Control of the dynamic response of a damped membrane by distributed forces

The problem of damping out the oscillations of a rectangular membrane by means of distributed forces is solved analytically. The membrane may be subject to viscous damping and is clamped along the boundaries. The motion of the membrane is initiated by given initial displacement and velocity conditions. The basic control problem is to minimize the deflection and the velocity of displacements in a given period of time with the minimum possible expenditure of force. A quadratic vector performance index is chosen as the cost functional which comprises the functionals of the deflection, velocity and the distributed force. The necessary conditions of optimality are obtained from a control theory approach and formulated in the form of a maximum principle in terms of an adjoint variable. The multi-objective control formulation permits the decision maker to shift the weight of the control to the minimization of any one of the quantities of interest and explore the optimum capabilities of the structural element. Numerical results are given for various problem parameters and the efficiency of the control mechanism is investigated. The optimal tradeoff curves, which represent the points of optimum performance, are given for a couple of example problems with multiple objectives.     

The vibration characteristics of a beam with an axial force

Equations of motion are found for a non-uniform damped Timoshenko beam with a distributed axial force. Principal modes may be extracted by numerical means when the boundary conditions are specified, and the appropriate orthogonality conditions are given. The theory of linear forced vibration can thus be derived. It is an implicit requirement that all axial forces are conservative. That is to say, tangential, follower and partial follower axial forces (whether applied at an extremity or distributed along the beam) are excluded.     

Revisiting the moving force problem

The problem of the vibration of a beam subject to a travelling force is considered. The purpose of the study is to develop simple tools for finding the maximum deflection of a beam for any given velocity of the travelling force. It is shown that, for given boundary conditions, there exists a unique response-velocity dependence function. A technique to determine this function is suggested, which is based on the assumption that the maximum beam response can be adequately approximated by means of the first beam mode. To illustrate this, the maximum response function is calculated analytically for a simply supported (SS) beam and constructed numerically for a clamped-clamped beam. The effect of the higher modes on the maximum response is investigated, and the relative error of the one-mode approximation for a SS beam is constructed. The estimates obtained substantiate the assumption about adequacy of the one-mode approximation in a wide range of velocities; in particular, the relative error in the neighborhood of the velocity that results in the largest response is less than one percent.     

Vibration and stability of a non-uniform Timoshenko beam subjected to a follower force

An analysis is presented for the vibration and stability of a non-uniform Timoshenko beam subjected to a tangential follower force distributed over the center line by use of the transfer matrix approach. For this purpose, the governing equations of a beam are written in a coupled set of first-order differential equations by using the transfer matrix of the beam. Once the matrix has been determined by numerical integration of the equations, the eigenvalues of vibration and the critical flutter loads are obtained. The method is applied to beams with linearly, parabolically and exponentially varying depths, subjected to a concentrated, uniformly distributed or linearly distributed follower force, and the natural frequencies and flutter loads are calculated numerically, from which the effects of the varying cross-section, slenderness ration, follower force and the stiffness of the supports on them are studied.     

The Navier-Stokes limit of stationary solutions of the nonlinear Boltzmann equation

We consider the flow of a gas in a channel whose walls are kept at fixed (different) temperatures. There is a constant external force parallel to the boundaries which may themselves also be moving. The system is described by the stationary Boltzmann equation to which are added Maxwellian boundary conditions with unit accommodation coefficient. We prove that when the temperature gap, the relative velocity of the planes, and the force are all sufficiently small, there is a solution which converges, in the hydrodynamic limit, to a local Maxwellian with parameters given by the stationary solution of the corresponding compressible Navier-Stokes equations with no-slip voundary conditions. Corrections to this Maxwellian are obtained in powers of the Knudsen number with a controlled remainder.     

Dynamic contact analysis of a tensioned beam with a moving mass–spring system

The dynamic contact problem of a tensioned beam with clamped-pinned ends is analyzed when the beam contacts a moving mass–spring system. The contact and contact loss conditions are expressed in terms of constraint equations after considering the dynamic contact between the beam and the moving mass. Using these constraints and equations of motion for the beam and moving mass, dynamic contact equations are derived and then discretized using the finite element method, which is based on the Lagrange multiplier method. The time responses for the contact forces are computed from these discretized equations. The contact force variations and contact loss are investigated for the variations of the moving mass velocity, the beam tension, the moving mass, and the stiffness of the moving mass–spring system. In addition, the possibility of contact loss and safe contact conditions between the moving mass and the tensioned beam are also studied.     

确定分布的展向Lorentz力调制下的槽道湍流涡结构

采用直接数值模拟方法,对槽道湍流中确定分布的Lorentz力的流动控制与减阻问题进行研究.讨论了Lorentz力作用于槽道湍流后,流场的特性和涡结构的特性,并对此类Lorentz力对槽道湍流的控制与减阻机理进行了讨论.研究发现:1)Lorentz力诱导的层流流场壁面附近存在梯度极大的展向速度剪切层,该剪切层容易形成流向涡结构;2)在给定合适参数的确定分布的Lorentz力作用下,湍流流场仅剩周期分布的准流向涡;3)与未控制流场相比,控制后的流场中,准流向涡的抬升高度大大降低,从而减小猝发强度,使壁面阻力下降.     

