Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.

Half-integer Shapiro steps in MgB_(2) focused He ion beam Josephson junctions

Half-integer microwave induced steps(Shapiro steps)have been observed in many different Josephson junction systems,which have attracted a lot of attention because they signify the deviation of current phase relation(CPR)and uncover many unconventional physical properties.In this article,we first report the discovery of half-integer Shapiro steps in MgB_(2)focused He ion beam(He-FIB)Josephson junctions.The half-integer steps'dependence on microwave frequency,temperature,microwave power,and magnetic field is also analyzed.We find that the existence of half-integer steps can be controlled by the magnetic field periodically,which is similar to that of high temperature superconductor(HTS)grain boundary junctions,and the similarity of the microstructures between gain boundary junctions and He-FIB junctions is discussed.As a consequence,we mainly attribute the physical origin of half-integer steps in MgB_(2)He-FIB junctions to the model that a He-FIB junction is analogous to a parallel junctions'array.Our results show that He-FIB technology is a promising platform for researching CPR in junctions made of different superconductors.

Dynamic Response of Stepped Beams Under Impulsive Loading

Aim To analyze dynamic failure of aerospace strutures subjected lateral impulsive loading. Methods Structures were modeled as rigid-perfectly plastic free-free stepped beams. Basic equations of motion un set up for analysis. Results Final pat deformation and rigid motion solutions were determined for a uniform impulsive loading. The critical rupture conditions for a space shuttle and a missile were obtained. Conclusion Failure is possible for aerospace structures under a uniform impulsive loading, but it is mere difficult in space.

Three-to-one internal resonance in multiple stepped beam systems

In this study, the vibrations of multiple stepped beams with cubic nonlinearities are considered. A three-to-one internal resonance case is investigated for the system. A general approximate solution to the problem is found using the method of multiple scales （a perturbation technique）. The modulation equations of the amplitudes and the phases are derived for two modes. These equations are utilized to determine steady state solutions and their stabilities. It is assumed that the external forcing frequency is close to the lower frequency. For the numeric part of the study, the three-to-one ratio in natural frequencies is investigated. These values are observed to be between the first and second natural frequencies in the cases of the clamped-clamped and clamped-pinned supports, and between the second and third natural frequencies in the case of the pinned-pinned support. Finally, a numeric algorithm is used to solve the three-to-one internal resonance. The first mode is externally excited for the clamped-clamped and clamped-pinned supports, and the second mode is externally excited for the pinned-pinned support. Then, the amplitudes of the first and second modes are investigated when the first mode is externally excited. The amplitudes of the second and third modes are investigated when the second mode is externally excited. The force-response, damping-response, and .frequency- response curves are plotted for the internal resonance modes of vibrations. The stability analysis is carried out for these plots.

Thermal-induced snap-through buckling of simply-supported functionally graded beams

The instability of functionally graded material(FGM)structures is one of the major threats to their service safety in engineering applications.This paper aims to clarify a long-standing controversy on the thermal instability type of simply-supported FGM beams.First,based on the Euler-Bernoulli beam theory and von K′arm′an geometric nonlinearity,a nonlinear governing equation of simply-supported FGM beams under uniform thermal loads by Zhang’s two-variable method is formulated.Second,an approximate analytic solution to the nonlinear integro-differential boundary value problem under a thermal-induced inhomogeneous force boundary condition is obtained by using a semiinverse method when the coordinate axis is relocated to the bending axis(physical neutral plane),and then the analytical predictions are verified by the differential quadrature method(DQM).Finally,based on the free energy theorem,it is revealed that the symmetry breaking caused by the material inhomogeneity can make the simply-supported FGM beam under uniform thermal loads occur snap-through postbuckling only in odd modes;furthermore,the nonlinear critical load of thermal buckling varies non-monotonically with the functional gradient index due to the stretching-bending coupling effect.These results are expected to provide new ideas and references for the design and regulation of FGM structures.

