Combined analytical and numerical solution for an elastically supported Timoshenko beam to a moving load

A combined analytical and numerical method is presented to get a response for an elastically supported Timoshenko beam to a moving load. The analytical steady-state solution as a particular solution is established and summed with the numerically calculated homogeneous solution. A steady-state solution is sought analytically through the direct application of the Fourier transform to the moving step load. It is shown to be a compact formula composed of exponential and sinusoidal functions depending on the load velocity. The homogeneous solution is established numerically to cancel out the discontinuities and the inconsistent boundary and initial conditions of the steady-state solution. The discontinuities produced by the steady-state solution are removed using the physical characteristics related to the bar wave. Some response curves are shown to compare the beam motions at different load velocities.     

Parametric instability of a Leipholz beam due to distributed frictional axial load

In this paper, the parametric instability of a beam subjected to a moving distributed contact load that also oscillates in the transverse direction of the beam is studied. Due to the presence of friction between the beam and the moving contact surface, the beam is excited by a pulsating, distributed, follower-type axial load, which results in the problem of a Leipholz column subjected to parametric excitation. The study of this prototypical one-dimensional model is intended to provide further understanding of the instability of systems that have similar loading conditions such as automotive disc brake pads rubbed by the oscillatory rotor or beam-like structures. Effects of several parameters such as boundary conditions, coefficient of friction, intermediate supports, and waviness of the contact load on the instability are examined. Results show that the combination resonance of both the sum and difference types exists for the boundary conditions considered in this study. It is also found that the shearing motion of the friction material plays an important role in determining the stability of the Leipholz beam model. Analogous behavior of instability between the present model and the disc brake pad system is also discussed.     

On the response of an elastically supported rigid disk with a moving massive load

An analysis of the dynamic response of an elastically supported 3-degree-of-freedom rigid circular disk excited by a moving massive load is presented. A solution is obtained by transforming a set of ordinary nonlinear differential equations with periodic coefficients to a set of linear differential equations with constant coefficients. Three different types of system instability are observed. An unstable region exists immediately above the critical speed of the disk. Another unstable region arises when the load velocity is such that the frequency of two different disk modes is nearly the same. A terminal instability region exists for all load speeds above a certain limiting value. The addition of viscous damping may destabilize the system.     

Diffractive focusing fan-out element for the parallel DNA sequencer

Various issues of creation of diffractive optical elements transforming one laser beam with small divergence to a matrix of converging beams with a diffraction size of focused spots in the plane of object illumination and their application for problems of DNA sequencing and microscopy are considered. The parameters of diffractive elements are calculated and optimized in the approximation of the Fresnel–Kirchhoff diffraction theory. Diffractive elements are fabricated by the method of direct laser writing on a photoresist by using a circular laser writing system. Experimental characteristics of a diffractive element creating a matrix consisting of 33 × 33 beams, which are focused in one plane at a distance of 210 mm, are presented. The degree of nonuniformity of beam intensities determined by the ratio of beam intensities in the central region to intensities of peripheral beams is 1/2.5, which is potentially sufficient to be used in DNA sequencing problems. The maximum distortions of spot positions in the entire focusing field is <0.15%.     

Non-linear bending of thin, ideally elastic rods

A number of methods are available for the solution of elastica problems including the analytical elliptic-integral approach, various predictor-corrector methods and discrete analyses based on non-linear finite-element theory. In this paper an alternative discrete approach is proposed based on obtaining, by Dynamic Relaxation, finite difference solutions to the governing differential equations.Results from the method are presented for the large deflection behaviour of a cantilever beam and a circular ring and satisfactory correlation is demonstrated with the results of previously published exact analyses.     