双阳极磁控注入枪设计参数对其性能的影响分析

 对34GHz基波回旋管双阳极磁控注入枪的优化做了详细的研究和计算，数值模拟了阳极电压、注电流、枪体尺寸加工误差、外加直流磁场等因素对电子枪的影响。模拟结果表明：增大阳极电压不但可以提高速度比，而且可以降低横向速度零散。磁场压缩比减小，使电子注具有最小速度零散的电流值增大；同时，电子注的速度比降低，最小横向速度零散值也增大。必须慎重选择阳极形状，以提高电子枪的性能并保证电子注的稳定性；同时，还发现由于阳极结构的变化导致阴极电场分布的变化，使电子注的注电流在各因子变化过程中出现了微小的扰动。减小Bc可以增大电子注的速度比，还可以减小电子注的横向速度零散，但是当电子注的速度比增大到一定值时，电子注的性能就会变得不太稳定。     

A Suitable Active Control for Suppression the Vibrations of a Cantilever Beam

In our consideration, a comparison between four different types of controllers for suppression the vibrations of the cantilever beam excited by an external force is carried out. Those four types are the linear velocity feedback control, the cubic velocity feedback control, the non-linear saturation controller (NSC) and the positive position feedback (PPF) controller. The suitable type is the PPF controller for suppression the vibrations of the cantilever beam. The approximate solution obtained up to the first approximation by using the multiple scale method. The PPF controller effectiveness is studied on the system. We used frequency-response equations to investigate the stability of a cantilever beam. We notified that, there is a good agreement between the analytical solution and the numerical solution.     

Diagnostic system for two dimension intensity distribution of laser beam

The diagnostic system for two dimension(2-D)intensity distribution of laserbeam is a measuring instrument for many parameters of laser beam.2-D intensity distributionplot of laser beam is obtained by the two dimension scanning mirror which is controlled by amicrocomputer to scan the laser beam on a detector.Many parameters of laser beam such asthe isointensity distribution plot,the beam diameter,the beam waist diameter,the laser pow-er,the diverge angle and the beam brightness,are given by means of the microcomputer pro-cessing the data measured.Theoretical analysis of beam parameter transform is given.     

Focusing of an atomic beam by a two-dimensional magneto-optical trap

A method for focusing neutral atoms based on the light-pressure force in a nonuniform magnetic field is proposed and analyzed. Its particular scheme is realized by means of a two-dimensional magneto-optical trap using a thermal beam of Rb atoms. A feature of this focusing method is the linear dependence of the focal length on the longitudinal velocity of atoms in contrast to the quadratic dependence in the known methods of focusing material-particle beams. The minimum size of the waist of the focused atomic beam is equal to 270 μm. Owing to focusing by means of the two-dimensional magneto-optical trap, the velocity monochromatization of a thermal atomic beam is realized: the width of the distribution of the longitudinal atomic velocities in the beam is reduced from 350 to 60 m/s. Original Russian Text ? P.N. Melentiev, P.A. Borisov, S.N. Rudnev, A.E. Afanasiev, V.I. Balykin, 2006, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2006, Vol. 83, No. 1, pp. 16–20.     

离子俘获的线性理论及其应用

从线性理论出发,研究了电子束团在储存环里均匀分布和束团串两种情况下离子俘获的条件;在离子系统里引入Twiss参量,推导出电子束团串俘获离子的阈值流强的公式;并以此讨论北京正负电子对撞机(BEPC)在同步辐射专用运行时观察到的电子束流现象,提出采用束团串运行来克服BEPC中的束流寿命下降.     

Active-passive vibration absorber of beam-cart-seesaw system with piezoelectric transducers

In contrast with fully controllable systems, a super articulated mechanical system (SAMS) is a controlled underactuated mechanical system in which the dimensions of the configuration space exceed the dimensions of the control input space. The objectives of the research are to develop a novel SAMS model which is called beam-cart-seesaw system, and renovate a novel approach for achieving a high performance active-passive piezoelectric vibration absorber for such system. The system consists of two mobile carts, which are coupled via rack and pinion mechanics to two parallel tracks mounted on pneumatic rodless cylinders. One cart carries an elastic beam, and the other cart acts as a counterbalance. One adjustable counterweight mass is also installed underneath the seesaw to serve as a passive damping mechanism to absorb impact and shock energy. The motion and control of a Bernoulli-Euler beam subjected to the modified cart/seesaw system are analyzed first. Moreover, gray relational grade is utilized to investigate the sensitivity of tuning the active proportional-integral-derivative (PID) controller to achieve desired vibration suppression performance. Consequently, it is shown that the active-passive vibration absorber can not only provide passive damping, but can also enhance the active action authority. The proposed software/hardware platform can also be profitable for the standardization of laboratory equipment, as well as for the development of entertainment tools.     