STABILITY AND LOCAL BIFURCATION IN A SIMPLY-SUPPORTED BEAM CARRYING A MOVING MASS

The stability and local bifurcation of a simply-supported flexible beam （Bernoulli- Euler type） carrying a moving mass and subjected to harmonic axial excitation are investigated. In the theoretical analysis, the partial differential equation of motion with the fifth-order nonlinear term is solved using the method of multiple scales （a perturbation technique）. The stability and local bifurcation of the beam are analyzed for 1/2 sub harmonic resonance. The results show that some of the parameters, especially the velocity of moving mass and external excitation, affect the local bifurcation significantly. Therefore, these parameters play important roles in the system stability.

Evaluation of Atomic Correlation Functions for Stepped Inhomogeneous Surfaces

The atomic correlation functions of inhomogeneities are exactly evaluated for three-level stepped inhomogeneous surfaces with three sorts of randomly distributed domains.An analytical expression is derived for the intensity of the diffraction electron beam.It is shown that for this surface the diffraction spot is split into a central spike and a diffused profile,which consists of three kinds of Lorentzian-like broadenings produced by both the steps and inhomogeneities.

On the Innovation,Design,Construction,and Experiments of OMEGA-Based SSPS Prototype:The Sun-Chasing Project

This study systematically introduces the development of the world’s first full-link and full-system ground demonstration and verification system for the OMEGA space solar power satellite(SSPS).First,the OMEGA 2.0 innovation design was proposed.Second,field-coupling theoretical models of sunlight concentration,photoelectric conversion,and transmitting antennas were established,and a systematic optimization design method was proposed.Third,a beam waveform optimization methodology considering both a high beam collection efficiency and a circular stepped beam shape was proposed.Fourth,a control strategy was developed to control the condenser pointing toward the sun while maintaining the transmitting antenna toward the rectenna.Fifth,a high-efficiency heat radiator design method based on bionics and topology optimization was proposed.Sixth,a method for improving the rectenna array’s reception,rectification,and direct current(DC)power synthesis efficiencies is presented.Seventh,high-precision measurement technology for high-accuracy beam-pointing control was developed.Eighth,a smart mechanical structure was designed and developed.Finally,the developed SSPS ground demonstration and verification system has the capacity for sun tracking,a high concentration ratio,photoelectric conversion,microwave conversion and emission,microwave reception,and rectification,and thus satisfactory results were obtained.

强杂波背景下调频步进DBS技术研究

针对强地物杂波背景下弹载雷达目标检测与识别的技术难题,提出将高分辨距离像(high resolution range profile,HRRP)技术和多普勒波束锐化技术联合对地面进行二维高分辨成像,提高雷达在杂波下目标检测与识别的性能。该方法以线性调频步进频(linear frequency modulation stepped frequency,LFM-SF)信号为基本波形,首先对平台速度产生的多普勒效应等问题进行了详细讨论并校正;然后通过距离像抽取获得各帧对应的HRRP序列,并采用方位快速傅里叶变换(fast Fourier transform,FFT)实现方位高分辨;最后对实际飞行状态下平台造成的误差进行运动补偿,完成对波束内区域的二维分辨。实测数据的处理验证了所提算法的有效性与实用性。

CFRP砂轮高速外圆磨削稳定性分析

为分析不同影响因素对CFRP砂轮高速外圆磨削稳定性的影响,采用铁木辛柯梁理论对具有阶梯特征的工件进行动力学分析,结合锤击试验测得砂轮动态特性,对高速磨削过程中的砂轮-工件两自由度系统进行了磨削稳定性分析。在对阶梯工件进行动力学分析的过程中,发现阶梯特征对于动态特性的影响较小,误差小于2%。在稳定性分析中发现,不同的砂轮转速和不同的工件磨削位置均会影响磨削稳定性。磨削位置越靠近工件中心,工件刚度越弱,磨削稳定性降低易诱发颤振;而在靠近顶尖支撑的位置,由于工件刚度增强,该位置的磨削稳定性将同时受到工件和砂轮的动力学性能的影响。通过磨削试验验证了分析方法的有效性,试验结果表明,工件磨削位置的刚度差异将会影响加工表面质量,由磨削失稳导致的粗糙度增幅可达51.6%。

