Optimal distributed control of a continuous beam with damping

Optimal control of a damped two-span beam is studied with the objective of minimizing its deflection and velocity in a given period of time with the minimum possible expenditure of force. The beam undergoes transient vibrations and is subject to given displacement and velocity initial conditions. The control is exercised by means of a transverse distributed force. The multiple objectives of the problem lead to a vector performance criterion which is reduced to a scalar one by using the concept of Pareto optimality. Necessary and sufficient conditions of optimality are expressed in the form of a maximum principle which leads to an explicit expression for the control force. The behaviour of the controlled beam is numerically studied which indicates that optimally controlled distributed forces are effective in damping out the dynamic response. Relations between various objectives are studied by means of optimal trade-off curves showing the best performance of the controlled beam.     

浅海随机相位起伏声场中速度估计的互谱分析方法

浅海条件下,目标运动速度是基于波导不变量声源被动定位的关键因素,利用浅海波导环境下的声场简正波理论,研究了浅海随机相位起伏的波束域声场互相关信号的特点,并通过声速剖面的二阶统计量对随机相位扰动进行了有效的补偿,提出利用波束域声场互相关信号进行谱分析的速度估计方法,仿真实验表明了该方法的有效性。利用2013年7月海试实验数据,该方法准确的估计出了目标的速度,并与GPS实测速度对比,速度估计的相对误差在10%以内。     

Beam and phase effects in angle-beam-through-transmission method of ultrasonic velocity measurement

The accuracy of a plane wave approximation for phase velocity measurements in isotropic and anisotropic material using the angle-beam-through-transmission method has been investigated numerically and experimentally. In this method the velocity is measured in different propagation directions as a function of incidence angle. The effect of two factors on the measurement accuracy have been discussed: intrinsic phase shift of the transmitted signal through a fluid-solid interface and beam diffraction due to the finite beam size of receiver and transmitter. It is shown that the interface-induced phase shift can introduce an error in time delay measurements of the shear wave after the first critical angle and that this time delay error can be accurately corrected for. Numerical results obtained by a time-domain beam model show that except at the critical angles, the finite width of the transmitter and receiver only affects the amplitudes of the transmitted signals and has almost no effect on the measured zero-cross time delay; therefore the plane wave approximation for obtaining phase velocity from the measured time delay data by this method and the plane wave interface-induced phase correction are fully applicable.     

First-order approximation in studying beam spreading of cosh-Gaussian and cos-Gaussian beam in Kolmogorov turbulence

With the help of extended Huygens–Fresnel principle and the expansion of the mutual coherence function in a Taylor series, the analytical expression of the first-order approximation for the average intensity of a cosh-Gaussian and cos-Gaussian beam in Kolmogorov turbulence has been obtained. Based on the analytical expression of the first-order approximation, the variation of average intensity in Kolmogorov turbulence has been examined. Comparing with numerical integration, the relative error due to the quadratic structure function and first-order approximation of the mutual coherence function is studied and discussed. It is shown that the analytical expression of the first-order approximation provides a more precise approach to study the beam spreading of the cosh-Gaussian and cos-Gaussian beam in Kolmogorov turbulence, no matter whether the effect of turbulence is weak or strong.     

On the dynamics of interaction between a moving mass and an infinite one-dimensional elastic structure at the stability limit

The paper herein deals with the study of the dynamic behaviour generated by the instability of the vibration of a loaded mass, uniformly moving along an Euler-Bernoulli beam on a viscoelastic foundation, induced by the anomalous Doppler waves excited in the beam. This issue is relevant for the case of modern trains travelling along a track with soft soil when the trains speed exceeds the phase velocity of the waves induced in the track. The model corresponds to a railway vehicle reduced to a loaded wheel running along a (half) track. The beam takes account of the bending stiffness of the rail and the mass of the track, including the mass of the rail, semi-sleepers and half of the ballast layer, where the viscoelastic foundation represents the subgrade. The model includes the wheel/rail Hertzian contact and it allows the simulation of the possibility of contact loss. The nonlinear equations of motion are integrated using a numerical approach based on the Green’s function method. When the vibration becomes unstable, the system evolution is a limit cycle characterised by a succession of shocks, due to the action of two opposite factors: the anomalous Doppler waves that pump energy at the interface between the moving mass and the beam, thus forcing the mass to take off, and the static load that push the mass downwards. The frequency of the shocks increases at higher velocity and the magnitude of the impact force decreases; the most dangerous velocity is the critical one, which represents the stability limit of the linear approximation of the motion equations. The transient behaviour that precedes the limit cycle appearance is being analysed. The Hertzian contact influences the time history of the limit cycle and the magnitude of the impact force and, therefore, it is essential to be included in the model. To the authors’ knowledge, this problem has never been dealt with.     