微波谐振腔中电子与微波作用的非稳态过程研究

 在微波腔中微波场影响电子的运动，同时电子束作为电流源也产生辐射，影响微波场，这种相互作用包含线性和非线性过程。根据Maxwell理论，微波腔中的实际微波场可以按微波腔的模式展开，而且不同模式与电子束之间的相互作用不同。将电子束作为激励源，根据Maxwell方程和电子受到的洛伦兹力，建立不同模式在电子束作用下的激励方程和电子束电子在不同模式作用下的运动方程（即微波谐振腔中电子束与微波场相互作用的自洽方程组），并由此进一步分析一维情况下单间隙微波腔中微波建场、辐射场呈指数增长和饱和等非稳态作用过程，该过程涉及到电子束与微波作用的线性和非线性过程。     

极点配置法弹性平板有源隔声系统优化

对混响声场中的弹性平板有源隔声系统进行优化。根据激励频率范围确定受控模态阶次,在模态空间中建立系统降阶方程,基于极点配置方法,采用分布式系统增加受控模态的阻尼,降低低频共振声传输。同时设计模态滤波器,为控制器提供所需的状态信息。为提高控制效能,本文对传感器和作动器布放位置进行优化,尝试不同极点配置方案,并对耦合控制与独立模态控制方法的隔声效果进行比较。仿真结果显示,极点配置法有源隔声可以有效降低共振声传输,优化布放和独立模态控制方式下,控制力明显降低。优化后的有源隔声系统效能有所提升。      

Micro-vibration suppression of equipment supported on a floor incorporating magneto-rheological elastomer core

In this study, magneto-rheological elastomers (MREs) are adopted to construct a smart sandwich beam for micro-vibration control of equipment. The micro-vibration response of a smart sandwich beam with MRE core which supports mass-concentrated equipment under stochastic support-motion excitations is investigated to evaluate the vibration suppression capability. The dynamic behavior of MREs as a smart viscoelastic material is characterized by a complex modulus dependent on vibration frequency and controllable by external magnetic fields. A frequency-domain solution method for the stochastic micro-vibration response of the smart sandwich beam supporting mass-concentrated equipment is developed based on the Galerkin method and random vibration theory. First, the displacements of the beam are expanded as series of spatial harmonic functions and the Galerkin method is applied to convert the partial differential equations of motion into ordinary differential equations. With these equations, the frequency-response function matrix of the beam–mass system and the expression of the velocity response spectrum are then obtained, with which the root-mean-square (rms) velocity response in terms of the one-third octave frequency band can be calculated. Finally, the optimization problem of the complex modulus of the MRE core is defined by minimizing the velocity response spectrum and the rms velocity response of the sandwich beam, through altering the applied magnetic fields. Numerical results are given to illustrate the influence of MRE parameters on the rms velocity response and the response reduction capacity of the smart sandwich beam. The proposed method is also applicable to response analysis of a sandwich beam with arbitrary core characterized by a complex shear modulus and subject to arbitrary stochastic excitations described by a power spectral density function, and is valid for a wide frequency range.     

大回旋电子束双磁会切电子枪的设计

 分析了Ka波段二次谐波回旋行波管双磁会切电子枪的理论模型,计算了电子枪的设计参数;采用EGUN软件进行模拟,设计出了产生大回旋电子束的双磁会切电子枪。该枪电压为70 kV,电流为3.35 A,电子束横纵速度比为1.62,速度零散为4.2%。给出了电子束速度比、速度零散沿轴线的分布,进而讨论了阳极电压对电子束性能的影响,结果表明选择适当的阳极电压和阴极磁场对得到好的电子束参量作用明显。     

A study on radial directional natural frequency and damping ratio in a vehicle tire

The measurement of radial directional natural frequency and damping ratio in a vehicle tire has been studied. Natural frequencies and damping ratios in the radial direction of various tires, from passenger car tires to truck bus tires, are reported. The radial direction modal parameters of tires subjected to different levels of inflation pressure, have been determined by using a frequency response function method. To obtain the theoretical natural frequency and mode shape, the plane vibration of a tire has been modeled as though it were that of a circular beam. By using the Tielking method that is based on Hamilton’s principle, theoretical results have been determined by considering the rotational velocity, tangential and radial stiffness, radial directional velocity and tension force which is due to tire inflation pressure. The results show that experimental conditions can be considered as the parameters that shift the natural frequency and damping ratio.     

低速度零散会切电子枪的设计和数值仿真

根据拉格朗日方程对电子在平滑会切磁场中的径向波动与速度零散的关系进行讨论。运用Matlab,Magic软件相互结合的方法设计电子枪结构和磁场。用Matlab程序模拟单电子在给定电场、磁场中的运动,分析了单电子径向速度对零散的影响,并优化磁场分布。设计的磁场可以有效地减小单电子束径向速度,降低电子束速度零散。用Magic软件对电流为1 A、能量为30 keV的电子束在优化磁场中的运动进行仿真,得到的电子束速度比约为2,速度零散小于2.5%,轴向速度零散小于8.5%。