浅埋深大采高工作面矿压显现规律研究

以三道沟煤矿85214工作面为工程背景,对浅埋深大采高工作面矿井的矿压显现规律进行研究,利用理论分析的方法,建立固支梁和悬臂梁模型,确定工作面初次来压步距和周期来压步距分别为104.91和19.90 m。基于覆岩浅埋结构性质,建立短砌体梁和台阶岩梁模型,确定支护阻力分别为5 624和14 461 kN;利用现场试验的方法,对井下支架工作阻力数据实测分析,确定工作面初次来压步距106 m,周期来压步距16.8 m,月平均次数11次,平均支架载荷37.5 MPa,支承压力主要分布于工作面中部区域。研究结果证明了来压步距模型的合理性和有效性,并确定了浅埋深条件下覆岩结构呈现短砌体梁结构和台阶岩梁结构的破断特点,可为矿井生产提供依据。

深井工作面矿压显现规律模拟研究

为确定古城煤矿S1306工作面初次来压步距、周期来压步距和支架选型的合理性,本文通过理论分析、数值模拟等方法进行工作面矿压规律研究,基于组合梁理论,计算确定古城煤矿S1306工作面初次来压步距44.03 m,周期来压步距15.75 m,与实测值相符,利用数值模拟进行工作面不同推进范围下的塑性区、垂直应力和位移的模拟,确定工作面老顶初次垮落步距为46~49 m,周期来压步距为11~13 m,与实测值较吻合,且工作面支架阻力符合工作面生产要求。

基于二次摄动法的SMA层合梁非线性自由振动分析

为对SMA(形状记忆合金)层合梁的非线性自由振动进行分析,使用Brison一维本构模型描述SMA的力学特性,基于不同剪切函数和Von Karman大变形理论,建立梁质点位移与应变之间的关系,使用Hamilton变分原理,获得在弹性地基上两端简支SMA层合梁的动力学方程并进行无量纲处理。使用二次摄动法获得SMA层合梁的非线性自由振动方程。研究不同SMA体积分数、预应变、SMA铺设角度、温度变化对非线性振动的影响。

山区公路大纵坡小半径曲线路基梁场的提梁及移梁技术

在山势陡峭、地势曲折的山岭地区建造预制梁场进而提梁、移梁施工,需要克服大坡度高差、小半径曲线的地形困难。通过对场地进行变化坡度处置、提梁门式起重机的技术改造,达到轨行式大型重载门式起重机在曲线叠加高差的轨道上安全平稳工作。本研究从北京市门头沟区国道109高速公路项目实例入手,对施工进行研究总结,为山区主线路基上建造预制梁场提梁移梁施工提供参考,具有一定的推广价值。

单桩基础施工中步进式伸缩梁系统的设计及应用

本文首先从现有单桩抱桩装备的抱桩系统中存在的问题出发,通过第一代步进式伸缩梁系统的设计,成功解决了推力油缸行程小的问题;其次,通过第二代步进式伸缩梁系统的设计,简化了第一代系统的构成,同时解决了推力油缸直接接触单桩的问题,从根本上解决了油缸可能损坏的问题,大大提升了系统可靠性;最后,将步进式伸缩梁系统成功应用在实际工程中,进一步验证了设计的可靠性。

基于STEP 7的步进式加热炉炉温控制系统

对步进式加热炉炉温控制系统创建了一个自动化解决方案,使加热炉炉温燃烧控制实现全自动操作,并保证加热炉正常连续运行。同时介绍了脉冲式燃烧控制技术原理在本系统中的应用特点,介绍了STEP 7和WinCC V6.0软件开发环境向用户提供操作方便、界面友好的自动化开发平台。

