Convergence of Galerkin truncation for dynamic response of finite beams on nonlinear foundations under a moving load

The present paper investigates the convergence of the Galerkin method for the dynamic response of an elastic beam resting on a nonlinear foundation with viscous damping subjected to a moving concentrated load. It also studies the effect of different boundary conditions and span length on the convergence and dynamic response. A train–track or vehicle–pavement system is modeled as a force moving along a finite length Euler–Bernoulli beam on a nonlinear foundation. Nonlinear foundation is assumed to be cubic. The Galerkin method is utilized in order to discretize the nonlinear partial differential governing equation of the forced vibration. The dynamic response of the beam is obtained via the fourth-order Runge–Kutta method. Three types of the conventional boundary conditions are investigated. The railway tracks on stiff soil foundation running the train and the asphalt pavement on soft soil foundation moving the vehicle are treated as examples. The dependence of the convergence of the Galerkin method on boundary conditions, span length and other system parameters are studied.     

A finite element model using multi-layered shell element in laser forming

Due to its enormously high flexibility laser forming has been gaining importance in recent years. This rapidness and flexibility demand very precise controlling strategies especially when simulating the process of large plates and challenging the limited computation power of the current workstation. A simple, robust and accurate modeling method of laser forming has been demonstrated to solve this problem. The simplified model is meshed by multi-layered shell element, simulated with a more real scanning method and fewer parameters. The intelligent meshing strategies have reduced the number of elements dramatically. Thus the simulation efficiency has been improved significantly. By comparing the simulation results under the simplified model with the results under the traditional model for laser forming, the applicability of proposed method has been proven. The method of these simplified models is also suitable to simulate complex finite element models, which take much time to simulate. It would throw some light on the thermal mechanically coupled-field simulation of large sheet.     

Equation of state and elastic properties of ACrO3 (A=Pb,Ca, Sr and Ba) perovskites under high pressure

We employ the spin-polarized generalized gradient approximation within the density functional theory to investigate the equation of state, magnetism and elastic constant of cubic ACrO₃ (A=Pb, Ca, Sr, and Ba) perovskite. The antiferromagnetic phase is the most stable state at zero pressure. Under pressure, the ferromagnetic state will transform to the non-magnetic state. Considering the effect of magnetism, the equilibrium lattice constant, the bulk modulus and the high pressure equations of state agree well with the available experiments. By using the energy-strain method, the predicted elastic properties are satisfactory.     

A 168-W high-power single-frequency amplifier in an all-fiber configuration

We present a high-power,single-frequency,narrow linewidth fiber amplifier based on master oscillator power amplification chains in an all-fiber configuration.The effect of the delivery fiber on the maximum output power is studied.A home-made 1064-nm seed laser with a 20-kHz linewidth is boosted to 129 W,and limited by stimulated Brillouin scattering(SBS) when the delivery fiber is 1.2 m long.By shortening the delivery fiber length to 0.7 m,the SBS threshold is increased efficiently and the maximum output power rises to 168 W with an 82.9% power conversion efficiency.The experimental results indicate that the output power can be further raised by shortening the delivery fiber length and increasing the pump power.     

A density-functional theory investigation on desorption of O2 on Sn（111） and its comparison with initial oxidation on the X（111） （X=Si,Ge, Sn,Pb） surfaces

<正>The first-principles calculations are performed to investigate the adsorption of O₂ molecules on an Sn（111） 2×2 surface.The chemisorbed adsorption precursor states for O₂ are identified to be along the parallel and vertical channels, and the surface reconstructions of Sn（lll） induced by oxygen adsorption are studied.Based on this,the adsorption behaviours of O₂ on X（111）（X=Si,Ge,Sn,Pb） surfaces are analysed,and the most stable adsorption channels of O₂ on X（111）（X=Si,Ge,Sn,Pb） are identified.The surface reconstructions and electron distributions along the most stable adsorption channels are discussed and compared.The results show that the O₂ adsorption ability declines gradually and the amount of charge transferred decreases with the enhancement of metallicity.     

Correspondence between quantum-optical transform and classical-optical transform explored by developing Dirac’s symbolic method

By virtue of the new technique of performing integration over Dirac’s ket–bra operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel–Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel operator (GFO) to correspond to the generalized Fresnel transform (GFT) in classical optics. We derive GFO’s normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used. All these have confirmed Dirac’s assertion: “...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory”.     

基于天文观测的相机标定及姿态测量技术研究

为利用相机进行天文观测以实现高精度的相机姿态测量,必须先对相机参数进行精确标定。针对传统相机标定方法工作距离有限的问题,提出了以恒星为控制点的相机标定方法,根据球面天文学方法计算观测时刻控制点的世界坐标,利用摄像测量原理建立了恒星观测模型,求解相机的内外参数并分析了误差因素。实验结果表明,该标定方法在不依赖于精密、复杂的外部设备情况下可达到较高精度,并具有较强的抗噪声能力。将标定结果用于天文观测并求解相机姿态,航向角和俯仰角的解算重复性优于10″,能够满足高精度姿态测量的需求。该方法可进一步推广应用于星敏感器的标定。     

准相位型光子筛设计

提出了一种准相位型光子筛。该准相位型光子筛通过改变暗环上小孔直径与带宽的比值,对焦点处的相位分布进行调制,使通过亮环和暗环上小孔的光波在焦点处发生相长干涉,生成聚焦光斑。该准相位型光子筛无需对基底进行特殊处理,即可完成相位型光子筛的制作,降低了加工难度。和普通振幅型光子筛相比,在相同最小加工尺寸的条件下,准相位型光子筛具有较大的数值孔径,可降低聚焦光斑尺寸。并且,和多区光子筛相比,在同样的最小加工尺寸及数值孔径的条件下,准相位型光子筛光斑尺寸及质量均优于对方。为大数值孔径光子筛设计提供了一种新的设计方法。     

0.4 THz回旋行波管的设计与模拟

利用三维粒子模拟仿真软件,对共焦波导结构的0.4 THz回旋行波管进行了注波互作用的模拟研究。以共焦波导的冷腔色散以及衍射损耗入手,最终选定HE06模作为互作用工作模式。为了对寄生振荡进行抑制,在互作用结构中引入了截断。在模拟过程中,通过调节束压、束流、工作磁场、电子束横纵速度比,得到了最优的工作参数。最终,在束压34 kV、磁场14.25、束流2 A、横纵速度比0.75的工作参数下,当输入信号为1 W时,得到了最高2.76 kW的功率输出,增益超过34 dB,3 dB带宽为8 GHz,效率达到4%。     

Spectroscopic properties of thulium ions in bismuth silicate glass

A new type of bismuth silicate glass (Bi2O3-SiO2-ZnO-Al2O3-La2O3) doped with Tm2O3 is prepared by melt-quenching method. The thermal stability of the glass is examined by differential scanning calorimetry. No crystallization peak is found. Using the absorption and emission spectra, the absorption and emission cross-sections are calculated. Their maximum data are 2.9×10-21cm2 at 1663 nm and 4.7×10-21cm2 at 1826 nm, respectively. Using the Judd-Ofelt theory, the radiation transition probabilities and radiative lifetimes are obtained. The extended overlap integral method is applied to analyze energy transfer process among the Tm3+ ions. The transfer constants of cross-relaxation and energy migration among the Tm3+ ions at the 3H4 level are 7.60×10-40 and 14.98×10-40 cm6 /s, respectively. The critical transfer radius for cross-relaxation is 0.99 nm. The cross relaxation process is easy to realize and is favorable for obtaining ～2-μm laser.