Dynamic response of a finite length euler-bernoulli beam on linear and nonlinear viscoelastic foundations to a concentrated moving force

In this paper the dynamic response of a simply-supported, finite length Euler-Bernoulli beam with uniform cross-section resting on a linear and nonlinear viscoelastic foundation acted upon by a moving concentrated force is studied. The Galerkin method is utilized in order to solve the governing equations of motion. Results are compared with the finite element solution for the linear foundation model in order to validate the accuracy of the solution technique. A good agreement between the two solution techniques is observed. The effect of the nonlinearity of foundation stiffness on beam displacement is analyzed for different damping ratios and different speeds of the moving load. The results for the time response of the midpoint of the beam are presented graphically.     

Rotary inertia and temperature effects on non-linear vibration, steady-state response and stability of an axially moving beam with time-dependent velocity

Free non-linear transverse vibration of an axially moving beam in which rotary inertia and temperature variation effects have been considered, is investigated. The beam is moving with a harmonic velocity about a constant mean velocity. The governing partial-differential equations are derived from the Hamilton's principle and geometrical relations. Under special assumptions, the two partial-differential equations can be mixed to form one integro-partial-differential equation. The multiple scales method is applied to obtain steady-state response. Elimination of secular terms will give us the amplitude of vibration. Additionally, the stability and bifurcation of trivial and non-trivial steady-state responses are analyzed using Routh-Hurwitz criterion. Eventually, numerical examples are presented to show rotary inertia, non-linear term, temperature gradient and mean velocity variation effects on natural frequencies, critical speeds, bifurcation points and stability of trivial and non-trivial solutions.     

具有可动边界和间隙的机械系统自激振动分析和数值模拟

在研究某些机械自激振动时 ,本文以初轧机为例 ,考虑了连接轴可动性和间隙对初轧机自激振动的影响 ,提出了一个新的力学模型 ,从理论分析出发 ,建立了带有可动边界和间隙情况下的初轧机自激振动微分方程式 ,探讨了该系统振动特性 ,得到消除自激振动的条件。所得到的结果可供生产实际参考     

Dynamics of an axially moving Bernoulli-Euler beam: Spectral element modeling and analysis

The spectral element model is known to provide very accurate structural dynamic characteristics, while reducing the number of degree-of-freedom to resolve the computational and cost problems. Thus, the spectral element model for an axially moving Bernoulli-Euler beam subjected to axial tension is developed in the present paper. The high accuracy of the spectral element model is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions. The effects of the moving speed and axial tension on the vibration characteristics, wave characteristics, and the static and dynamic stabilities of a moving beam are investigated.     

轴向运动简支-固支梁的横向振动和稳定性

研究一端简支一端固支轴向运动梁的横向振动和稳定性。提出在给定边界条件下确定一匀速运动梁固有频率和模态函数的方法。当轴向运动速度在其常平均值附近作简谐波动时,应用多尺度法给出轴向变速运动梁参数共振时的不稳定条件。用数值仿真说明相关参数对固有频率和不稳定边界的影响。     

回转梁动力学方程求解的数值方法研究

考虑驱动力矩、重力、哥氏力、运动阻力和惯性耦合力,根据考虑横向弯曲变形的Euler-Bemoulli细梁模型,并考虑离心力作用下的拉伸变形,建立回转运动梁的动力学模型。将梁根部的回转角度分解为整体刚性运动回转角度和刚体运动和柔性运动激发刚柔耦合回转角。将梁的柔性振动位移也分解为由整体刚性回转角所激发的动力激励振动和刚柔耦合回转角运动及刚柔耦合项共同激发的刚柔耦合振动。整体刚性回转角和动力激励振动,通过数值方法(如龙格-库塔法)求解,而将刚柔耦合回转角和刚柔耦合振动,通过奇异摄动法求解。通过数值方法和奇异摄动法相结合的方法,能够正确计算刚柔耦合回转角及其对梁振动位移的影响,更精确、深入地分析回转梁的动力学特性。     

A computer vision system for the inspection of light emitting diodes

This paper outlines the development of a computer vision system to enhance classification criteria for the inspection of infrared light emitting diodes (LEDs). Infrared LEDs used for fibre optics and optical switches are presently classified solely on the basis of power output. This test is performed by focusing the light beam from the LED through a circular aperture onto a solar cell. The output current from the solar cell is translated into a power output reading for the LED. The approach is limited in that it provides no information about other characteristics such as the misalignment of the beam from the mechanical centre or the intensity distribution of the beam. Improved classification criteria and testing methods based on emitted light intensity distribution can be utilised in engineering revision, setting specifications, monitoring manufacturing problems and classification for different applications.     

