A velocity matching car-following model on a closed ring in which overtaking is allowed

Car-following models seek to describe the behaviour of a group of vehicles as they move along a stretch of road. In such models the behaviour of each vehicle is taken to be dependant on the motion of the vehicle in front and overtaking is not permitted. In this paper the effect of removing this ‘no-overtaking’ restriction is investigated. The resulting model is described in terms of a set of coupled time delay differential equations and these are solved numerically to analyse their post-transient behaviour under a periodic perturbation. For certain parameter choices this behaviour is found to be chaotic, and the degree of chaos is estimated using the Grassberger–Procaccia dimension.     

Chaotic vibration of a nonlinear full-vehicle model

The present work investigates the chaotic responses of a nonlinear seven degree-of-freedom ground vehicle model. The disturbances from the road are assumed to be sinusoid and the time delay between the disturbances is investigated. Numerical results show that the responses of the vehicle model could be chaotic. With the bifurcation phenomenon detected, the chaotic motion is confirmed with the dominant Lyapunov exponent. The results can be useful in dynamic design of a vehicle.     

ONE-DIMENSIONAL CELLULAR AUTOMATON MODEL OF TRAFFIC FLOW BASED ON CAR-FOLLOWING IDEA

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A spatial motion analysis model of tracked vehicles with torsion bar type suspension

A spatial motion analysis model for high-mobility tracked vehicles was constructed for evaluation of ride performance, steerability, and stability on rough terrain. Ordinary high-mobility tracked vehicles are equipped with independent torsion bar type suspension system, which consists of road arms and road wheels. The road arm rotates about the axis of torsion bar, and rigidity of the torsion bar and cohesion of damper absorb sudden force change exerted by interaction with the ground. The motion of the road arms should be considered for the evaluation of off-road vehicle performance in numerical analysis model. In order to obtain equations of motion for the tracked vehicles, the equations of motion for the vehicle body and for the assembly of a road wheel and a road arm were constructed separately at first. Two sets of equations were reduced with the constraint equations, which the road arms are mechanically connected to the vehicle body. The equations of motion for the vehicle have been expressed with minimal set of variables of the same number as the degrees of freedom for the vehicle motion. We also included the effect of track tension in the equations without constructing equations of motion for the tracks. Numerical simulation based on the vehicle model and experiment of a scale model passing over a trapezoidal speed bump were performed in order to examine the numerical model. It was found that the numerical results reasonably predict the vehicle motion.     

具有局部非线性动力系统周期解及稳定性方法

对于具有局部非线性的多自由度动力系统，提出一种分析周期解的稳定性及其分岔的方法该方法基于模态综合技术，将线性自由度转换到模态空间中，并对其进行缩减，而非线性自由度仍保留在物理空间中在分析缩减后系统的动力特性时，基于Ｎｅｗｍａｒｋ法的预估－校正－局部迭代的求解方法，与Ｐｏｉｎｃａｒé映射法相结合，推导出一种确定周期解，并使用Ｆｌｏｑｕｅｔ乘子判定其稳定性及分岔的方法     

考虑胎路多点接触的电动汽车?路面耦合系统振动分析

轮毂电机驱动电动汽车的簧下质量大, 使得轮胎动载荷增加, 且电机激励进一步加剧车轮振动. 同时, 轮胎与路面单点接触的简化模型, 其动力学计算结果与实际存在差别. 鉴于此, 考虑电机的电磁激励、胎路多点接触和非线性地基, 建立了电动汽车?路面系统机电耦合动力学模型, 通过Galerkin法推导了非线性地基梁的垂向振动, 利用积化和公式推导了非线性地基梁中非线性项积分的精确表达式, 提出了路面截断阶数选取的简易方法, 并通过路面位移响应的收敛性进行了验证. 在此基础上, 研究了胎路多点接触、非线性地基、电机激励、车速、路面不平顺幅值等对路面及车辆响应的影响. 结果表明, 非线性地基及多点接触对车辆响应的影响中, 轮胎动载荷的影响最大, 车身加速度和悬架动挠度的影响较小, 且考虑电机激励时, 二者对车辆响应的影响显著增大. 从对路面响应的影响看, 电机激励的影响最大, 非线性地基的影响次之, 多点接触的影响较小. 所建模型及研究方法可为电动汽车的垂向动力学分析提供一种新思路.      

