Peridynamic Shell Model Based on Micro-Beam Bond

Peridynamics(PD)is a non-localmechanics theory that overcomes the limitations of classical continuummechanics(CCM)in predicting the initiation and propagation of cracks.However,the calculation efficiency of PDmodels is generally lower than that of the traditional finite elementmethod(FEM).Structural idealization can greatly improve the calculation efficiency of PD models for complex structures.This study presents a PD shell model based on the micro-beam bond via the homogenization assumption.First,the deformations of each endpoint of themicro-beam bond are calculated through the interpolation method.Second,the micro-potential energy of the axial,torsional,and bending deformations of the bond can be established from the deformations of endpoints.Finally,the micro moduli of the shellmodel can be obtained via the equivalence principle of strain energy density(SED).In addition,a new fracture criterion based on the SED of the micro-beam bond is adopted for crack simulation.Numerical examples of crack propagation are provided,and the results demonstrate the effectiveness of the proposed PD shell model.

Coupled vibrations and frequency shift of compound system consisting of quartz crystal resonator in thickness-shear motions and micro-beam array immersed in liquid

The dynamic characteristics of a quartz crystal resonator（QCR） in thicknessshear modes（TSM） with the upper surface covered by an array of micro-beams immersed in liquid are studied. The liquid is assumed to be inviscid and incompressible for simplicity. Dynamic equations of the coupled system are established. The added mass effect of liquid on micro-beams is discussed in detail. Characteristics of frequency shift are clarified for different liquid depths. Modal analysis shows that a drag effect of liquid has resulted in the change of phase of interaction（surface shear force）, thus changing the system resonant frequency. The obtained results are useful in resonator design and applications.

Vibration and wave propagation analysis of twisted micro-beam using strain gradient theory

In this research, vibration and wave propagation analysis of a twisted micro- beam on Pasternak foundation is investigated. The strain-displacement relations （kine-matic equations） are calculated by the displacement fields of the twisted micro-beam. The strain gradient theory （SGT） is used to implement the size dependent effect at micro-scale. Finally, using an energy method and Hamilton＇s principle, the governing equations of motion for the twisted micro-beam are derived. Natural frequencies and the wave prop- agation speed of the twisted micro-beam are calculated with an analytical method. Also, the natural frequency, the phase speed, the cut-off frequency, and the wave number of the twisted micro-beam are obtained by considering three material length scale parameters, the rate of twist angle, the thickness, the length of twisted micro-beam, and the elastic medium. The results of this work indicate that the phase speed in a twisted micro-beam increases with an increase in the rate of twist angle. Moreover, the wave number is in- versely related with the thickness of micro-beam. Meanwhile, it is directly related to the wave propagation frequency. Increasing the rate of twist angle causes the increase in the natural frequency especially with higher thickness. The effect of the twist angle rate on the group velocity is observed at a lower wave propagation frequency.

Size-dependent thermoelastic initially stressed micro-beam due to a varying temperature in the light of the modified couple stress theory

The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress(MCS)theory.Although many models have been incorporated into the literature,there is still room for introducing an improved model in this context.In this work,we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity.The MCS theory is used to investigate the material length scale effects.Using the Laplace transform,the temperature,deflection,displacement,flexure moment,and stress field variables of the micro-beam are derived.The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced.The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables.

Transverse shear and normal deformation effects on vibration behaviors of functionally graded micro-beams

A quasi-three dimensional model is proposed for the vibration analysis of functionally graded(FG)micro-beams with general boundary conditions based on the modified strain gradient theory.To consider the effects of transverse shear and nor-mal deformations,a general displacement field is achieved by relaxing the assumption of the constant transverse displacement through the thickness.The conventional beam theories including the classical beam theory,the first-order beam theory,and the higher-order beam theory are regarded as the special cases of this model.The material proper-ties changing gradually along the thickness direction are calculated by the Mori-Tanaka scheme.The energy-based formulation is derived by a variational method integrated with the penalty function method,where the Chebyshev orthogonal polynomials are used as the basis function of the displacement variables.The formulation is validated by some comparative examples,and then the parametric studies are conducted to investigate the effects of transverse shear and normal deformations on vibration behaviors.

