Transverse free vibration analysis of a tapered Timoshenko beam on visco-Pasternak foundations using the interpolating matrix method

The characteristics of transverse free vibration of a tapered Timoshenko beam under an axially conservative compression resting on visco-Pasternak foundations are investigated by the interpolating matrix method. The research is executed in view of a three-parameter foundation which includes the eff ects of the Winkler coeffi cient, Pasternak coeffi cient and damping coeffi cient of the elastic medium. The governing equations of free vibration of a non-prismatic Timoshenko beam under an axially conservative force resting on visco-Pasternak foundations are transformed into ordinary diff erential equations with variable coeffi cients in light of the bending rotation angle and transverse displacement. All the natural frequencies orders together with the corresponding mode shapes of the beam are calculated at the same time, and a good convergence and accuracy of the proposed method is verifi ed through two numerical examples. The infl uences of foundation mechanical characteristics together with rotary inertia and shear deformation on natural frequencies of the beam with diff erent taper ratios are analyzed. A comprehensive parametric numerical study is carried out emphasizing the primary parameters that describe the dynamic property of the beam.

Method of reverberation ray matrix for static analysis of planar framed structures composed of anisotropic Timoshenko beam members

Based on the method of reverberation ray matrix（MRRM）, a reverberation matrix for planar framed structures composed of anisotropic Timoshenko（T） beam members containing completely hinged joints is developed for static analysis of such structures.In the MRRM for dynamic analysis, amplitudes of arriving and departing waves for joints are chosen as unknown quantities. However, for the present case of static analysis, displacements and rotational angles at the ends of each beam member are directly considered as unknown quantities. The expressions for stiffness matrices for anisotropic beam members are developed. A corresponding reverberation matrix is derived analytically for exact and unified determination on the displacements and internal forces at both ends of each member and arbitrary cross sectional locations in the structure. Numerical examples are given and compared with the finite element method（FEM） results to validate the present model. The characteristic parameter analysis is performed to demonstrate accuracy of the present model with the T beam theory in contrast with errors in the usual model based on the Euler-Bernoulli（EB） beam theory. The resulting reverberation matrix can be used for exact calculation of anisotropic framed structures as well as for parameter analysis of geometrical and material properties of the framed structures.

CRACK IDENTIFICATION IN STEPPED CANTILEVER BEAM COMBINING WAVELET ANALYSIS WITH TRANSFORM MATRIX

This paper illustrates the crack identification method combining wavelet analysis with transform matrix. Firstly, the fundamental vibration mode was applied to wavelet analysis. The crack location was found by the peaks of the wavelet coefficients. Secondly, based on the identified crack locations, a simple transform matrix method requiring only the first two tested natural frequencies was used to further identify the crack depth. The present method can be used for crack identification in a complex structure. Numerical results of crack identification of a stepped cantilever beam show that the suggested method is feasible.

Compact Multibeam Array with Miniaturized Butler Matrix for 5G Applications

This paper presents the design and implementation of a miniaturized beam steering network that produces broadside beams when it is fed with a compact antenna array.Butler Matrix(BM)was used as the beam steering network.It was completely built from a miniaturized 3 dB hybrid-couplers in planar microstrip technology.It was configured by feeding the BM with a Planar Inverted-E Antenna(PIEA)array separated at 0.3λas against the 0.5λseparation.This makes the BM produce a major radiation pattern at the broadside.Apart from the miniaturization,no modification was made from the BM side.However,employing effective mutual coupling reduction techniques helped to design the compact PIEA array.The validity of this BM based multibeam PIEA array was demonstrated by comparing the simulation results of the reflection coefficients,transmissions coefficients and the radiation pattern with measurements.The measurement results showed good agreement with simulations.

