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.      

地震作用下主-从结构的被动优化控制研究

提出了一种利用主－从结构间的相互作用来减少在地震作用下结构响应的控制方法。该方法通过优化设计主－从结构间的被动耗能单元,最大限度地耗散结构的相对振动能量能减小主、从结构的整体振动水平,或最大限度地吸收主结构的相对振动能量以减小主结构的振动。文章首先导出了在平稳白噪声激励下被动耗能单元优化刚度和阻尼的一般表达式,并分析了不同结构参数对控制效果的影响,比较了在不同的平稳过滤白噪声激励下主－从结构相对位     

基于胡聿贤谱的带支撑广义Maxwell阻尼隔震结构随机响应分析

工程中通过设置支撑将阻尼器和建筑结构连接, 但常为了简化分析, 将支撑的水平刚度看成无穷大, 即不考虑支撑对耗能结构随机地震响应的影响. 实际上, 考虑有限水平刚度的支撑对耗能结构响应的影响更加符合工程实际, 为考虑支撑影响的广义Maxwell耗能隔震结构在胡聿贤谱地震激励下的响应分析, 提出一种求解随机地震响应的简明解析解法. 将带支撑广义Maxwell阻尼器等效本构关系、隔震结构运动方程以及胡聿贤谱滤波方程联合组成非经典阻尼系统, 运用复模态法对该非经典阻尼系统解耦, 通过不同响应模态获得耗能隔震系统系列响应基于白噪声激励的Duhamel积分表达式; 利用Dirac函数的性质, 将系统系列响应协方差简化为无积分运算的表达式, 根据功率谱密度函数与其协方差函数的Wiener-Khinchin关系, 得到耗能隔震系统系列响应功率谱和地面加速度功率谱, 基于随机振动理论中谱矩的定义, 得到耗能隔震系统系列响应0 ~ 2阶谱矩. 算例通过与虚拟激励法对比分析, 验证所提方法在该耗能隔震系统分析的正确性和高效性, 并讨论了不同支撑刚度对阻尼器减震效果的影响.      

A further investigation about a simple model of the hunting behavior of some old locomotives

This study is concerned with forced damped purely nonlinear oscillators and their behaviour at different excitation frequencies. First, their dynamics is considered numerically for the response determined in the vicinity of a backbone curve with the aim of detecting coexisting responses that have not been found analytically so far. Both the cases of low and high excitation amplitudes are investigated. Second, the angular excitation frequency is lowered significantly for different powers of nonlinearity, and the system’s behaviour is examined qualitatively, which has not been considered previously related to a general class of purely nonlinear oscillators. It is illustrated that the response at a low-valued angular excitation frequency has a form of bursting oscillations, consisting of fast oscillations around a slow flow. Finally, approximate analytical solutions are presented for the slow and fast flow for a general class of purely nonlinear oscillators.     

Planar nonlinear dynamic analysis of cable-stayed bridge considering support stiffness

Support stiffness is one of important factors on structure dynamics. Considering the vertical support stiffness, a multi-cable-stayed shallow-arch model of the cable-stayed bridge is established. Its differential equation governing the planar motion of cables and the shallow arch and the boundary conditions are derived by Hamilton’s principle. Firstly, the in-plane free vibration of the system is explored in order to find the modal functions and the possible internal resonances of nonlinear dynamics. Then, the 1:2:2 internal resonance among the different modes of the shallow arch and two cables are investigated by the multiple time scale method and pseudo-arclength algorithm. Meanwhile, the frequency-/force–response curves are used to explore the nonlinear behaviors of the system, especially the influence of vertical support stiffness, excitation frequency and amplitude on the internal resonance of the system is considered. To a certain extent, the support stiffness can reduce the response amplitudes of members by absorbing some energy from excitation.

