Single aspherical lens for deastigmatism, collimation, and circularization of a laser beam

An astigmatic and elliptically diverging laser beam generated by a gain-guided laser diode can be converted into a collimated and circular beam with a single specially designed lens. The designed lens also corrects for the astigmatism present in the laser diode. The input surface of the lens has a different concave and convex aspherical profile in the transverse and the longitudinal direction, respectively, for astigmatism correction. The output surface possesses a convex aspherical and a straight profile in the transverse and the longitudinal direction, respectively, for collimation and circularization of the final output laser beam.     

Measurements of thermal diffusivity of boron-silicon film-on-glass structure using phase detection method of photothermal deflection spectroscopy

The phase detection method of photothermal deflection spectroscopy in the transverse configuration was used to measure the overall thermal diffusivity of silicon-boron (Si-B) alloy film on Corning 7059 glass substrate. Results were attained by observing the phase of deflection of the probe beam when it scanned above the film surface relative to the pump beam. Measurements were repeated for different modulation frequencies of the pump beam. Furthermore, both bouncing and skimming configurations were used. The effect of varying the distance between the probe beam and film surface was investigated.     

Further study on the refined theory of rectangle deep beams

Based on the refined theory for narrow rectangular deep beams, two different displacement boundary conditions of the fixed end of a cantilever beam are used to study the deformation of the beam. One is the conventional simplified displacement boundary condition, and the other is a new boundary condition determined by the least squares method. Three load cases are investigated, which are a transverse shear force at the free end of the beam, a uniformly distributed load at the top surface, and a linearly distributed load at the top surface, respectively. Solutions are given for both the refined theory and the Timoshenko beam theory and are compared with the known solutions from the elastic theory and results by the finite element method. It is shown that the solutions of the refined theory coincide with those of the elastic theory; the solutions from the Timoshenko theory by using the two different displacement boundary conditions are the same; the refined theory by using the new boundary condition provides better results than using the conventional boundary condition and also better than those of the Timoshenko beam theory.     

Fracture surface evolution and apparent delamination toughness in split composite beam specimens subjected to mixed mode I–III loading

The influence of specimen twisting during global anti-plane shear loading in composite split beam specimens is studied. Tests were conducted on specimens with different thicknesses and delamination lengths to produce different amounts of specimen twisting prior to fracture. It is shown that specimen twisting causes mode I stresses to develop, thereby producing mixed mode I–III conditions along the delamination front. This causes near-tip transverse cracks to initiate, prior to delamination advance, at an orientation related to the mode mix. Unlike in homogeneous materials, transverse crack extension is accompanied by planar delamination advance, and transverse crack rotation during extension is restricted by the laminate’s fibers. The overall fracture surface evolution is therefore strongly controlled by specimen geometry. The influence of these findings on the apparent delamination toughness as obtained from composite split beam and other types of mode III tests is discussed.     

Vp×B electron linear accelerator with TE-wave assisted by plasma for beam stabilization

The V_p × B acceleration scheme with the use of a transverse electromagnetic wave is demonstrated experimentally, in which a pre-ionized plasma is supplemented for obtaining a stable electron beam. The slow wave structure employed here is a dielectric loaded waveguide, and an electron beam in the accelerator induces surfaces charges on the dielectric. The electron beam on account of acceleration also produces a dilute plasma to neutralize the surface charges. An initial energy gain of 2.5 keV for the electron beam is observed from an incident energy of 60 keV without any external vertical magnetic field. When an external vertical magnetic field of 1.5 G is applied under the same conditions for performing the V_p × B scheme, an additional 1.5 keV energy gain is observed.     

横向有限应变对部分浸入水中平面运动柔性梁的非线性振动响应的影响

基于Hamilton原理,根据克希霍夫假设以及拉格朗日函数,得到部分浸入水中柔性梁的大挠度条件下的运动方程和边界条件。在运动方程和边界条件的推导过程中,考虑了横向有限变形,并运用格林应变张量表示非零的应变张量分量。然后,应用中心差分法对方程进行数值处理,研究不同涡旋脱落荷载作用下,横向有限应变对结构振动响应的影响。结果表明,涡旋脱落荷载超过一定幅值后,横向有限应变的影响比较明显,不应忽略。     

热冲击作用下轴向运动梁的振动特性研究

研究了两端简支不可移、轴向运动梁在热冲击作用下的横向振动特性,根据Timoshenko梁理论和Hamilton原理建立了梁的横向振动控制方程,采用微分求积法求解了梁的横向振动问题,分析了热冲击和轴向运动效应对梁固有特性的影响。研究发现:热冲击引起的梁的等效热轴力、热弯矩和弹性模量变化三因素中,热轴力对梁固有频率的影响起主导作用,材料的弹性模量变化和热弯矩起次要作用;当热冲击载荷大于或等于梁的临界压力时,达到梁的第一阶失稳模态;热冲击和轴向运动效应都会降低梁的固有频率,它们的联合作用会导致模态之间的耦合现象,使梁更易达到失稳状态。     