Semi-active control of 1D continuum vibrations under a travelling load

The paper presents a method for computing the response of a 1D elastic continuum supported by a set of semi-active viscous dampers and induced by a load travelling over it. The magnitude of the moving force has been assumed to be constant by neglect of the inertia forces. Full analytical solution is based on the power series method and is given in an arbitrary time interval. The time-marching scheme allows us to continue a solution in successive layers with initial conditions taken from the end of previous stages. The semi-active open loop control strategy is proposed. Shapes of damping functions are defined as a form of piecewise constant function. The control strategy is suboptimal and it outperforms the passive case. Numerical results are presented for the cases of a string and a Bernoulli-Euler beam.     

Simultaneous Measurement of Velocity and Equivalent Diameter on Non-Spherical Particles

The performance of a laser-based optical technique to measure simultaneously the velocity and equivalent diameter of nonsphercial particles was evaluated. The size information was provided by the absolute intensity of diffractively scattered light by a particle crossing a single laser beam, which is concentric with a laser Doppler probe volume. The response curve (size-intensity relationship) of the technique was estimated by calculations using the Fraunhofer approximation. Experiments with spherical glass and polyethylene and non-spherical metal and ceramic particles ranging from 20 to 200 μm confirmed the operation of the technique and in all the measurements the maximum error of the average diameter was 10 μm as compared with size information provided by a microscope.     

基于GCV-FFT方法的超声速压缩拐角流场气动光学效应计算

研究超声速压缩拐角流动，基于Rytov近似，采用广义卷积-快速Fourier变换（GCV-FFT），直接求解非均匀介质中的Helmholtz方程，获得激光光束的散射场和衍射场的复振幅分布.给出包括光强、光程差、斯特列尔比、相对光强、光束质心位置和有效光束宽度等气动光学参量.可以看出，激光光束在湍流场区域内传输，光强度分布逐渐出现起伏和偏离.穿过流场区域后，由于衍射作用，光束产生较大幅度的扭曲、偏离和破碎.压缩拐角区的流场对光束质量的影响明显大于充分发展湍流区.从相对光强的分布形态来看，光束的破碎似乎与流场的小尺度相干结构相关.采用传统的OPD均方差或加权均方差值估算获得的斯特列尔比的误差较大，更为准确的方法应该通过计算PSF来进行评估.     

STUDY OF OPTICAL PUMPING OF ALKALI ATOMIC BEAM IN STRONG MAGNETIC FIELDS

We have gained a very comprehensive set of results for infrared diffraction (10.6μm wavelength) from fabricated single grooves of reflection with widths in the range of 5μm to 65μm. The experimental results show that the diffraction can still occur when the groove width becomes comparable to or less than the wavelength of the probing light. Variations of the diffraction intensities have a very regular sinusoidal relationship with the polarization angle of the incident light; and the diffraction intensities are the when the incident light is TM polarized. However, the diffraction intensities will be a minimum when the incident light is TE polarized; and the biger the diffraction angle, the higher the rate of change of the diffractive intensity with increasing polarization angle of the incident light.     

Localization of Spherical Particles under the Action of Gradient Forces in the Field of a Zero-Order Bessel Beam. Rayleigh–Gans Approximation

The amplitude of the gradient force acting on a transparent spherical particle in the field of a zero-order Bessel beam has been calculated in the Rayleigh–Gans approximation. The expression obtained for the gradient-force amplitude takes into account the heterogeneity of the acting radiation in the volume of the particle. The optimal conditions of trapping and transportation of the particle (parameters of the particle, liquid, and of the Bessel beam) to the localization region have been determined using the solution of the kinetic equation of particle motion in a liquid. It is shown that for certain relationships between the particle radius and the Bessel beam width the localization region is shifted relative to the central maximum of the beam. This is due to the equal action of the gradient forces caused by the central maximum and the first interference ring of the Bessel beam. A qualitative comparison of the results obtained with the known experimental data has been performed.     

Soliton-Like Bi-plasma Polaron

In the framework of phonon-plasmon cooperative effect mechanism, the differential equation for the wavefunction of the travelling soliton-like bi-plasma polaron (BPP) is derived. Then it is proven that the solution can be simply one-dimensional form. Meanwhile, the velocity range of the travelling soliton-like BPP is studied, thereby, we found that the quantity η=ε_∞/ε₀ of the materials, where the travelling soliton-like BPP can exist, should be very small, i.e. η→0. This result is consistent with the recently reported ones. Finally, an analytic approximation solution is given.     

Method for solving the nonlinear diffusion equation

We discuss the properties of the nonlinear diffusion equation which was presented for the approximation of high-concentration arsenic and boron profiles. Typical features of the profile are a flat region near the surface, a decreasing intermediate region and a tail region dropping sharply down compared with an error function complement. Earlier the nonlinear equation of the diffusion where the diffusion coefficient is directly proportional to the concentration of the impurities has been proposed. This proposal has been made on the theoretical assumption that diffusion is the result of Brownian movement and must occur with a finite velocity.     

