Free vibration analysis of a rotating hub–functionally graded material beam system with the dynamic stiffening effect

A comprehensive dynamic model of a rotating hub–functionally graded material (FGM) beam system is developed based on a rigid–flexible coupled dynamics theory to study its free vibration characteristics. The rigid–flexible coupled dynamic equations of the system are derived using the method of assumed modes and Lagrange's equations of the second kind. The dynamic stiffening effect of the rotating hub–FGM beam system is captured by a second-order coupling term that represents longitudinal shrinking of the beam caused by the transverse displacement. The natural frequencies and mode shapes of the system with the chordwise bending and stretching (B–S) coupling effect are calculated and compared with those with the coupling effect neglected. When the B–S coupling effect is included, interesting frequency veering and mode shift phenomena are observed. A two-mode model is introduced to accurately predict the most obvious frequency veering behavior between two adjacent modes associated with a chordwise bending and a stretching mode. The critical veering angular velocities of the FGM beam that are analytically determined from the two-mode model are in excellent agreement with those from the comprehensive dynamic model. The effects of material inhomogeneity and graded properties of FGM beams on their dynamic characteristics are investigated. The comprehensive dynamic model developed here can be used in graded material design of FGM beams for achieving specified dynamic characteristics.     

Surface defect linear modes in one-dimensional photonic lattices

We report on the existence of surface defect linear modes at an interface between the defect of one-dimensional photonic lattices and the uniform media. The interface defect can significantly affect the properties of linear modes. Such new type of modes exists in the first bandgap for positive defects; while they exist in the second bandgap for negative defects. Particularly, when a Gaussian beam, which is similar to the linear mode, is launched at the defect site, we find that the Gaussian beam can be strongly confined at defect site and robustness along longitudinal direction for a long distance. When launched at a small angle into the defect site, the Gaussian beam exhibits stable snake propagation.     

Mathematical model of the dynamics of micropolar elastic thin beams. Free and forced vibrations

A method of hypotheses has been developed to construct a mathematical model of micropolar elastic thin beams. The method is based on the asymptotic properties of the solution ofan initial boundary value problem in a thin rectangle within the micropolar theory of elasticity with independent displacement and rotation fields. An applied model of the dynamics of micropolar elastic thin beams was constructed in which transverse shear strains and related strains are taken into account. The constructed dynamics model was used to solve problems of free and forced vibrations of a micropolar beam. Free vibration frequencies and modes, forced vibration amplitudes, and resonance conditions were determined. The obtained numerical calculation results show the specific features of free vibrations of thin beams. Micropolar thin beams have a free vibration frequency which is almost independent of the thin beam size, but depends only on the physical and inertial properties of the micropolar material. It is shown for the micropolar material that the free vibration frequency values of beams can be readily adjusted and hence a large vibration frequency separation can be achieved, which is important for studying resonance.     

The symmetry properties of stable polynomial Gaussian beam profiles

We consider the symmetry properties of polynomial Gaussian beam profiles (intensity distributions) that remain stable during propagation, apart from being scaled and possibly rotated. These beams are expressed as special linear combinations of the Laguerre-Gaussian modes. Two kinds of symmetries are present: discreet rotational symmetries and mirror symmetries. The symmetry properties are shown to depend on the particular subset of Laguerre-Gaussian modes that is used to construct the stable beam. We demonstrate the symmetry properties of a few examples of stable beams through numerical simulations.     

HOMs simulation and measurement results of IHEP02 cavity

In accelerator RF cavities, there exists not only the fundamental mode which is used to accelerate the beam, but also higher order modes(HOMs). The higher order modes excited by the beam can seriously affect beam quality, especially for the higher R/Q modes. 1.3 GHz low-loss 9-cell superconducting cavity as a candidate for ILC high gradient cavity, the properties of higher order mode has not been studied carefully. IHEP based on existing low loss cavity, designed and developed a large grain size 1.3 GHz low-loss 9-cell superconducting cavity(IHEP02cavity). The higher order mode coupler of IHEP02 used TESLA coupler's design. As a result of the limitation of the mechanical design, the distance between higher order mode coupler and end cell is larger than TESLA cavity.This paper reports on measured results of higher order modes in the IHEP02 1.3 GHz low-loss 9-cell superconducting cavity. Using different methods, Q e of the dangerous modes passbands have been obtained. The results are compared with TESLA cavity results. R/Q of the first three passbands have also been obtained by simulation and compared with the results of the TESLA cavity.     