     

逆压电效应对双稳态压电俘能器的性能影响研究

为了研究逆压电效应对压电俘能效果的具体影响,本文首先分析了双稳态压电俘能器的分布参数型能量表达式,然后应用广义Hamilton变分原理推导了该俘能系统的动力学方程,最后采用谐波平衡法获得了动力响应解析解。通过对比不同激励频率下的数值仿真结果,讨论了逆压电效应对俘能系统动力响应的影响规律。结果表明,逆压电效应在不同工况下对俘能效果的影响并非单纯起抑制作用,在一定激励强度的高频激励下,逆压电效应对俘能效果的影响起增强作用;弱强度激励下的俘能效果则全程受到抑制作用。     

Stability and instability of controlled motions of a two-mass pendulum of variable length

The problem of parametric control of plane motions of a two-mass pendulum (swing) is considered. The swing model is a weightless rod with two lumped masses one of which is fixed on the rod and the other slides along it within bounded limits. The control is the distance from the suspension point to the moving point. The proposed control law of swing excitation and damping consists in continuously varying the pendulumsuspension length depending on the phase state. The stability of various controlled motions, including the motions near the upper and lower equilibria, is studied. The Lyapunov functions that prove the asymptotic stability and instability of the pendulum lower position in the respective cases of the pendulum damping and excitation are constructed for the proposed control law. The influence of the viscous friction forces on the pendulum stable motions and the onset of stagnation regions in the case of its excitation is analyzed. The theoretical results are confirmed by graphical representation of the numerical results.     

Interaction of subway LIM vehicle with ballasted track in polygonal wheel wear development

This paper develops a coupled dynamics model for a linear induction motor (LIM) vehicle and a subway track to investigate the influence of polygonal wheels of the vehicle on the dynamic behavior of the system. In the model, the vehicle is modeled as a multi-body system with 35 degrees of freedom. A Timoshenko beam is used to model the rails which are discretely supported by sleepers. The sleepers are modeled as rigid bodies with their vertical, lateral, and rolling motions being considered. In order to simulate the vehicle running along the track, a moving sleeper support model is introduced to simulate the excitation by the discrete sleeper supporters, in which the sleepers are assumed to move backward at a constant speed that is the same as the train speed. The Hertzian contact theory and the Shen- Hedrick-Elkins’ model are utilized to deal with the normal dynamic forces and the tangential forces between wheels and rails, respectively. In order to better characterize the linear metro system (LMS), Euler beam theory based on modal superposition method is used to model LIM and RP. The vertical electric magnetic force and the lateral restoring force between the LIM and RP are also taken into consideration. The former has gap-varying nonlinear characteristics, whilst the latter is considered as a constant restoring force of 1 kN. The numerical analysis considers the effect of the excitation due to polygonal wheels on the dynamic behavior of the system at different wear stages, in which the used data regarding the polygonal wear on the wheel tread are directly measured at the subway site.     

Multiple Internal Resonance in Suspended Cables under Random In-Plane Loading

The random excitation of a suspended cable with simultaneous internal resonances is considered. The internal resonances can take place among the first in-plane and the first two out-of-plane modes. The external loading is represented by a wide-band random process. The response statistics are estimated using the Fokker-Planck-Kolmogorov (FPK) equation, together with Gaussian and non-Gaussian closures. Monte Carlo simulation is also used for numerical verification. The unimodal in-plane motion exists in regions away from the internal resonance condition. The mixed mode interaction is manifested within a limited range of internal detuning parameters, depending on the excitation power spectrum density and damping ratios. The Gaussian closure scheme failed to predict bounded solutions of mixed mode interaction. The non-Gaussian closure results are in good agreement with the Monte Carlo simulation. The on-off intermittency of the autoparametrically excited modes is observed in the Monte Carlo simulation over a small range of excitation levels. The influence of the cable parameters, such as damping ratios, sag-to-span ratio, internal detuning parameters, and excitation level on the autoparametric interaction, is studied. It is found that the internal detuning and excitation level are the two main parameters which affect the autoparametric interaction among the three modes. Due to the system's nonlinearity, the response of the three modes is strongly non-Gaussian and the coupled modes experience irregular modulation.     

Application of Special Nonsmooth Temporal Transformations to Linear and Nonlinear Systems under Discontinuous and Impulsive Excitation

Linear and nonlinear mechanical systems under periodic impulsive excitation are considered. Solutions of the differential equations of motion are represented in a special form which contains a standard pair of nonsmooth periodic functions and possesses a convenient structure. This form is also suitable in the case of excitation with a periodic series of discontinuities of the first kind (a stepwise excitation). The transformations are illustrated in a series of examples. An explicit form of analytical solutions has been obtained for periodic regimes. In the case of parametric impulsive excitation, it is shown that a nonequidistant distribution of the impulses with dipole-like temporal shifts may significantly effect the qualitative characteristics of the response. For example, the sequence of instability zones loses its different subsequences depending on the parameter of the shifts. It is shown that the method's applicability can be extended for nonperiodic regimes by involving the idea of averaging.     

