Vibration suppression of a string through cyclic application and removal of constraints

A new method for the control of string vibration is presented. The method relies on application and removal of a constraint at one point on the string close to one of its boundaries. Application of the constraint temporarily results in two vibrating strings, one of which is significantly shorter in length than the other. The vibration of the shorter length string decays rapidly due to high damping and results in reduction in the overall energy of the system. Removal of the constraint does not change the energy of the system but allows the constraint to be applied repeatedly for vibration suppression. A mathematical model of the cycle of constraint application and removal is presented and multiple cycles of constraint application and removal are simulated. Experiments were performed with a coiled extension spring which behaves like a lightly damped string. Simulation and experimental results match well with each other and demonstrate the efficacy of the simple control strategy.     

Vibration of a string wrapping and unwrapping around an obstacle

The problem of a string vibrating against a smooth obstacle is investigated in this paper. The obstacle is located at one of the boundaries and the string is assumed to wrap and unwrap around the obstacle during vibration. The wrapping of the obstacle is modeled by a series of perfectly inelastic collisions between the obstacle and adjacent segments of the string and unwrapping is assumed to be energy conserving. The geometry of the string is determined iteratively starting from an initial configuration where the string is vibrating in a single mode and is not in contact with the obstacle. The obstacle can be regarded as a passive mechanism for vibration suppression in which the energy lost during each cycle of oscillation depends on the energy content of the string at the beginning of the cycle. Numerical simulation results are provided for the string vibrating in different modes for circular- and elliptic-shaped obstacles. The loss of energy is found to be greater for higher modes of oscillation and for obstacles that induce greater length of wrapping.     

Energy based simulation of a Timoshenko beam in non-forced rotation. Influence of the piano hammer shank flexibility on the sound

A nonlinear model for a vibrating Timoshenko beam in non-forced unknown rotation is derived from the virtual work principle applied to a system of beam with mass at the end. The system represents a piano hammer shank coupled to a hammer head. An energy-based numerical scheme is then provided, obtained by non-classical approaches. A major difficulty for time discretization comes from the nonlinear behavior of the kinetic energy of the system. This new numerical scheme is then coupled to a global energy-preserving numerical solution for the whole piano. The obtained numerical simulations show that the pianistic touch clearly influences the spectrum of the piano sound of equally loud isolated notes. These differences do not come from a possible shock excitation on the structure, or from a changing impact point, or a “longitudinal rubbing motion” on the string, since neither of these features is modeled in our study.     

Stability analysis of traffic flow with extended CACC control models

To further investigate car-following behaviors in the cooperative adaptive cruise control(CACC) strategy,a comprehensive control system which can handle three traffic conditions to guarantee driving efficiency and safety is designed by using three CACC models.In this control system,some vital comprehensive information,such as multiple preceding cars' speed differences and headway,variable safety distance(VSD) and time-delay effect on the traffic current and the jamming transition have been investigated via analytical or numerical methods.Local and string stability criterion for the velocity control(VC) model and gap control(GC) model are derived via linear stability theory.Numerical simulations are conducted to study the performance of the simulated traffic flow.The simulation results show that the VC model and GC model can improve driving efficiency and suppress traffic congestion.     

Cooperative adaptive bidirectional control of a train platoon for efficient utility and string stability

This paper proposes cooperative adaptive control schemes for a train platoon to improve efficient utility and guarantee string stability. The control schemes are developed based on a bidirectional strategy, i.e., the information of proximal(preceding and following) trains is used in the controller design. Based on available proximal information(prox-info) of location, speed, and acceleration, a direct adaptive control is designed to maintain the tracking interval at the minimum safe distance. Based on available prox-info of location, an observer-based adaptive control is designed to achieve the same target, which alleviates the requirements of equipped sensors to measure prox-info of speed and acceleration. The developed schemes are capable of on-line estimating of the unknown system parameters and stabilizing the closed-loop system, the string stability of train platoon is guaranteed on the basis of Lyapunov stability theorem. Numerical simulation results are presented to verify the effectiveness of the proposed control laws.     