BEAM BROADENING SYNTHESIS FOR SAR ANTENNA ARRAY BASED ON PROJECTION MATRIX ALGORITHM

A new beam broadening synthesis technique for Synthetic Aperture Radar(SAR) antenna array, namely Projection Matrix Algorithm(PMA) is presented. The theory of PMA is introduced firstly, and then the iterative renewed manner is improved to resolve the unbalance problem under amplitude and phase control. In order to validate the algorithm correct and effective, an actual engineering application example is investigated. The beam synthesis results of 1.0~4.5 times broadening under the phase only control and the amplitude and phase control using improved PMA are given. The results show that the beam directivity, the beam broadening, and the side-lobe level requirements were met. It is demonstrated that the improved PMA was effective and feasible for SAR application.

Matrix beam LED智能光通量输出系统研究

分析一种前沿的Matrix beam发光二极管(LED)智能光通量输出系统,侧重于对现阶段汽车车灯的Matrix beam发光二极管的研究,可自由设置各发光二极管的电流参数,因此达到差异化光通量输出的目的,进而匹配于发光二极管车灯造型及配光的要求。

用于夹层梁静动力及屈曲分析的新型组合结构单元

推导出新型组合结构单元,用于考虑界面滑移的3层部分作用夹层组合梁的静动力及屈曲特性分析.基于铁木辛柯梁理论,建立考虑夹层梁部分作用效应的能量原理.针对其受力特性,在节点位移、横截面转角和界面滑移插值时均采用含内部自由度的高阶插值函数,以解决含界面有限元数值分析中常遇到的“滑移锁定”现象.通过变分原理得到夹层梁的刚度矩阵、质量矩阵以及几何刚度矩阵的显示表达式.基于MATLAB编译相应夹层结构的有限元程序并验证其准确性.对不同截面3层夹层组合梁进行不同荷载条件和边界条件下的静动力及屈曲特性分析,并探讨不同夹层组合梁跨高比和不同界面抗剪连接刚度下的计算结果及其误差的变化规律.所推导的显示表达式新型组合结构单元计算效率高,并便于推广应用于其他有限元程序或商业软件子程序中.

振动梁离散模型的一类模态反问题

讨论了一类对系统的刚度主子阵存在一定约束的条件下,部分或缺损的模态信息构造振动梁模型刚度矩阵的模态反问题.由特征信息得到矩阵方程组,根据给定的频率数据是否属于系统,分三种情形求解.分别利用牛顿-康托洛维奇定理和线性方程组的基本理论,得到了模态反问题存在唯一解的充要条件,并给出了解的显式表达式和数值算法;证明了对应算法的收敛性和数值稳定性分析,结合工程实例,通过数值实验表明了理论的正确性和算法的有效性,并分析说明了计算过程是数值稳定的.

埃尔米特梁单元的分块对角与高阶质量矩阵

埃尔米特梁单元常用的集中质量矩阵,是由挠度自由度对应的一致质量矩阵元素通过行求和或节点积分构造.然而,数值结果表明该集中质量矩阵在求解包含自由端的梁振动问题时,会出现频率精度掉阶现象.本文首先从保障质量矩阵最优收敛性的数值积分精度出发,分别针对三次和五次梁单元,发展了质量矩阵的梯度增强节点积分方案.利用梯度增强节点积分方案,可以得到具有分块对角形式的单元质量矩阵,而其组装的整体质量矩阵除边界节点外仍然呈现对角形式.对于两种单元,其分块对角质量矩阵分别具有4阶最优精度和6阶次优精度.再者,将标准一致质量矩阵和具有同阶精度的梯度增强节点积分质量矩阵进行优化组合,建立了具有超收敛特性的高阶质量矩阵.最后,通过数值算例系统验证了三次和五次单元的分块对角与高阶质量矩阵的频率计算精度.