Analysis of the lateral dynamics of a vehicle and driver model running straight ahead

In this paper, we show that even an extremely simple nonlinear vehicle and driver model can show complex behaviors, like multi-stability and sensible dependence on the initial condition. The mechanical model of the car has two degrees of freedom, and the related equations of motion contain the nonlinear characteristics of the tires. The driver model is described by a single (nonlinear) equation, characterized by three parameters that describe how the driver steers the vehicle. Namely such parameters are the gain (steering angle per lateral deviation from desired path), the preview distance, and the reaction time delay. Bifurcation analysis is adopted to characterize straight ahead motion at different speeds, considering separately the two cases of understeering or oversteering cars. In the first case, we show that at suitable speeds the model can have three different attracting oscillating trajectories on which the system can work and that are reached due to different disturbances. In the second case, we confirm that instability arises if the forward speed is too high. The final results of the paper, bifurcation diagrams, can be used for many considerations critical both from the theoretical and from the practical viewpoints.     

THREE DIMENSIONAL MODELING AND DYNAMIC ANALYSIS OF FOUR—WHEEL—STEERING VEHICLES

The paper presents a nonlinear dynamic model of 9 degrees of freedom for four-wheel-steering vehicles. Compared with those in previous studies, this model includes the pitch and roll of the vehicle body, the motion of 4 wheels in the accelerating or braking process, the nonlinear coupling of vehicle body and unsprung part, as well as the air drag and wind effect. As a result, the model can be used for the analysis of various maneuvers of the four-wheel-steering vehicles. In addition, the previous models can be considered as a special case of this model. The paper gives some case studies for the dynamic performance of a four-wheel-steering vehicle under step input and saw-tooth input of steering angle applied on the front wheels, respectively. The project supported by the National Natural Science Foundation of China (59625511)     

Nonlinear dynamic analysis of a quarter vehicle system with external periodic excitation

In this paper, a nonlinear dynamic model of a quarter vehicle with nonlinear spring and damping is established. The dynamic characteristics of the vehicle system with external periodic excitation are theoretically investigated by the incremental harmonic balance method and Newmark method, and the accuracy of the incremental harmonic balance method is verified by comparing with the result of Newmark method. The influences of the damping coefficient, excitation amplitude and excitation frequency on the dynamic responses are analyzed. The results show that the vibration behaviors of the vehicle system can be control by adjusting appropriately system parameters with the damping coefficient, excitation amplitude and excitation frequency. The multi-valued properties, spur-harmonic response and hardening type nonlinear behavior are revealed in the presented amplitude-frequency curves. With the changing parameters, the transformation of chaotic motion, quasi-periodic motion and periodic motion is also observed. The conclusions can provide some available evidences for the design and improvement of the vehicle system.     

悬索在考虑1:3内共振情况下的动力学行为

研究了悬索在受到外激励作用下考虑1∶3内共振情况下的两模态非线性响应.对于一定范围内悬索的弹性-几何参数而言,悬索的第三阶面内对称模态的固有频率接近于第一阶面内对称模态固有频率的三倍,从而导致1∶3内共振的存在.首先利用Galerkin方法把悬索的面内运动方程进行离散,然后利用多尺度法对离散的运动方程进行摄动得到主共振情况下的平均方程.接下来对平均方程的稳态解、周期解以及混沌解进行了研究.最后利用Runge-Kutta法研究了悬索两自由度离散模型的非线性响应.     