基于比例积分控制原理预测钻井全过程原始地层温度的新方法研究

应用比例积分控制原理将瞬态传热模型预测结果与出口 温度实测数据逐步进行反馈可准确预测原始静态地层温度. 为此, 本文基于井下各控制组件质量、动量及能量守恒原理, 建立了实际井身结构与钻具组合条件下循环和停止循环期间井筒-地层温度分布全瞬态传热模型, 应用全隐式有限差分法进行求解, 并引入比例积分控制原理对比分析实测温度与预测温度的误差范围进而精确、 快速获取原始地层温度. 结合一口深井基础数据计算表明, 套管下入深度改变了井筒-地层间热交换效率, 进而影响了近井壁地层温度分布状况; 同时, 钻井过程中循环和停止循环作业过程改变了井下各控制组件的初始条件与边界条件, 致使近井壁原始地层温度分布距离产生变化. 建立的数学模型和研究方法可为石油钻井、地热井开采及地球深部原始地层温度信息准确、 经济、快速获取提供理论基础. 关键词： 原始地层温度 循环与停止循环 瞬态传热模型 比例积分控制原理     

Active vibration control in Duffing mechanical systems using dynamic vibration absorbers

This paper deals with the multi-frequency harmonic vibration suppression problem in forced Duffing mechanical systems using passive and active linear mass–spring–damper dynamic vibration absorbers. An active vibration absorption scheme is proposed to extend the vibrating energy dissipation capability of a passive dynamic vibration absorber for multiple excitation frequencies and, simultaneously, to perform reference position trajectory tracking tasks planned for the nonlinear primary system. A differential flatness-based disturbance estimation scheme is also described to estimate the unknown multiple time-varying frequency disturbance signal affecting the differentially flat nonlinear vibrating mechanical system dynamics. Some numerical simulation results are provided to show the efficient performance of the proposed active vibration absorption scheme and the fast estimation of the vibration disturbance signal.     

Vibration of strings with nonlinear supports

The dynamic string motion, which displacement is unilaterally constrained by the rigid termination condition of an arbitrary geometry has been simulated and analyzed. The treble strings of a grand piano usually terminate at a capo bar, which is situated above the strings. The apex of a V-shaped section of the capo bar defines the end of the speaking length of the strings. A numerical calculation based on the traveling wave solution is proposed for modeling the nonlinearity inducing interactions between the vibrating string and the contact condition at the point of string termination. It was shown that the lossless string vibrates in two distinct vibration regimes. In the beginning the string starts to interact in a nonlinear fashion with the rigid terminator, and the resulting string motion is aperiodic. Consequently, the spectrum of the string motion depends on the amplitude of string vibrations, and its spectral structure changes continuously with the passage of time. The duration of that vibration regime depends on the geometry of the terminator. After some time of aperiodic vibration, the string vibrations settle in a periodic regime where the resulting spectrum remains constant.     

时滞反馈控制扭转振动系统的振动

研究了采用时滞反馈来控制扭转振动系统的振动问题.在一个带有非线性动力吸振器的扭转振动系统中,采用时滞反馈来控制主系统的振动.研究了反馈增益系数和时滞对主系统振动的影响.研究结果表明,对某一固定的反馈增益系数,存在时滞的某段调节区间,可以通过调节时滞来抑制主系统的振动.在时滞的调节区间内存在一个最佳点,主系统的振动被抑制到最小值.可以同时调节反馈增益系数和时滞两参数,当反馈增益系数和时滞都调节到最佳值时,主系统振动的振幅由0.24减小到0.03,取得了很好的减振效果. 关键词： 时滞反馈 扭转振动 减振     

A self-adaptative oscillator

The dynamics of a system where a mass is free to slide on a vibrating string is investigated as the excitation frequency is varied. One degree of freedom is thus added to the system studied by Helmholtz in which a mass was fixed on a vibrating string. This new system exhibits a specific dynamics characterized by the existence of a self- adaptative behaviour. When the driving frequency falls into wide and well defined frequency bands, a long transient is observed by which the mass adjusts its position so that the whole system becomes resonant. In the gaps between these bands, bifurcations give other equilibrium positions. A theoretical model is proposed. It accounts for all the experimental results. In the case where two masses are present on the string, two degrees of freedom are added and the set of equilibrium positions would be expected to be infinite. However, in the experiment, the two masses are observed to go to positions where they are symmetrical with respect to the middle of the string. A selection mechanism due to the string stretching is pointed out. Received 15 October 1998     