Study on the frame structure modeling of the beam element formulated by absolute Nodal coordinate approach

Accurate seismic analyses of large deformable moving structures are still unsolved problems in the field of earthquake engineering In order to analyze these problems, the nonlinear finite element method formulated by the absolute nodal coordinate approach is noticed Because, this formulation has several advantages over the standard procedures on mass matrix, elastic forces and damping forces in the case of large displacement problems But, it has not been fully studied to build frame structure models by using beam elements in the absolute nodal coordinate formulation In this paper, we propose the connecting method of the beam elements formulated by the absolute nodal coordinate The coordinate transformation matrix of this element is introduced into the frame structure This beam element has the characteristic that the mass matrix and bending stiffiness matrix are constant even if in the case of large displacement problems, and this characteristic is being kept after the transformation In order to verify the proposed method, we show the numerical simulation results of frame structures for a vibration problem and a large displacement problem     

Non-uniform Euler-Bernoulli beams under a single moving oscillator: An approximate analytical solution in time domain

Dynamic responses of simply supported non-uniform beams traversed by a moving oscillator are analysed in this paper. An approximate analytical method based on Rayleigh-Ritz (R-R) formulation is developed. The fundamental approximate mode obtained from R-R method is used in the present formulation to determine the responses of the beam and the oscillator. Effects of surface irregularities on the displacement and acceleration responses of the beam and the vehicle are also analysed. The results are compared with those obtained using Finite element method (FEM). A numerical example is provided to illustrate the validity of the present method which shows that the proposed method is simple, computationally more efficient compared to FEM and gives fairly good results. Though the single-mode approach used in the present paper is a classical one and numerous studies on the responses of uniform beams under moving loads have been reported in the past, its application to non-uniform beams (for which there does not exist any closed form expression for mode shapes) under a moving load, especially a moving oscillator, is presented for the first time.     

A finite thin circular beam element for in-plane vibration analysis of curved beams

In this paper, the stiffness and the mass matrices for the in-plane motion of a thin circular beam element are derived respectively from the strain energy and the kinetic energy by using the natural shape functions of the exact in-plane displacements which are obtained from an integration of the differential equations of a thin circular beam element in static equilibrium. The matrices are formulated in the local polar coordinate system and in the global Cartesian coordinate system with the effects of shear deformation and rotary inertia. Some numerical examples are performed to verify the element formulation and its analysis capability. The comparison of the FEM results with the theoretical ones shows that the element can describe quite efficiently and accurately the in-plane motion of thin circular beams. The stiffness and the mass matrices with respect to the coefficient vector of shape functions are presented in appendix to be utilized directly in applications without any numerical integration for their formulation.     

大学去行政化四问

大学去行政化是当前广受社会关注、政府和大学急需改革的重要问题。但由于种种原因,大学去行政化必将十分艰难。其中还有很多问题需要深入思考。这些问题至少包括：去何种行政化？去行政化的主体是谁？如何去行政化？去行政化还有哪些障碍需要克服？等等。总体而言,厘清“去何种行政化”是大学去行政化的前提,明确“去行政化的主体是谁”是大学去行政化的关键,探索“如何去行政化”的路径是大学去行政化的基本方式,克服“去行政化的障碍”则为大学去行政化创造重要条件。只有对这些问题作出深刻思考,并实事求是地回答和解决这些问题,大学去行政化才有可能成为现实。     