Nonlinear oscillations and chaotic motions in a road vehicle system with driver steering control

The nonlinear dynamics of a differential system describing the motion of a vehicle driven by a pilot is examined. In a first step, the stability of the system near the critical speed is analyzed by the bifurcation method in order to characterize its behavior after a loss of stability. It is shown that a Hopf bifurcation takes place, the stability of limit cycles depending mainly on the vehicle and pilot model parameters. In a second step, the front wheels of the vehicle are assumed to be subjected to a periodic disturbance. Chaotic and hyperchaotic motions are found to occur for some range of the speed parameter. Numerical simulations, such as bifurcation diagrams, Poincaré maps, Fourier spectrums, projection of trajectories, and Lyapunov exponents are used to establish the existence of chaotic attractors. Multiple attractors may coexist for some values of the speed, and basins of attraction for such attractors are shown to have fractal geometries.     

Chaotic attitude and reorientation maneuver for completely liquid-filled spacecraft with flexible appendage

The present paper investigates the chaotic attitude dynamics and reorientation maneuver for completely viscous liquid-filled spacecraft with flexible appendage. All of the equations of motion are derived by using Lagrangian mechanics and then transformed into a form consisting of an unperturbed part plus perturbed terms so that the system＇s nonlinear characteristics can be exploited in phase space. Emphases are laid on the chaotic attitude dynamics produced from certain sets of physical parameter values of the spacecraft when energy dissipation acts to derive the body from minor to major axis spin. Numerical solutions of these equations show that the attitude dynamics of liquid-filled flexible spacecraft possesses characteristics common to random, non- periodic solutions and chaos, and it is demonstrated that the desired reorientation maneuver is guaranteed by using a pair of thruster impulses. The control strategy for reorientation maneuver is designed and the numerical simulation results are presented for both the uncontrolled and controlled spins transition.     

基于分数阶磁流变液阻尼器模型的车辆悬架组合控制

磁流变液阻尼器的分数阶Bingham模型结构形式简单, 而且可以更好地描述系统的滞回特性. 建立了含有分数阶Bingham模型的单自由度1/4车辆悬架系统模型, 利用磁流变液阻尼器对在路面简谐激励下的非线性车辆悬架系统进行振动控制. 研究了含有分数阶Bingham模型的悬架系统在天棚阻尼半主动控制下的主共振响应, 利用平均法得到了系统的近似解析解. 求解了系统定常解的幅频响应方程, 并根据李雅普诺夫稳定性理论得到了悬架系统的稳定性条件. 通过绘制数值解和解析解的幅频响应曲线对比图, 验证了近似解析解的正确性. 利用簧载质量垂直方向的加速度均方根值分析了半主动控制对车辆乘坐舒适性的影响, 发现天棚阻尼半主动控制策略在低频激励区域反而会降低车辆的乘坐舒适性. 因此提出了一种被动控制与半主动控制相结合的组合控制策略, 并分析了半主动控制参数对振动控制效果的影响. 分析结果表明, 该组合控制策略不但能够提高车辆的乘坐舒适性, 而且能有效抑制悬架系统的主共振振动幅值.      

Chaotic Motion in a Spinning Spacecraft with Circumferential Nutational Damper

The dynamics of a simplified model of a spinning spacecraft with a circumferential nutational damper is investigated using numerical simulations for nonlinear phenomena. A realistic spacecraft parameter configuration is investigated and is found to exhibit chaotic motion when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitude and frequency. Such a torque, in practice, may arise in the platform of a dual-spin spacecraft under malfunction of the control system or from an unbalanced rotor or from vibrations in appendages. The equations of motion of the model are derived with Lagrange's equations using a generalisation of the kinetic energy equation and a linear stability analysis is given. Numerical simulations for satellite parameters are performed and the system is found to exhibit chaotic motion when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitude and frequency. The motion is studied by means of time history, phase space, frequency spectrum, Poincaré map, Lyapunov characteristic exponents and Correlation Dimension. For sufficiently large values of torque amplitude, the behaviour of the system was found to have much in common with a two well potential problem such as a Duffing oscillator. Evidence is also presented, indicating that the onset of chaotic motion was characterised by period doubling as well as intermittency.     