Analysis of energy dissipation in an elastic moving string with a viscous damper at one end

In this paper transverse vibration of an axially moving viscoelastic string with a viscous damper at one end is investigated analytically. The string is assumed to be travelling with constant velocity and the length of string is constant or time varying. The linear and nonlinear mathematical models are derived using the Lagrangian function and implemented using a finite element method. The method considers a time varying state space function applied to the linear model, the Newmark-Beta method is used to solve the response for the nonlinear problem numerically. The case of energy dissipated by a viscoelastic damper at one end of the string for different axial string velocities is considered. When a disturbance arrives at the boundary an exact value for the damper which provides maximum energy dissipation is investigated. Finally, numerical simulations are presented to establish the feasibility of the method.     

Detection of defects in cylindrical structures using a time reverse method and a finite-difference approach

The detection and characterization of defects in structures is an important issue in non-destructive testing. To avoid the scanning of large samples, guided elastic waves, which propagate along the structure, are excited. These waves interact with a defect, which results in a scattered wave field. In an experiment, the displacements of these scattered waves are recorded over time for a fixed axial coordinate at a number of circumferential positions of a circular cylindrical tube. Since in complex structures it is difficult to determine the axial and particularly circumferential position of the defect directly from the time signals, a time reversed numerical simulation is performed. There the measured displacement histories are reversed in time and used as displacement excitations in a simulation of the tested structure. A three-dimensional code in cylindrical coordinates, based on a velocity-stress finite-difference method, is used to simulate the wave propagation. As long as the geometric and material parameters are chosen equivalent to the performed experiment, the scattered waves travel back through the simulated structure and interfere, even if no defect is present in the numerical model. The result is an increase of the amplitudes of the stress and displacement components at the location where the defect was in the tested sample.     

Non-destructive testing of tubes using a time reverse numerical simulation (TRNS) method

A method for the detection of defects in cylindrical structures and the determination of their positions and orientations is presented in this paper. The scattered field, which is generated by the interaction of excited guided waves with a defect, is evaluated with an approach named time reverse numerical simulation method (TRNS). Since the excited waves and the scattered field propagate along the sample, the time-consuming scanning of the whole tube can be eliminated. The scattered displacement field is measured in three dimensions over time with a laser vibrometer at different locations distributed equally around the circumference at a fixed axial coordinate far away from the defect. Instead of analyzing the complicated time signals directly, they are played back in time. If the recorded displacement histories of the scattered field are reversed in time and played back in an identical structure, the waves travel back the same path and interfere to a maximum at their origin. The result is an amplitude increase at the position of the defect where the scattered field was generated. Instead of playing back the recorded time signals in an experiment, this step is replaced by a numerical simulation. Only this enables the visualization and detection of the amplitude increase. As long as the simulation is of high accuracy, the position of the maximum interference corresponds exactly to the location of the defect in the experiment, although no defect is implemented in the simulation.     

基于声辐射模态的有源结构声传入及其辐射控制

从辐射模态的概念和角度研究利用结构误差传感方法对弹性封闭空间结构声辐射进行传感和有源控制。首先分析了辐射模态的数学和物理意义并揭示了辐射模态与声腔模态之间的内在耦合关系。通过声辐射模态建立了弹性封闭空间结构声辐射传感和有源控制模型,并提出了通过传感器阵列测量结构表面有限点的振速分布和设计特定的辐射模态空间滤波器来获得控制所需的误差信号。在此基础上对封闭空间结构声辐射有源控制和误差传感策略进行了深入的理论和数值仿真分析,重点讨论了传感器的数量和布放对辐射模态传感及其有源控制效果的影响。结果表明:辐射模态与声腔模态的耦合具有严格的选择性,各阶辐射模态的形状和与相耦合的主导声模态在耦合面上的形状非常相似;利用结构传感技术传感封闭空间的辐射模态时测点不足或空间采样不足将可能产生较严重的模态泄漏问题,使得不希望的结构模态泄露进所测的辐射模态当中来。在低频范围内,一般只需传感并最小化前三阶有效辐射模态声势能,在更低频和空间声模态频率附近,只需最小化前一阶最有效辐射模态声势能,便能和总声势能最小化策略控制效果基本一样。      