Effect of strain-gradients of surface micro-beams on frequency-shift of a quartz crystal resonator under thickness-shear vibrations

With introduction of the first-order strain-gradient of surface micro-beams into the energy density function,we developed a two-dimensional dynamic model for a compound quartz crystal resonator（QCR） system,consisting of a QCR and surface micro-beam arrays.The frequency shift that was induced by micro-beams with consideration of strain-gradients is discussed in detail and some useful results are obtained,which have important significance in resonator design and applications.

Instability of functionally graded micro-beams via micro-structure-dependent beam theory

This paper focuses on the buckling behaviors of a micro-scaled bi-directional functionally graded （FG） beam with a rectangular cross-section, which is now widely used in fabricating components of micro-nano-electro-mechanical systems （MEMS/NEMS） with a wide range of aspect ratios. Based on the modified couple stress theory and the principle of minimum potential energy, the governing equations and boundary conditions for a micro-structure-dependent beam theory are derived. The present beam theory incorporates different kinds of higher-order shear assumptions as well as the two familiar beam theories, namely, the Euler-Bernoulli and Timoshenko beam theories. A numerical solu- tion procedure, based on a generalized differential quadrature method （GDQM）, is used to calculate the results of the bi-directional FG beams. The effects of the two exponential FG indexes, the higher-order shear deformations, the length scale parameter, the geomet- ric dimensions, and the different boundary conditions on the critical buckling loads are studied in detail, by assuming that Young＇s modulus obeys an exponential distribution function in both length and thickness directions. To reach the desired critical buckling load, the appropriate exponential FG indexes and geometric shape of micro-beams can be designed according to the proposed theory.

Size-dependent behaviors of viscoelastic axially functionally graded Timoshenko micro-beam considering Poisson effects

A size-dependent continuum-based model is developed for the functionally graded(FG)Timoshenko micro-beams with viscoelastic properties,in which material parameters vary according to the power law along its axial direction.The size effect is incorporated by employing the modified couple stress theory and Kelvin-Voigt viscoelastic model,so that viscous components are included in the stress and the deviatoric segments of the symmetric couple stress tensors.The components of strain,curvature,stress and couple stress are formulated by combining them with the Timoshenko beam theory.Based on the Hamilton principle,the governing differential equations and boundary conditions for the micro-beam are expressed with arbitrary beam section shape and arbitrary type of loads.The size effect,FG effect,Poisson effect,and the influence of the beam section shape on the mechanical behaviors of viscoelastic FG micro-beams are investigated by taking the simply supported micro-beam subjected to point load as an example.Results show that the size effect on deflection,normal stress and couple stress are obvious when the size of the micro-beam is small enough,and the FG effects are obvious when the size of the micro-beam is large enough.Moreover,the Poisson ratio influences the size effect significantly and the beam section shape is also an important factor influencing the mechanical behavior of the micro-beam.

Influence of surface micro-beams with large deflection on the resonance frequency of a quartz crystal resonator in thickness-shear mode vibrations

We study the dynamic behavior of a quartz crystal resonator （QCR） in thickness-shear vibrations with the upper surface covered by an array of micro-beams （MBs） under large deflection. Through taking into account the continuous conditions of shear force and bending moment at the interface of MBs/resonator, dependences of frequency shift of the compound QCR system versus material parameter and geometrical parameter are illustrated in detail for nonlinear and linear vibrations. It is found that the frequency shift produces a little right （left） translation for increasing elastic modulus （length/radius ratio） of MBs. Moreover, the frequency right （left） translation distance caused by nonlinear deformation becomes more serious in the second-order mode than in the first-order one,

Effects of local thickness defects on the buckling of micro-beam

A buckling model of Timoshenko micro-beam with local thickness defects is established based on a modified gradient elasticity.By introducing the local thickness defects function of the micro-beam,the variable coefficient differential equations of the buckling problem are obtained with the variational principle.Combining the eigensolution series of the complete micro-beam with the Galerkin method,we obtain the critical load and buckling modes of the micro-beam with defects.The results show that the depth and location of the defect are the main factors affecting the critical load,and the combined effect of boundary conditions and defects can significantly change the buckling mode of the micro-beam.The effect of defect location on buckling is related to the axial gradient of the rotation angle,and defects should be avoided at the maximum axial gradient of the rotation angle.The model and method are also applicable to the static deformation and vibration of the micro-beam.