Bending analysis of a functionally graded piezoelectric cantilever beam

A new analysis based on Airy stress function method is presented for a functionally graded piezoelectric material cantilever beam. Assuming that the mechanical and electric properties of the material have the same variations along the thickness direction, a two-dimensional plane elasticity solution is obtained for the coupling electroelastic fields of the beam under different loadings. This solution will be useful in analyzing FGPM beam with arbitrary variations of material properties. The influences of the functionally graded material properties on the structural response of the beam subjected to different loads are also studied through numerical examples.     

Z-扫描技术的灵敏度分析

单光束激光Z-扫描技术是利用光束的横向特性来研究材料的光学非线性的,其灵敏度的提高有助于测量微弱折射率变化。从入射光束、调制方式、光束检测等方面论述了Z-扫描技术的灵敏度。顶环光束入射相对于标准Z-扫描技术的高斯光束入射其灵敏度可提高2.5倍,但要求光源的输出能量达到一定值,仅适用于测定较小的非线性相移;在光路中插入调制元件后放大因子可达到780,但调节光路难以调节焦移效应。利用CCD作为探测器的TPDZ-扫描技术能够测量小于λ/15000的非线性相位畸变,CCD能够充分获得光束的横向信息,有望成为另一种测量光学非线性的常用方法。     

NEW ADMISSIBLE FUNCTIONS FOR THE DYNAMIC ANALYSIS OF A SLEWING FLEXIBLE BEAM

An important question associated with the modelling of a slewing beam is the discretization of a continuous elastic beam. If discretization is performed by the assumed mode method, the question arises about the type of admissible functions to be used in series expansions. In this regard, the eigenfunctions of a non-rotating clamped–free uniform beam known as cantilever modes have been widely used as admissible functions for the dynamic analysis of the slewing beam. The discretization will be sufficient provided that the set of admissible functions is complete and a sufficiently large number of functions is used. However, there are cases that we need to approximate the model with a small number of admissible functions. Examples are numerical simulation and control design. In this paper, new admissible functions which approximate the dynamic characteristics of the slewing beam more accurately than the eigenfunctions of the non-rotating clamped–free uniform beam is developed and its efficiency is verified by numerical examples.     

Single shot spatial and temporal coherence properties of the SLAC Linac Coherent Light Source in the hard x-ray regime

We measured the transverse and longitudinal coherence properties of the Linac Coherent Light Source (LCLS) at SLAC in the hard x-ray regime at 9 keV photon energy on a single shot basis. Speckle patterns recorded in the forward direction from colloidal nanoparticles yielded the transverse coherence properties of the focused LCLS beam. Speckle patterns from a gold nanopowder recorded with atomic resolution allowed us to measure the shot-to-shot variations of the spectral properties of the x-ray beam. The focused beam is in the transverse direction fully coherent with a mode number close to 1. The average number of longitudinal modes behind the Si(111) monochromator is about 14.5 and the average coherence time τ(c)=(2.0±1.0) fc. The data suggest a mean x-ray pulse duration of (29±14) fs behind the monochromator for (100±14) fc electron pulses.     

左手材料平板对傍轴高斯光束聚焦特性分析

在傍轴近似下,推导出了左手材料平板聚焦系统的传输矩阵,并利用ABCD定律得到了高斯光束在左手材料中和经过平板透镜聚焦后的传输公式。高斯光束在左手材料内部和像空间的传输公式的研究表明:像高斯光束和物高斯光束束腰大小一致,即左手材料平板透镜实际上对高斯光束没有聚焦作用。研究同时表明左手材料平板对高斯光束的聚焦与几何光学成像规律完全一致,而不存在一般透镜聚焦时的焦移效应。     