Numerical analysis of TOF measurements in pulsed laser ablation

The results of numerical simulation of pulsed laser ablation both in vacuum and into a background gas are presented. The influences of different processes, such as time evolution of the surface temperature, interspecies interactions (elastic collisions, recombination-dissociation reaction), interaction with an ambient gas, and excitations-relaxation processes on time-of-flight (TOF) distributions are examined. Experimentally obtained time-of-flight distributions are further analyzed, based on the results of numerical simulation. It is found that with the aid of numerical results one can explain not only the shape of the TOF distribution, but also the distance dependency of its maximum position (mean delay time). In addition, the mechanisms leading to the appearance of bimodal time-of-flight distribution are revealed. The study presents particular interest for the analysis of experimental results obtained during pulsed laser ablation.     

Mechanical characteristics of strained vibrating strings and a vibration-induced electric field

The mechanical characteristics of vibrating strings strained between rigid supports and a vibration-induced electric field are studied. Experiments are conducted with nylon, rubber, and metallic strings. Vibrations are excited by a pinch at different sites along the string. The motion of the string is filmed, and the attendant electric field is detected. Experimental data are analyzed under the assumption that the field is induced by unlike charges generated by the moving string. It is found that the field allows one to determine the time characteristics of the motion of the string and discriminate the types of its deformations. Young moduli observed under the static extension of thin nylon strings are compared with those calculated from the natural frequencies of vibration measured for differently strained strings. The mathematical pattern of the motion of the string is compared with the real situation.     

Designing musical structures using a constrained optimization approach

The paper discusses the application of numerical optimizing techniques to musical structures. It is shown that the natural tendency to emulate the instrument maker by optimizing the characteristic frequencies of the structure is not always the most appropriate strategy, and that in cases where one or more possible solutions exist it is more appropriate to specify the frequency requirements as a constraint. The strategy is illustrated using a xylophone bar.     

利用频域β-warping变换的浅海修正纯方位目标运动分析方法

针对纯方位目标运动分析方法收敛时间较长的问题,提出了一种利用频域β-warping变换的浅海修正纯方位目标运动分析方法.该方法利用频域β-warping变换从声强干涉结构中提取与目标距离成线性关系的时延,进而估计距离特征量,并利用距离特征量推导得到的目标状态向量的线性约束修正纯方位扩展卡尔曼滤波算法。数值仿真结果表明,对于浅海匀速直线运动目标,在信噪比不低于8 dB的情况下,与常规纯方位扩展卡尔曼滤波算法相比,改进算法将距离估计的收敛时间由26.5 min缩短至11.5 min.在浅海水平不变波导远场条件下,该方法可以快速稳定地估计距离特征量,并能够对目标进行可靠地跟踪定位。      

Simulation study on ramp inflow for hybrid autonomous driving

In view of the complexity of the ramp traffic system on the expressway and the diversity of hybrid automatic driving, the safety distance of vehicles and the corresponding car following model are analyzed based on the combination of driver’s personality characteristics and the characteristics of different automatic driving levels of the vehicle–road​ coordination system, and the risk model is established to screen the potentially dangerous vehicles in the ramp merging process. Based on game theory, this paper constructs a ramp coordination and merging control model suitable for hybrid automatic driving. The model takes the safety benefit and efficiency benefit as the objective function, predicts the benefit value under different strategies and makes the optimal strategy under the current conditions. The proposed model is verified by the joint simulation of Python and sumo. the simulation results show that the average number of combined vehicles is 1.91 times higher, the combined position is 50.11% earlier and the average driving time is 28.35% less than that without control strategy and there is obvious advantage when the density is high compared with vehicles without control strategy.     

自适应控制飞行光学聚焦特性

 在对高阶模飞行光学聚焦特性进行研究的基础上，提出了应用自适应飞行光学聚焦系统来解决飞行光学聚焦特性的问题，对自适应飞行光学聚焦系统的调节特性进行了数值模拟，结果表明该系统能够实现对长距离飞行光学激光加工过程中焦点位置与焦斑大小的控制。