The influence of strong crosswinds on safety of different types of road vehicles

Strong crosswinds have a great influence on the safety of road vehicles. Different vehicle types may have different behavior under strong crosswinds, thereby leading to different dominant accident modes and accident risks. In order to compare the crosswind stability of road vehicles, a probabilistic method based on reliability analysis has been applied in this paper. The crosswind is simulated as a stochastic gust model with nonstationary wind turbulence. The vehicles are classified into several categories. For each vehicle type, a worst case vehicle model and the corresponding aerodynamic coefficients have been identified. Dominant accident modes and failure probabilities have been computed and are compared. The influence of road conditions (dry/wet) and wind directions on the crosswind stability has been taken investigated. The proposed model makes it possible to compare the effect of crosswind on different vehicle types based on a risk analysis.

     

Complicated nonlinear responses of a simply supported FGM rectangular plate under combined parametric and external excitations

In this paper, we use the asymptotic perturbation method based on the Fourier expansion and the temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported rectangular plate made of functionally graded materials (FGMs) subjected to a through-thickness temperature field together with parametric and external excitations. Material properties are assumed to be temperature-dependent. Based on the Reddy’s third-order plate theory, the governing equations of motion for the plate are derived using the Hamilton’s principle. The Galerkin procedure is employed to obtain a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms. The resonant case considered here is 1:2 internal resonance, principal parametric resonance-1/2 subharmonic resonance. Based on the averaged equation in polar coordinate form, the stability of steady state solutions is analyzed. The phase portrait, waveform and Poincaré map are used to analyze the periodic and chaotic motions of the FGM rectangular plate. It is found that the FGM rectangular plate exhibits the chaotic motions under certain circumstances. It is seen that the nonlinear dynamic responses of the FGM rectangular plate are more sensitive to transverse excitation. The excitation force can be used as a controlling factor which can change the response of the FGM rectangular plate from periodic motion to the chaotic motion.     

Dynamic buckling of a beam with transverse constraints

A nonlinear dynamic system with continuously distributed mass is studied using several approaches: experimentally, numerically as well as analytically. The nonlinearity of the system consists of geometrical constraints imposed on the motion. It is harmonically loaded and it is demonstrated that for certain choices of the loading parameters, periodic, quasi-periodic or chaotic behaviour may occur depending on the initial conditions. An important issue is to investigate the number of degrees of freedom needed in order to analytically model the system accurately enough that the important characteristics of the motion are retained in the solution. It is found that the impact conditions at the constraints are of crucial importance and a new approach is proposed for modelling of the impacts. The method is based on the fact that the free motion can be approximated with quite a few degrees of freedom, while at impact all the infinite number of degrees of freedom are considered.     

Order and chaos in a new 3D dynamical model describing motion in non-axially symmetric galaxies

We present a new dynamical model describing 3D motion in non-axially symmetric galaxies. The model covers a wide range of galaxies from a disk system to an elliptical galaxy by suitably choosing the dynamical parameters. We study the regular and chaotic character of orbits in the model and try to connect the degree of chaos with the parameter describing the deviation of the system from axial symmetry. In order to obtain this, we use the Smaller ALingment Index (SALI) method to extensive samples of orbits obtained by integrating numerically the equations of motion, as well as the variational equations. Our results suggest that the influence of the deviation parameter on the portion of chaotic orbits strongly depends on the vertical distance z from the galactic plane of the orbits. Using different sets of initial conditions, we show that the chaotic motion is dominant in galaxy models with low values of z, while in the case of stars with large values of z the regular motion is more abundant, both in elliptical and disk galaxy models.