浅埋近距离煤层群工作面支架选型技术研究

为了确保浅埋近距离煤层群工作面的安全高效开采,以陕西神木矿区锟源煤矿近距离2-2煤采空区下,3-1煤工作面开采作为工程背景,采用理论分析、数值模拟和相似模拟的研究方法,分析近距离煤层上层煤开采后,下分层3-1煤工作面开采时工作面支架的合理支护强度。理论计算工作面支架支护强度为0.695 MPa,数值模拟3-1煤工作面支架支护强度为0.4~0.77 MPa,相似模拟3-1煤工作面支架支护强度为0.45~0.78 MPa,该工作面工作阻力大于7 435 kN,与现场实测数据相吻合。由此表明,现有支架选型不满足支护要求,选用支护阻力为8 200 kN的液压支架可满足工作面支护要求。该研究补充了在浅埋近距离煤层群开采情况下工作面支架选项技术研究,为神木地区浅埋近距离煤层群的安全高效回采提供了理论依据。

深圳某超高层结构设计重点及难点分析

深圳某超B级高度的超高层塔楼,采用钢管混凝土框架柱+钢筋混凝土框架梁+钢筋混凝土核心筒结构。塔楼相对于裙房部分有较大的偏心,同时因为建筑功能要求存在有多处跃层透空空间。采用盈建科、ETABS等软件对项目进行了整体计算、构件设计及楼板应力分析。针对塔楼偏置、楼板不连续、核心筒收进等不规则项,对于结构构件采取适当的构造加强,以满足抗震性能目标。对于外框梁不闭合的问题,采取对比分析,确保水平地震剪力可有效传递。结果表明,项目结构体系选择恰当,结构布置、构件截面取值合理,具有良好的抗震性能。

高速公路软基路堤改扩建若干问题与建议

基于大量高速公路改扩建工程实践,对软基路堤改扩建的若干问题给出建议。水塘路段不能在塘底进行地基处理施工时宜采用搅拌桩,采用刚性桩时宜按桩承堤设计。既有边坡下软基处理工作面宜采用削陡边坡或钢板桩支护等方式形成。拼宽路堤沿其与既有路堤的界面滑动稳定性满足要求时,可不设置台阶。普通土拼宽路堤台阶壁宜倾斜、平台宜水平或轻微外倾。竖壁台阶高度大于44cm时会在台阶壁附近形成虚土区,需利用液压夯实或冲击碾压等对虚土进行压实,台阶高度大于2m时可利用注浆将虚土胶结。轻质土拼宽路堤不应用作挡土墙,应设置易于施工的排水设施,以避免轻质土拼宽路堤后面积水。轻质土拼宽路堤滑动稳定分析时,应只考虑斜坡范围内的交通荷载。除长螺旋桩机施工的钻孔桩外,其他桩帽之间不必设置连梁。

Purification and Properties of a New L-Sorbose Dehydrogenase Accelerative Protein from Bacillus megaterium Bred by Ion-Beam Implantation

Bacillus megaterium BM302 bred by ion-beam implantation produces L-sorbose dehydrogenase accelerative protein （SAP） to accelerate the activity of L-sorbose dehydrogenase （SDH） of Gluconobacter oxydans in the 2-keto-L-gulonic acid （2KLG） fermentation from L-sorbose by the mixed culture of B. megaterium BM302 and G. oxydans. The SAP purified by three chromatographic steps gave 35-fold purification with a yield of 13% and a specific activity of 5.21 units/mg protein. The molecular weight of the purified SAP was about 58 kDa. The SDH accelerative activity of SAP at pH 7 and 50℃ was the highest. Additionally, it retained 60% activity at a pH range of 6.5 ～ 10 and was stable at 20℃ ～ 60℃. After 0.32-unit SAP was added to the single cultured G. oxydans strains, the SDH activity was apparently accelerated and the 2KLG yield of GO29, GO112, GO and GI13 was enhanced 2.1, 3.3, 3.5 and 2.9 folds respectively over that of the strains without the addition of SAP.