Modeling size-dependent behaviors of axially functionally graded Bernoulli-Euler micro-beam

This work focus on the mechanical behaviors,which are related to the size effect,functionally graded(FG)effect and Poisson effect,of an axially functionally graded(AFG)micro-beam whose elastic modulus varies according to sinusoidal law along its axial direction.The displacement field of the AFG micro-beam is set according to the Bernoulli-Euler beam theory.Employing the modified couple stress theory(MCST),the components of strain,curvature,stress and couple stress are expressed by the second derivative of the deflection of the AFG micro-beam.A size-dependent model related to FG effect and Poisson effect,which includes the formulations of bending stiffness,deflection,normal stress and couple stress,is developed to predict the mechanical behaviors of the AFG microbeam by employing the principle of minimum potential energy.The mechanical behaviors of a simply supported AFG micro-beam are numerically investigated using the developed model for demonstrating the size effects,FG effects and Poisson effects of the AFG micro-beam.Results show that the mechanical behaviors of AFG micro-beams are distinctly size-dependent only when the ratio of micro-beam height to material length-scale parameter is small enough.The FG parameter is an important factor that determines and regulates the size-dependent behaviors of AFG micro-beams.The influences of Poisson’s ratio on the mechanical behaviors of AFG micro-beams are not negligible,and should be also considered in the design and analysis of an AFG micro-beam.This work supplies a theoretical basis and a technical reference for the design and analysis of AFG micro-beams in the related regions.

Analytic solution for size-dependent behaviors of micro-beam under forced vibration

This paper focuses on the size-dependently mechanical behaviors of a micro-beam under forced vibration.Governing equations of a micro-beam under forced vibration are established by using the modified couple stress theory,Bernoulli-Euler beam theory and D’Alembert’s principle together.A simply supported micro-beam under forced vibration is solved according to the established governing equations and the method of separation of variables.The dimensionless deflection,amplitude mode and period mode are defined to investigate the size-dependently mechanical behaviors of a micro-beam under forced vibration.Results show that the performance of a micro-beams under forced vibration is distinctly size-dependent when the ratio of micro-beam height to material length-scale parameter is small enough.Both frequency ratio and loading location are the important factors that determine the sizedependent performance of a micro-beams under forced vibration.

Micro-beam XRF localization by a laser beam

A new method for micro-beam XRF localiztion is presented.A laser beam along with an incident X-ray hits on the surface of a sample.The micro region on the sample that reached by X-ray beam can be localized by means of the visible spot of the laser beam.This method is suitable for X-ray microprobes using an X-ray tube or synchrotron radiation as excitation sources.

Development of an Intermediate Energy Heavy-Ion Micro-Beam Irradiation System

The micro-beam irradiation system,which focuses the beam down to micron order and precisely delivers a predefined number of ions to a predefined spot of micron order,is a powerful tool for radio-biology,radio-biomedicine and micromachining.The Institute of Modern Physics of Chinese Academy of Sciences is developing a heavy-ion micro- beam irradiation system up to intermediate energy.Based on the intermediate and low energy beam provided by Heavy Ion Research Facility of Lanzhou,the micro-beam system takes the form of the magnetic focusing.The heavy-ion beam is conducted to the basement by a symmetrical achromatic system consisting of two vertical bending magnets and a quadrupole in between.Then a beam spot of micron order is formed by a magnetic triplet quadrupole of very high gradient.The sample can be irradiated either in vacuum or in the air.This system will be the first opening platform capable of providing heavy ion micro-beam,ranging from low(10MeV/u)to intermediate energy(100MeV/u), for irradiation experiment with positioning and counting accuracy.Target material may be biology cell,tissue or other non-biological materials.It will be a help for unveiling the essence of heavy-ion interaction with matter and also a new means for exploring the application of heavy-ion irradiation.

空化现象对水导激光微水束稳定性的影响研究

为了探寻空化现象对水导激光微水束稳定性影响,利用计算流体动力学的方法,分别在不考虑空化和考虑空化的情况下,对从典型喷嘴出射的水射流进行了数值模拟分析,研究了空化现象的产生机理及对微水束稳定性的影响。结果表明,在入口直径为0.1 mm、圆柱段长径比为1、上边缘锐利的喷嘴结构下,随着入口压力从0.2 MPa增大到16 MPa,水射流与喷嘴壁面分离后再次附着的长度逐渐增大,并且空化会导致该长度延长;在入口压力小于6 MPa的情况下,不考虑空化的水射流在稳定后会贴着喷嘴壁面流下,而添加空化模型使得水束形成翻转流。该研究对设计满足水导激光工艺的喷嘴结构有着重要的参考价值。