Bifurcations and chaos in parametrically excited single-degree-of-freedom systems

The behavior of single-degree-of-freedom systems possessing quadratic and cubic nonlinearities subject to parametric excitation is investigated. Both fundamental and principal parametric resonances are considered. A global bifurcation diagram in the excitation amplitude and excitation frequency domain is presented showing different possible stable steady-state solutions (attractors). Fractal basin maps for fundamental and principal parametric resonances when three attractors coexist are presented in color. An enlargement of one region of the map for principal parametric resonance reveals a Cantor-like set of fractal boundaries. For some cases, both periodic and chaotic attractors coexist.     

多点非均匀调制演变随机激励下结构地震的响应

针对大跨度结构在非均匀调制演变随机激励作用下,考虑行波效应时的非平衡随机地震响应问题,应用虚拟激励法进行了分析,由于虚拟激励法自动计及了参振振型的互相关项以及激励之间的互相关项,理论上是精确解,时变功率谱的计算采用精细逐步积分格式,使计算效率进一步得到提高。     

Wave-induced liquefaction of a saturated sand layer

The paper presents a theoretical study of the dynamic liquefaction of a saturated sand layer. The motion of the sand is induced by a periodic disturbance at the lower boundary of the layer, which simulates the influence of a plane excitation wave coming from below. The initial boundary value problem is solved numerically with the use of the hypoplastic constitutive equation for particular sand. Both horizontal and vertical disturbances are considered. The repeated deformation caused by a strong dynamic disturbance results in the reduction of the effective pressure and in the liquefaction of the sand. The degree of liquefaction as a function of the depth is nonuniform. The liquefaction patterns produced by vertical and horizontal disturbances are completely different. Received February 22, 2000     

汽车行驶诱发地表振动的解析研究

本文从汽车动力学出发,建立 1/4 汽车与半空间地基耦合振动的动力学模型,并采用弹性滚子接触模型来反映轮胎包容性. 模型中同时考虑轮-地之间的纵向和竖向作用力,构建系统动力控制方程,利用 Fourier 和 Laplace 积分变换进行求解,推导出地表振动位移的解析解. 在数值算例中,利用离散傅里叶逆变换和 Crump 法进行数值反演,得出地表振动位移的空间分布,由此讨论了轮胎着地长度和轮-地相互作用力的变化规律,并对地表振动位移的参数影响作出分析. 结果表明,地面不平度对轮-地之间作用力的影响最为显著,地面越不平顺则轮-地作用力和地表振动位移越大. 车速对轮-地作用力的大小影响有限,但对载荷激励频率影响较大,车速增大则激励频率增大,地表振动位移随之增大. 在较低车速时,轮胎包容性对轮-地作用力和地表振动产生一定影响,轮胎充气压力增大,轮-地作用力和地表振动位移增大,但随着车速升高,这种影响将逐渐消失.      

ANALYTICAL STUDY ON GROUND VIBRATION INDUCED BY MOVING VEHICLE 1)

本文从汽车动力学出发,建立 1/4 汽车与半空间地基耦合振动的动力学模型,并采用弹性滚子接触模型来反映轮胎包容性. 模型中同时考虑轮-地之间的纵向和竖向作用力,构建系统动力控制方程,利用 Fourier 和 Laplace 积分变换进行求解,推导出地表振动位移的解析解. 在数值算例中,利用离散傅里叶逆变换和 Crump 法进行数值反演,得出地表振动位移的空间分布,由此讨论了轮胎着地长度和轮-地相互作用力的变化规律,并对地表振动位移的参数影响作出分析. 结果表明,地面不平度对轮-地之间作用力的影响最为显著,地面越不平顺则轮-地作用力和地表振动位移越大. 车速对轮-地作用力的大小影响有限,但对载荷激励频率影响较大,车速增大则激励频率增大,地表振动位移随之增大. 在较低车速时,轮胎包容性对轮-地作用力和地表振动产生一定影响,轮胎充气压力增大,轮-地作用力和地表振动位移增大,但随着车速升高,这种影响将逐渐消失.     