衍射光学元件改善激光谐振腔输出特性的研究

运用矩阵本征值方法,对用位相型二元光学元件构成的激光谐振腔进行了数值计算,重点分析了圆形反射镜腔在不同菲涅耳数条件下的模结构参量特性.结果表明,这种谐振腔可以有效地提高基模与高阶模的模式分离度,并且可以根据需要,定制出理想的输出光束 关键词： 模式分离 衍射光学元件 激光谐振腔 矩阵本征值     

Plasma circular cylindrical waveguide in lossy material

The surface modes in the plasma circular cylindrical waveguide in a lossy material are analyzed, particularly for the variations of their propagation properties with plasma parameters and surrounding material. The characteristic equations of surface modes are derived, and their relevant approximate solutions are given. The limit results of this paper are consistent with that given in literature’s. The analysis show that it can be used to improve the properties of mode suppressors and fabricat cut-off attenuators.     

Plasmonic modes in periodic metal nanoparticle chains: a direct dynamic eigenmode analysis

We demonstrate an efficient eigendecomposition method for analyzing the guided modes in metal nanoparticle chains. The proposed method has the advantage of simultaneously showing the dispersion relation and the mode quality. It can also separate the material properties from the geometrical properties. Its efficiency therefore does not depend on the complexity of the material polarizability. We used the method to analyze the guided modes of a single and a pair of metal nanoparticle chains. The rigorous dynamic dipole polarizability typically gives a redshift compared with the results obtained from the broadly used quasi-static dipole polarizability with radiation correction.     

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.     

Optical properties of metamaterial-based devices modulated by a liquid crystal

Due to the fact that it is possible to manipulate light with photonic crystals (PCs), PCs hold a great potential for designing new optical devices. There has been an increase in research on tuning the optical properties of PCs to design devices. We presented a numerical study of optical properties of metamaterial-based devices by liquid crystal infiltration. The plane wave expansion method and finite-difference time-domain method for both TE and TM modes revealed optical properties in photonic crystal structures in an air background for a square lattice. E7 type has been used as a nematic liquid crystal and SrTiO₃ as a ferroelectric material. We showed the possibility of the metamaterials for a two-dimensional photonic crystal cavity on a ferroelectric base infiltrated with a nematic liquid crystal.     

Application of aluminum and titanium foils in low-energy wide-aperture electron accelerators

We have reported on the results of theoretical and experimental investigations of characteristics of aluminum and titanium foils used in devices to extract electron beams from wide-aperture low-energy accelerators with a high current density. The mechanical properties of foils at different temperatures and the electron beam transmission and absorption coefficients have been compared. The results of analyzing the dependences of the efficiency of the electron beam extraction from accelerators on the type of the electron–optical system, material, and thickness of the foil for various sizes of extraction windows and the same type of the slot support grids have been presented. We have proposed an analytic model for calculating the temperature of the foil in the unit cell of the support grid. The electron transmittance and absorbance, as well as the temperature regimes of the foils, have been calculated using different methods.     

Grazing diffraction of X-ray radiation in a planar single-crystal waveguide

The propagation of an X-ray beam through a plane-parallel waveguide is studied with allowance for Bragg grazing diffraction on the crystalline structure of the plates. Expressions for the waveguide modes are obtained and nondecaying waveguide modes are shown to exist at angles that are larger than the critical one (the angle of total external reflection), which permits one to increase the capture angle of radiation incident on the waveguide. The calculated intensity at the waveguide output is compared with the intensity of waveguide modes in the absence of grazing diffraction in the waveguide material.     

特定折射率材料及光学薄膜制备

根据太阳电池阵激光防护膜性能优化的需要,应用离子辅助电子束双源共蒸工艺方法制备了优化设计所需的特定折射率的薄膜材料并用于制备激光防护膜。测试结果显示:用该工艺方法制备的掺杂材料薄膜的折射率n=1.75,与优化设计所需数值相符;激光防护膜性能优良,太阳辐射能透过率提高6%以上,实现了对该激光防护膜性能的进一步优化。为了使该双源共蒸方法适于大面积薄膜的制备,应用均匀性挡板技术来提高该方法制备大面积薄膜的膜厚均匀性,使制备的掺杂材料薄膜在口径为400 mm时的不均匀性小于2.1%。该双源共蒸方法制备工艺简单、可靠,适于实际工程应用。薄膜性能测试结果与理论优化结果相符,达到预期优化目标。