快速H+2在固体中穿行时产生的动力学相互作用力及库仑爆炸图形的演化

模拟了快速H⁺₂在固体中穿行时产生的库仑爆炸过程．作用在单个氢离子H⁺上的力分别由阻止力、屏蔽的库仑力及尾力所组成．借助于等离子-极点近似介电函数,屏蔽的库仑力和尾力可由线性介电响应理论来确定．假定在初始入射时分子轴相对入射速度方向的取向是随机的．模拟结果表明：由于动力学相互作用力的影响,分子离子在穿行过程中其分子轴的取向明显地偏向于入射速度的方向. 关键词：     

An approximate method of predicting the response of periodically supported beams subjected to random convected loading

The space-averaged response of an infinite, elastically supported, periodic beam subjected to convected random loading has been studied by using an approximate “assumed mode” method. The complex wave motion in the beam is represented by any number of suitably chosen complex modes. With a good, yet simple, choice of mode which satisfies certain boundary conditions on one periodic beam element, a “single mode approximation” can yield very accurate values of the average response. This has been verified for a wide range of the support stiffnesses and loading convection velocities. Consideration has also been given to the ratio of the maximum response in the beam to the space-averaged response. The method has been applied only to uniform beams in this paper, but it should be readily applicable to periodic systems consisting of non-uniform beam elements.     

随机粗糙度对风力机翼型气动性能影响

建立人工神经网络、径向基函数网络和支持向量回归机三种近似模型,结合蒙特卡洛方法与表征粗糙度参数随机特性的概率模型对风力机翼型气动性能进行不确定性分析。结果表明,支持向量回归机具有最佳预测精度。对于风力机翼型FX 63-137,最大升力系数对吸力面前缘粗糙度的敏感性明显高于压力面;对于吸力面或压力面,前缘粗糙带厚度对最大升力系数的影响稍大于其覆盖长度的影响。研究工作为风力机翼型的鲁棒性设计优化奠定了理论基础。     

Moment excitation and the measurement of moment mobilities

Frequency response functions (FRF), such as mobilities, are widely used in the analysis of vibration and structure-borne sound and it is important that this FRF data can be measured accurately for all important degrees of freedom. In some cases three translational and three rotational components of both excitation and response may be of importance; i.e. three forces and moments, and three velocities and angular velocities. Of these, the measurement of angular velocity due to moment excitation is one of the most challenging. This paper describes a known approach, sometimes referred to as the central difference method, which can be used for this purpose. The central difference method is thought to be one of the most practicable methods for measuring moment mobilities because it avoids the need for a moment exciter; instead finite differences are used to approximate the moment mobility which is a spatial derivative of the more easily measured velocity to force mobility ratio. There does however remain some doubt regarding the accuracy of the central difference method because of the finite difference approximation made and the method's possible susceptibility to random and bias errors. To better understand the finite difference error, an error analysis using a Taylor series expansion and simulated experiments for plate and beam structures are provided. It is then argued that random and bias errors associated with the measurement chain should now, with modern instrumentation, be less of a problem. An experimental validation of the method using two approaches is used to test this hypothesis. It is concluded that the central difference method provides a good balance between measurement effort and data quality making it widely applicable.     

An improved approximation of Bergmann's form for the Rayleigh wave velocity

In the present paper an improved approximation for the Rayleigh wave velocity in isotropic elastic solids is obtained using the method of least squares. It is of Bergmann’s form, i.e. the form of the ratio of two binomials. It is shown that this approximation is the best one of the Rayleigh wave velocity, in the sense of least squares, with respect to the class of functions whose elements are the ratio of two binomials. This approximation is much more accurate than Bergmann’s one. Its maximum percentage error is 10 times smaller than that of Bergmann’s. It is 7.6 times better than the one obtained recently by Royer and Clorennec [D. Royer, D. Clorennec, An improved approximation for the Rayleigh wave equation, Ultrasonics 46 (2007) 23–24]. An approximation of Bergmann’s form for the squared Rayleigh wave velocity is also derived and its maximum percentage error is 5 times smaller than that of Royer and Clorennec’s approximation. Some polynomial approximations with very high accuracy are also obtained.     

IONIZATION OF THE HYDROGEN NEGATIVE ION MOVING IN A UNIFORM MAGNETIC FIELD

The ionization of the travelling hydrogen negative ion with high velocity in a uniform magnetic field is discussed by using perturbation theory in the first approximation. The choice of the H -ion wave function is illustrated with emphasis. And it is shown that various wave functions of the H-ion affect calculation results. The theoretical cal-culation by using Rotenberg-Stein wave function with five parameters is consistent with the experimental results ob-tained by G. M. STINSON et a1. in 1969.     

Vibrational spectra of AlN/GaN superlattices: Theory and experiment

Computer simulation of the dynamics of layered AlN/GaN superlattices is performed to elucidate the microscopic nature of the vibrational states corresponding to the strongest bands in the Raman spectra. Experimental Raman spectra are shown to consist of two groups of lines, one of which exhibits a two-mode behavior and the other shows a one-mode behavior as the relative layer thicknesses are varied. The results of computer simulation and calculations within the dielectric-continuum approximation suggest that the behavior of the observed vibrational modes is dictated by the degree of their localization and that the interlayer coupling is due to long-range dipole-dipole interactions. It is shown that the delocalized modes, which exhibit one-mode behavior, can be used as a sensitive probe of the structure and composition of superlattices.