magnetic field. The results demonstrate the efficiency of the proposed methods for vibration analysis of embedded SWCNTs under magnetic field.     

Time-resolved measurement technique for pulsed electron beam envelope basing on framing and streaking principle

The time-resolved electron beam envelope parameters, including cross sectional distribution and beam centroid position, are very important for the study of beam transmission characteristics in a magnetic field and for verifying the rationality of the magnetic field parameters employed. One kind of high time-resolved beam envelope measurement system has recently been developed, constituted of a high-speed framing camera and a streak camera.It can obtain three panoramic images of the beam and time continuous information along the given beam profile simultaneously. Recently obtained data has proved that several fast vibrations of the beam envelope along the diameter direction occur during the front and the tail parts of the electron beam. The vibration period is several nanoseconds. The effect of magnetic field on the electron beam is also observed and verified. Beam debugging experiments have proved that the existing beam transmission design is reasonable and viable. This beam envelope measurement system will establish a good foundation for beam physics research.     

Higher order representation of the beam cross section deformation in large displacement finite element analysis

Most existing beam formulations assume that the cross section of the beam remains rigid regardless of the amplitude of the displacement. The absolute nodal coordinate formulation (ANCF); however, allows for the deformation of the cross section and leads to a more general beam models that capture the coupling between different modes of displacement. This paper examines the effect of the order of interpolation on the modes of deformation of the beam cross section using ANCF finite elements. To this end, a new two-dimensional shear deformable ANCF beam element is developed. The new finite element employs a higher order of interpolation, and allows for new cross section deformation modes that cannot be captured using previously developed shear deformable ANCF beam elements. The element developed in this study relaxes the assumption of planar cross section; thereby allowing for including the effect of warping as well as for different stretch values at different points on the element cross section. The displacement field of the new element is assumed to be cubic in the axial direction and quadratic in the transverse direction. Using this displacement field, more expressions for the element extension, shear and the cross section stretch can be systematically defined. The change in the cross section area is measured using Nanson’s formula. Measures of the shear angle, extension, and cross section stretch can also be systematically defined using coordinate systems defined at the element material points. Using these local coordinate systems, expressions for a nominal shear angle are obtained. The differences between the cross section deformation modes obtained using the new higher order element and those obtained using the previously developed lower order elements are highlighted. Numerical examples are presented in order to compare the results obtained using the new finite element and the results obtained using previously developed ANCF finite elements.     

Measurement of micro weld joint position based on magneto-optical imaging

In a laser butt joint welding process,it is required that the laser beam focus should be controlled to follow the weld joint path accurately.Small focus wandering off the weld joint may result in insufficient penetration or unacceptable welds.Recognition of joint position offset,which describes the deviation between the laser beam focus and the weld joint,is important for adjusting the laser beam focus and obtaining high quality welds.A new method based on the magneto-optical(MO)imaging is applied to measure the micro weld joint whose gap is less than 0.2 mm.The weldments are excited by an external magnetic field,and an MO sensor based on principle of Faraday magneto effect is used to capture the weld joint images.A sequence of MO images which are tested under different magnetic field intensities and different weld joint widths are acquired.By analyzing the MO image characteristics and extracting the weld joint features,the influence of magnetic field intensity and weld joint width on the MO images and detection of weld joint position is observed and summarized.