Formulation of reference surface element and its applications in dynamic analysis of delaminated composite beams

This paper presents a new finite element formulation, referred to as reference surface element (RSE) model, for numerical prediction of dynamic behaviour of delaminated composite beams and plates using the finite element method. The RSE formulation can be readily incorporated into all elements based on the Timoshenko beam theory and the Reissner–Mindlin plate theory taking into account the transverse shear deformations. The ‘free model' and ‘constrained model' for dynamic analysis of delaminated composite beams and/or plates have been unified in this RSE formulation. The RSE formulation has been applied to an existing 2-node Timoshenko beam element taking into account the transverse shear deformations and the bending–extension coupling. Frequencies and vibration mode shapes are determined through solving an eigenvalue problem. Numerical results show that the present RSE model is reliable and practical when used to predict frequencies and mode shapes of delaminated composite beams. The RSE formulation has also been used to investigate the effects of the number, size and interfacial loci of delaminations on frequencies and mode shapes of composite beams.     

轴向运动粘弹性夹层梁热力耦合振动频率分析

研究了温度场与位移场相互耦合时,轴向运动粘弹性夹层梁的横向振动特性。基于Euler-Bernouli梁理论和Kelvin粘弹性材料本构关系,建立了轴向运动粘弹性夹层梁横向振动控制方程;考虑材料变形与传热的相互影响,得到相应的热力耦合状态下轴向运动粘性夹层梁的耦合控制方程。采用Galerkin截断得到相应的热力耦合动力系统。用数值方法分析了相关热参数对梁振动频率的影响。     

The effect of a low-energy high-current pulsed electron beam on surface layers of porous zirconium ceramics

The effect of a high-current pulsed electron beam of low-energy electrons on surface layers of porous zirconium ceramics has been studied. It is established that electron treatment leads to melting of the surface layer and its subsequent crystallization accompanied by the formation of a microstructure differing from the initial state. It is established that porosity decreases in the treatment region, the size of grains increases, and their shape changes. Grains are found to arrange themselves in the direction to the sample surface. Their linear sizes in the transverse and longitudinal directions are, respectively, 1.4 and 7 μm on average, i.e., differ significantly. It is shown that the surface layer modified by an electron beam is characterized by elevated microhardness as compared with the initial state.     

Transverse beam instability in a 50 GeV×50 GeV muon-collider ring

The transverse beam instability due to a broad-band impedance in a 50 GeV×50 GeV muon-collider ring is numerically investigated. It is shown that the transverse beam size is increased by a factor of five when the impedance, Z_||/n, is 1.7 Ω. The transverse instability is shown to be cured by introducing tune spreads, such as BNS damping, chromaticity, amplitude-dependent tune shift, and beam–beam interaction. It is shown that any one of these tune spreads limits the growth of the beam size to less than 20%.     

Peculiarities of the MBE growth of nanowhiskers on GaAs(100) substrates

We have studied the formation of nanowhiskers (NWs) by molecular beam epitaxy (MBE) on GaAs(100) substrates. The MBE growth of NWs exhibits two stages (initial and developed) and leads to the formation of NWs with surface morphology of two types (nucleation and intergrowth). The stage of developed growth is characterized by the predominant formation of intergrown NWs oriented in the 〈111〉B direction, having (110) habit (including the NW tip surface) and hexagonal cross sections with a transverse size within 50–300 nm. It was found that the transverse size of a hexagonal NW may significantly differ from that of an Au-GaAs melt droplet. The ratio of longitudinal and transverse dimensions of intergrown NWs can be on the order of 150 and above. When the transverse size of NWs exceeds a certain value (about 200 nm), the crystal length exhibits a slight decrease. The existence of two types of morphology is indicative of inhomogeneous character of the NW growth on a GaAs(100) surface, which depends on the catalyst droplet size, effective thickness of the deposited GaAs layer, and the growth temperature.     

Study of an Optical Device Used to Homogenize a Laser Beam. Application to Emissivity Measurements on Semitransparent Materials at High Temperature

On an experimental apparatus designed to measure the directional spectral emissivity of semitransparent materials at high temperature (2000°C), a specific optical device (kaleidoscope) is mounted in order to homogenize the energy distribution of a CO₂ laser beam, which is used as a heating source. An objective of this work, for operating in the best conditions, is to obtain a uniform temperature of the tested sample. This study, based on Fourier optics, focuses on a square aperture kaleidoscope. A model was developed to simulate the energy distribution of the laser beam, at any transverse plane on the optical path. The final objective is to simulate the energy distribution on the sample surface to optimize the homogenization device taking into account the surface temperature gradient induced by the local energy distribution. To validate this model, quantitative comparisons of theoretical simulations and experimental thermal spots are performed.     