Vibro-acoustic behavior of an isotropic plate with arbitrarily varying thickness

This paper presents numerical simulation studies on the vibro-acoustic characteristics of an isotropic square plate with six different types of unidirectionally, arbitrarily varying thickness. Finite Element Method (FEM) is used to predict the free and forced vibration characteristics while Boundary Element Method (BEM) is used to predict the sound radiation characteristics. It is found that influence of taper ratio on mode shapes are significant. The resonant amplitude is influenced by changes in mode shapes along with excitation location. The influence of taper ratio and excitation location is significant on overall sound power level except for increasing-decreasing thickness variation. It is found that resonant amplitude and overall sound power level behavior is same for both linear and parabolic variation.     

Nonlinear Dynamics of Two-Degrees-of-Freedom Fluid Conveying Elasto-Visco-Plastic Model System

The local and global nonlinear dynamics of a two-degrees-of-freedom model system conveying fluid is studied. The undeflected model consistsof an inverted T formed by three rigid rods, with the tips of the twohorizontal rods resting on the viscous foundation. The foundationexhibits a visco-elasto-plastic response, including the Bauschingereffect. The vertical rigid rod of an annular cross-section is subjectedto a conservative (dead) force. Also, it conveys fluid having bothstatic and pulsation components. First, the method of multiple scales isused for the analysis of the local dynamics of the system withvisco-elastic response. Attention is focused on modal interactionphenomena in weak excitation at primary resonance and on hardsub-harmonic excitation. Two different asymptotic expansions areutilised to get a structural response for typical ranges of excitationparameters. Numerical integration of the governing equations is thenperformed to validate the results of asymptotic analysis in each case. Afull global nonlinear dynamics analysis of the visco-elasto-plasticsystem is performed. The role of plastic deformations in thedestabilisation of the system is discussed. Large-amplitude nonlinearoscillations of the visco-elasto-plastic system are studied, includingthe influence of material hardening and of static and periodiccomponents of pulsating fluid. Chaotic regimes of motion with andwithout plastic effects are considered. The results of the analysis maybe used in devices composed of a rather short tube connected to a notcompletely fixed foundation resting on the soil exhibitingelasto-plastic behaviour.     

Bursting phenomenon in a piecewise mechanical system with parameter perturbation in stiffness

In this paper the existence condition and generation mechanism of the possible bursting phenomenon in a piecewise mechanical system with different time scales are studied. As an example of mechanical systems, a piecewise linear oscillator with parameter perturbation in stiffness and subject to external excitation is examined. The order gaps between the time scales are considered in the model, which are related to the periodic excitation and the changing rates of the variables. The focus-type periodic bursting oscillation with two time scales is presented, and the corresponding generation mechanism is revealed by using slow–fast analysis method. Furthermore, the analytical solution of piecewise linear subsystem as well as the stability condition of the fast subsystem are explored to explain the transition of bursting behaviors coming from the variation of intrinsic parameter and external excitation. The results about bursting phenomenon and its generation mechanism would provide important theoretical basis on the mechanical manufacturing and engineering practice.     

Non-linear dynamics of the sandwich double circular plate system

Multi-frequency vibrations of a system of two isotropic circular plates interconnected by a visco-elastic layer that has non-linear characteristics are considered. The considered physical system should be of interest to many researches from mechanical and civil engineering. The first asymptotic approximation of the solutions describing stationary and no stationary behavior, in the regions around the two coupled resonances, is the principal result of the authors. A series of the amplitude-frequency and phase-frequency curves of the two frequency like vibration regimes are presented. That curves present the evolution of the first asymptotic approximation of solutions for different non-linear harmonics obtained by changing external excitation frequencies through discrete as well as continuous values. System of the partial differential equations of the transversal oscillations of the sandwich double circular plate system with visco-non-linear elastic layer, excited by external, distributed, along plate surfaces, excitation are derived and approximately solved for various initial conditions and external excitation properties. System of differential equations of the first order with respect to the amplitudes and the corresponding number of the phases in the first asymptotic averaged approximation are derived for different corresponding multi-frequency non-linear vibration regimes. These equations are analytically and numerically considered in the light of the stationary and no stationary resonant regimes, as well as the multi-non-linear free and forced mode mutual interactions, number of the resonant jumps.     

Numerical investigation of processes in strongly nonequilibrium Knudsen layers

Numerical solutions of model kinetic equations in Knudsen layers on surfaces with strong evaporation into the corresponding gas and excitation of internal degrees of freedom of the molecules are considered. It is shown that excitation of the molecules has a strong influence on the structure of the Knudsen layers and the parameters of the evaporating gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 72–81, May–June, 1981.