局域共振夹芯超结构梁带隙特性及实验研究

本文提出了一种新型局域共振夹芯超结构梁,该结构由夹芯梁基体和由软材料包裹质量块组成的局域共振单元构成。分别采用传递矩阵法和有限元法计算了该结构的带隙分布和振动传输特性,搭建了局域共振夹芯超结构梁的振动传输测试实验平台,并与数值计算结果进行对比验证,最后分析了结构参数对结构带隙分布特性的调控规律。研究结果表明,该结构在低频范围内共出现两条弯曲波带隙,带隙频率分别为196.1~339.0 Hz和377.2~655.6 Hz。而完全带隙位于弯曲波带隙内,频率范围为380.0~423.6 Hz。且在这两条弯曲波带隙范围内,弯曲振动传输会发生明显的减弱现象。另外,局域共振夹芯超结构梁的结构参数会对带隙分布特性产生较大影响,通过合理选择结构参数,可以实现局域共振夹芯超结构梁低频率和高带宽的减振要求。

Enabling the transfer matrix method to model serial-parallel compliant mechanisms including curved flexure beams

Compliant mechanisms with curved flexure hinges/beams have potential advantages of small spaces,low stress levels,and flexible design parameters,which have attracted considerable attention in precision engineering,metamaterials,robotics,and so forth.However,serial-parallel configurations with curved flexure hinges/beams often lead to a complicated parametric design.Here,the transfer matrix method is enabled for analysis of both the kinetostatics and dynamics of general serial-parallel compliant mechanisms without deriving laborious formulas or combining other modeling methods.Consequently,serial-parallel compliant mechanisms with curved flexure hinges/beams can be modeled in a straightforward manner based on a single transfer matrix of Timoshenko straight beams using a step-by-step procedure.Theoretical and numerical validations on two customized XY nanopositioners comprised of straight and corrugated flexure units confirm the concise modeling process and high prediction accuracy of the presented approach.In conclusion,the present study provides an enhanced transfer matrix modeling approach to streamline the kinetostatic and dynamic analyses of general serial-parallel compliant mechanisms and beam structures,including curved flexure hinges and irregular-shaped rigid bodies.

应用于高能激光器的XY离焦像差校正方法

针对高能激光器出光过程中出现的大量离焦和0°像散低阶像差现象,提出了基于哈特曼波前传感器和二维整形光路的XY离焦像差校正方法。首先,通过对Zernike多项式的离焦项和0°像散项进行线性组合得到XY离焦像差的表达式,该XY离焦像差系数的大小可直接表征X离焦和Y离焦的波前PV值。同时,通过微调高能激光器中二维整形光路中的镜子间距,可实现激光器输出光束XY离焦波面的补偿。因此,首先利用哈特曼波前传感器提取出光束的XY离焦像差系数大小,而后再根据XY离焦像差系数的大小实时闭环微调二维整形光路中的镜子间距,从而实现XY离焦像差的校正,改善输出光束的光束质量。实验结果表明,该方法可有效地将高能激光器输出光束XY离焦量的PV值由5.2μm和1.1μm校正到0.5μm以下,相应的光束质量β因子由3.1降到1.8,光束质量得到明显改善。

Norea矮塔斜拉桥索力优化

为确定柬埔寨Norea三跨双塔单索面混凝土矮塔斜拉桥的最优成桥索力,基于有限元模型,分别采用刚性支撑连续梁法、最小弯曲能法、影响矩阵法对成桥索力进行了分析和优化。结果表明:三种优化方法中以影响矩阵法得到的索力值效果最好,将最终优化索力值与原设计值对比,分析了斜拉桥的内力、位移以及应力变化,在恒荷载或恒荷载+附加荷载组合作用下,优化后的索力分布更加均匀,结构整体的弯矩、位移以及应力均有所减小,矮塔斜拉桥整体受力和线形更加理想。

基于前后向矩阵束方法的线性排布无人机集群目标规模估算

利用前后向矩阵束方法,提出了一种有效的“蜂群”无人机群目标个数估计方法用于目标检测。与传统的参数估算方法相比,所提方法对于稀疏信号也能准确地进行估算。首先,在一定的角度或频率下,获取线阵排列群目标的雷达散射截面;然后,根据已知的雷达回波构造Hankel-Toeplitz矩阵,并对该矩阵进行奇异值分解;最后,通过设置合适的阈值选取比例较大的奇异值,以此准确地估算线阵排列群目标的个数。此外,文中还讨论了不同信噪比对估算结果的影响。为了提高精度,文中采用多组不同方位角度的回波信号来联合估算群目标的个数。仿真结果表明,该方法能够有效、准确地估算线阵排列群目标的个数,而且估计结果不受噪声的影响,具有较好的鲁棒性。

GEOMETRICALLY NONLINEAR FINITE ELEMENT MODEL OF SPATIAL THIN-WALLED BEAMS WITH GENERAL OPEN CROSS SECTION

Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.