基于单目视觉的激光光束方向标定研究

在由激光位移传感器组成的测量系统中,激光光束的方向是一个关键参数.方位角和俯仰角对于一条激光光束是最为重要的两个参数.本文中提出一种基于单目视觉的激光光束方向测量方法.首先,将CCD相机放置于基础平面上方,保持相机光轴与基础平面接近于垂直状态,并利用误差为10μm的圆孔型标定板建立单目定位模型.然后将激光光束发生装置放置在基础平面上并保持位置固定,同时在基础平面上放置特制靶块,使激光光束可以投射到靶块斜面上并形成一个激光光斑.在基础平面上方放置的CCD相机可以清晰的采集到激光光斑、靶块斜面的图像,应用相关算法提取出光斑质心的二维图像坐标.沿激光光束方向以相等间距移动靶块,通过CCD相机采集每移动一次靶块在当前位置下的光斑、靶块图像.利用相关的转换公式,结合靶块本身固有参数,将光斑质心图像二维坐标转换为基础平面下的空间三维坐标.由于靶块的移动,会得到靶块不同位置下激光光斑质心的三维坐标,将这些三维坐标拟合成空间直线表征待测激光光束.拟合直线得俯仰角即为待测激光光束的俯仰角.实验中,应用高精度仪器对靶块参数进行测定,并使用高精度标定板标定相机内外参数建立相应的定位模型.测量精度主要通过单目视觉定位精度、光斑重心提取精度来保证.结果显示,待测光束的俯角最大误差达到0.02°,光束间夹角的最大误差为0.04°.     

The method of pseudocaustics for the experimental solution of simple elasticity problems

The optical method of pseudocaustics consists of directing a light beam on a plane specimen and obtaining enlarged the deformed shape of its boundary on a screen after the reflection and/or refraction of this beam on the specimen. In case of plane isotropic elastic media, the pseudocaustics can be used to get the derivative Ф'(z) of the complex potential Ф(z) of Muskhelishvili. In this paper this property of pseudocaustics was used for the experimental determination of both complex potentials Ф(z) and Ψ(z) in the whole specimen for both cases of the first and the second fundamental problems of plane elasticity. This can be achieved by one simple experiment and very little computational effort, not comprising the solution of any kind of equations. The proposed method was applied to the problem of an infinite elastic medium under tension with a circular hole. The experimental results obtained are in good agreement with the corresponding theoretical results.     

A common-path interferometer including integrated single-prism beam shaping

In this work, a common-path interferometer including integrated single-prism beam shaping is presented. Both theoretical considerations and experimental results on single-prism shaping of elliptical and circular laser beams were performed. Based on a single-prism beam shaper, a common-path interferometer without any classical beam splitter device was assembled and characterised. It is shown that the presented setup provides well-evaluable interference patterns with a Michelson contrast of 0.42–0.45.     

Dynamic responses and fuzzy control of a simply-supported beam subjected to a moving mass

This paper deals with the active vibration control of a simply-supported beam traversed by a moving mass using fuzzy control. Governing equations for dynamic responses of a beam under a moving mass are derived by Galerkin’s mode summation method, and the effect of forces (gravity force, Coliolis force, inertia force caused by the slope of the beam, transverse inertia force of the beam) due to the moving mass on the dynamic response of a beam is discussed. For the active control of dynamic deflection and vibration of a beam under the moving mass, the controller based on fuzzy logic is used and the experiments are conducted by VCM (voice coil motor) actuator to suppress the vibration of a beam. Through the numerical and experimental studies, the following conclusions were obtained. With increasing mass ratioy at a fixed velocity of the moving mass under the critical velocity, the position of moving mass at the maximum dynamic deflection moves to the right end of the beam. With increasing velocity of the moving mass at a fixed mass ratioy, the position of moving mass at the maximum dynamic deflection moves to the right end of the beam too. The numerical predictions of dynamic deflection of the beam have a good agreement with the experimental results. With the fuzzy control, more than 50% reductions of dynamic deflection and residual vibration of the tested beam under the moving mass are obtained.