原子力显微镜-扫描电子显微镜共定位表征系统的研发与应用

微纳加工过程中,常有样品需要进行聚焦离子束(FIB)溅射、切割,扫描电子显微镜(SEM)以及原子力显微镜(AFM)表征,而这三类仪器都需要将样品固定在样品台上才可测试,固定不佳会影响表征结果.但固定好的样品在不同仪器之间转移、拆卸、再固定的过程中极易受到破坏.基于以上问题,设计了AFM-SEM-FIB样品共定位系统,可实现样品在此三种仪器之间的无损转移及共定位,避免珍贵样品破坏及目标丢失,以及解决AFM扫描无法控制方向、迅速调整位点等问题.在微纳表征中有优异的表现,系统已被开发成产品并量产销售.

基于微能量收集的电力设备无线测温技术研究

针对电力设备无线测温技术的需求,文中设计了一种基于新型磁电发电装置的无线温度在线监测系统。该系统利用电力系统周围的杂散磁场为整套无线监测系统供电,并设计了新型压电摩擦耦合悬臂梁结构以提高磁场能收集的效率,同时温度测量模块采用低通滤波提高收集灵敏度,采用低主频工作模式及定时唤醒功能降低信号处理和传输能耗,兼具低功耗的温度采集功能和电气隔离的数据传输能力,保证整套设备的稳定可靠运行。实验测得电源模块在4 Oe,50 Hz的交变磁场下可产生峰峰值开路电压160 V,短路电流14μA整流后输出3.3 V稳定电压,在该电源供电下无线测温装置每5 s可收发一次温度数据。

矢量涡旋光场在激光微纳加工中的应用

矢量光场领域在过去20年出现了众多重要进展。考虑到多篇综述介绍了矢量光场产生方法以及调控技术,作者仅以矢量涡旋光场为线索总结了其在激光减材、改性以及增材等微纳加工领域的典型应用,回顾了矢量涡旋光在材料表面和内部的微纳结构加工、光存储以及立体微结构光刻等应用中的部分关键进展。详细介绍了基于定制光场的图案化光致表面周期结构以及立体微结构快速双光子光刻的原理与技术。最后,总结了矢量涡旋光场在激光微纳加工中的优势与挑战,展望了其在未来将赋能更多复杂应用。

热轴力对双层微梁谐振器热弹性阻尼的影响分析

近年来,已有不少关于复合材料层合梁/板谐振器热弹性阻尼的研究论文发表.然而,在这些研究中热轴力(热薄膜力)对热弹性阻尼的贡献都被忽略了.众所周知,若梁/板的材料性质分布关于几何中面不对称则其物理中面将偏离几何中面.于是,热-弹耦合振动引起的变温场不但会形成热弯矩,还会产生热轴力(热薄膜力),二者将共同产生热弹性阻尼.文章基于Euler-Bernoulli梁理论和经典热传导理论,建立了双层矩形截面微梁热-弹耦合振动数学模型,精确考虑了热轴力对微结构内能耗的贡献.然后,采用解析方法求得了用变形几何量表示的热轴力和热弯矩,进而求得了系统自由振动的复频率以及用逆品质因数表示的热弹性阻尼解析解.作为数值算例,选取由均匀的银(Ag)和氮化硅(Si_(3)N_(4))分层组成的双层微梁,通过大量的数值实验定量分析了分层体积分数变化对热弹性阻尼的影响规律,考察了热轴力对热弹性阻尼的影响程度.结果表明,忽略热轴力将会低估层合梁谐振器的热弹性阻尼.在金属银的体积分数为70%(氮化硅体积分数为30%)时,忽略热轴力后对热弹性阻尼的低估最大可达16.3%.

STABILITY ANALYSIS OF A CAPACITIVE FGM MICRO-BEAM USING MODIFIED COUPLE STRESS THEORY

Based on the Modified Couple Stress Theory,a functionally graded micro-beam under electrostatic forces is studied.The FGM micro-beam is made of two materials and material properties vary continuously along the beam thickness according to a power-law.Dynamic and static pull-in voltages are obtained and it is shown that the static and dynamic pull-in voltages for some materials cannot be obtained using classic theories and components of couple stress must be taken into account.In addition,it is shown that the values of pull-in voltages depend on the variation through the thickness of the volume fractions of the two constituents.