Dynamic stiffness method for free vibration of an axially moving beam with generalized boundary conditions

Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discussed for the first time. The beam is supported by torsional springs and vertical springs at both ends. By modifying the stiffness of the springs, generalized boundaries can replace those classical boundaries. Dynamic stiffness matrices are, respectively, established for axially moving Timoshenko beams and Euler-Bernoulli (EB) beams with generalized boundaries. In order to verify the applicability of the EB model, the natural frequencies of the axially moving Timoshenko beam and EB beam are compared. Furthermore, the effects of constrained spring stiffness on the vibration frequencies of the axially moving beam are studied. Interestingly, it can be found that the critical speed of the axially moving beam does not change with the vertical spring stiffness. In addition, both the moving speed and elastic boundaries make the Timoshenko beam theory more needed. The validity of the dynamic stiffness method is demonstrated by using numerical simulation.

Electron beam welding of SiCp/2024 and 2219 aluminum alloy

SiCp/2024 matrix composites reinforced with SiC particles and 2219 aluminum alloy were joined via centered electron beam welding and deflection beam welding,respectively,and the microstructures and mechanical properties of these joints were investigated.The results revealed that SiC particle segregation was more likely during centered electron beam welding(than during deflection beam welding),and strong interface reactions led to the formation of many Al4C3 brittle intermetallic compounds.Moreover,the tensile strength of the joints was 104 MPa.The interface reaction was restrained via deflection electron beam welding,and only a few Al4C3 intermetallic compounds formed at the top of the joint and heat affected zone of SiCp/Al.Quasi-cleavage fracture occurred at the interface reaction layer of the base metal.Both methods yielded a hardness transition zone near the SiCp/2024 fusion zone,and the brittle intermetallic Al4C3compounds formed in this zone resulted in high hardness.

Multi-objective Optimization of Non-uniform Beam for Minimum Weight and Sound Radiation

A multi-objective optimization of non-uniform beams is presented for minimum radiated sound power and weight. The transfer matrix method is used to compute the structural and acoustic responses of a non-uniform beam accurately and efficiently. The multi-objective particle swarm optimization technique is applied to search the Pareto optimal solutions that represent various compromises between weight and sound radiation. Several constraints are imposed, which substantially reduce the volume fraction of feasible solutions in the design space. Two nonuniform beams with different boundary conditions are studied to demonstrate the multi-objective optimal designs of the structure.

BEAM18x单元在杆系结构分析中的应用

简要介绍了ANSYS提供的BEAM18x单元的功能和Ti moshenko梁理论的基本假定,就该单元的长细比影响、曲梁应用,变截面、组合截面、剪切变形的处理及刚度矩阵推导等问题进行了讨论,总结了用BEAM18x单元进行杆系结构分析时的适用性与方法,有助于对BEAM18x单元的理解及应用。

Effect of pulse parameters on microstructure of joint in laser beam welding for SiC_p/6063 composite

The restraint effects of pulse frequency and pulse duty cycle on the precipitates of harmful needle like Al 4C 3 phase were studied in CO 2 impulsed laser welding through the experiment on the SiC p/6063 composite, and the microstructures of the weld under the different process parameters (pulse time from 1 ms to 20 ms,duty cycle from 50% to 91%) were analyzed. In order to compare, CO 2 continuous laser was conducted under the same efficiency. The results demonstrate that the proper laser pulse frequency and duty cycle can restrain the formation of Al 4C 3 effectively. However, the burning loss of SiC is more serious and the fluidity of molten pool is less in continuous laser welding than in impulsed laser welding.