Surface laser treatment of ductile irons

The effect of the laser surface treatment of three types of ductile iron (Grades 60-40-18, 80-55-06 and 100-70-03) was studied. Using a continuous CO₂ laser with a square 10 mm × 10 mm beam and uniform power density, the effect of beam scan rate at 2.5 and 5 kW power output was investigated. At each power rate, a range of scan rates was used to produce treatments with and without surface melting. The microstructure and hardness of the different zones of the treated material were analysed. It was found that layers of white iron of the same depth were produced in the three test irons when the operating conditions melted the surface material. Surface porosity can be eliminated by melting, although transverse cracks appeared on the surface with this treatment. Surface martensitic hardening produced a layer of uniform hardness only in the case of the grade 100-70-03 ductile iron with a perlitic matrix.     

Beam wander and M2-factor of partially coherent electromagnetic hollow Gaussian beam propagating through non-Kolmogorov turbulence

Propagation formulae for M²-factor and beam wander of partially coherent electromagnetic hollow Gaussian (PCEHG) beam in non-Kolmogorov turbulence are derived based on the extended Huygens–Fresnel principle and the second-order moments of the Wigner distribution function. Our results indicate that the normalized M²-factors of PCEHG beam with larger beam order, waist width, inner scale of turbulence, the generalized exponent parameter, and smaller transverse coherent widths, outer scale of turbulence, the generalized structure parameter are less affected by the turbulence. The root mean square beam wander and relative beam wander are more obvious for PCEHG beam with smaller beam order, larger inner and outer scales of turbulence, exponent parameter, transverse coherent widths, and the generalized structure parameter. What is more, the beam wander properties of PCEHG beam in non-Kolmogorov turbulence are very different from M²-factor and spreading properties of beam in turbulence.     

Crack identification in rotating shafts by coupled response measurements

In this paper a new method is applied in rotating cracked shafts to identify the depth and the location of a transverse surface crack. A local compliance matrix of different degrees of freedom is used to model the transverse crack in a shaft of circular cross section, based on available expressions of the stress intensity factors and the associated expressions for the strain energy release rates. It is known that when a crack exists in a structure, such as a beam, then the excitation in one-direction causes coupled vibrations in other directions. This property is used here to identify the crack. The shaft is modeled as a rotating Timoshenko beam including the gyroscopic effect and the axial vibration due to coupling. The method used here is based on the measurements of the axial vibration response due to different excitation frequencies and shaft revolutions. The figures presented are used to identify the crack.     

变截面压电层合梁自由振动分析

考虑压电材料的质量效应和刚度效应,将表面粘贴或埋入式压电悬臂梁看作变截面梁,研究压电材料对智能结构固有特性的影响。基于一阶剪切变形理论导出压电层合梁的抗弯刚度和横向剪切刚度,计及梁的剪切变形和转动惯量,采用Timoshenko理论推导变截面压电层合梁的频率方程。给出了T300/970压电层合梁和硬铝压电层合梁的前3阶固有频率,并和有限元结果、等截面梁的计算结果进行比较。计算表明,压电材料对压电结构固有频率和固有振型的影响显著,在以振动控制为目标的压电结构动力学建模过程中,有必要考虑压电材料的质量和刚度。     

Simulation of instabilities in the presence of beam feedback

The effect of longitudinal and transverse instabilities in electron storage rings is simulated by tracking many superparticles for many turns through a model of a machine lattice. This lattice model is defined by a series of machine elements such as RF stations (including longitudinal and transverse wake fields), beam pick-ups, feedback kicker magnets, etc. The machine elements may be interconnected in any specified way so as to produce for example feedback on the longitudinal or transverse beam motion. Each superparticle is treated in six-dimensional phase space and the effects of quantum excitation and radiation damping are included. Insofar as possible the program has been structured to allow study of all known single-beam effects (such as synchro-betatron resonances, transverse mode coupling etc.) in the presence or the absence of some form of beam feedback. The primary goal of the program was to study the effect of a reactive beam feedback system on the threshold for transverse mode coupling.     

A new FE model based on higher order zigzag theory for the analysis of laminated sandwich beam with soft core

A new finite element (FE) model has been developed based on higher order zigzag theory (HOZT) for the static analysis of laminated sandwich beam with soft core. In this theory, the in-plane displacement variation is considered to be cubic for both the face sheets and the core. The transverse displacement is assumed to vary quadratically within the core while it remains constant in the faces beyond the core. The proposed model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the beam. The nodal field variables are chosen in an efficient manner to overcome the problem of continuity requirement of the derivatives of transverse displacements. A C₀ quadratic beam finite element is implemented to model the HOZT for the present analysis. Numerical examples covering different features of laminated composite and sandwich beams are presented to illustrate the accuracy of the present model. Many new results are also presented which should be useful for future research.     

Best upper bounds on strain energy and surface displacements of an elastic body under boundary tractions

This work studies best upper bounds on strain energy and surface displacements of an elastic body under boundary tractions prescribed on its surface. It is found that two best bound constants, defined by two integral inequalities for strain energy and surface displacements, respectively, are equal and can be determined by an eigenvalue problem of linear elasticity characterized by spring-like elastic-boundary conditions with a negative spring constant. Explicit expressions for the best bound constants are derived for a circular body in plane strain and an elastic beam under transverse loading.