Free vibrations of a tire as a toroidal membrane

A tire is modeled as a toroidal membrane under internal pressure and mounted on a rim, to investigate its free vibration characteristics using a 12 d.o.f. rectangular membrane finite element. Such a modeling is valid if the tire is assumed to be incapable of supporting any weight in the absence of internal pressure. To verify the formulations of the membrane finite element, a flat rectangular membrane subject to in-plane loads and a circular cylindrical membrane under internal pressure are first analyzed. Analytical solutions for these cases are also derived. The analytical and numerical results are in good agreement. A toroidal membrane under internal pressure, assumed to model a low pressure tire, is studied next. Both the analytical derivation and the finite element solutions are presented. For the analytical solution the equations of motion yield a complicated differential equation for which an approximate solution is obtained by assuming that the parallel circle radius is constant as in the case of a bycycle wheel. The finite element solution successfully predicts the symmetrical and the twisting modes of vibration documented by other researchers, and is also in good agreement with the analytical results. The present formulations are useful to obtain a good first approximation of the free vibration response of a tire.     

Reducing slab track vibration into bridge using elastic materials in high speed railway

In this paper, the problem of vibration transmission from slab track structures into bridge is studied by theoretical analysis. A vehicle-track-bridge coupling system dynamics model is established based on a multibody dynamics theory and a finite element method. The system model consists of vehicle model, track-bridge model and wheel/rail interaction model. The vehicle model is established based on the multibody dynamics theory, and the tack-bridge model is established by the finite element method. The vehicle model and track-bridge model are coupled through wheel/rail interaction model, and the track irregularities are included. The system dynamic responses are calculated, and the effectiveness of elastic materials in vibration reducing is discussed. The results demonstrate that elastic materials like slab mat layer inserted between slab track and bridge can reduce vibration transmitted from track into the bridge. Some suggestions for the design and application of slab mat are provided in the end of the paper.     

Disk model for wheels moving over highway bridges with rough surfaces

In most previous analyses of vehicle-bridge interaction (VBI) problems in highways involving surface roughness, the wheels of vehicles have been treated as points, referred to as the point model, and the tracks as a series of hills and valleys. The point model is unrealistic for wheels, as they are of finite size and cannot touch the bottom of valleys. In this study, each wheel will be modeled instead as a rigid disk of finite size, referred to as the disk model, neglecting the tire deformations. The VBI element will be modified accordingly for computing the vehicle and bridge responses. Numerical examples are prepared to illustrate the effect of wheel size on the dynamic responses of the bridge and passing vehicles. It is concluded that the point model tends to introduce some unrealistic high-frequency vibrations on the system responses, while underestimating the amplitude of vehicle frequency in the vehicle response. The disk model should be adopted, if the velocity and acceleration responses of the bridge and the dynamic responses of the moving vehicle are of major concern.     

多振子梁弯曲振动中的局域共振带隙

从梁的弯曲振动方程出发,利用传递矩阵法,给出了无限周期结构的一维多振子声子晶体梁的弯曲振动能带结构,并利用有限元方法计算了有限周期结构梁的弯曲振动频率响应.建立了多振子声子晶体梁的简化模型,推导出带隙起始截止频率公式.结果表明:一维多振子声子晶体梁具有比单振子声子晶体梁更宽更丰富的振动带隙,可应用于呈倍频关系的减振降噪中;振动在带隙频率范围内频率响应具有明显的衰减;所建立的简化模型与理论模型结果符合较好.研究工作为梁类结构的减振提供一种新的思路.     

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.     

复式降噪块地铁车轮减振降噪特性

为探究一种复式降噪块装置及其组合形式对某S型辐板地铁车轮的减振降噪效果和机理,在半消声室内,分别对1种自由状态下的标准车轮和3种形式的复式降噪块车轮开展阻尼特性及振动声辐射特性试验,并通过有限元建模对其进行了模态计算。结果表明:复式降噪块装置可在全频段内提高车轮阻尼比,并对车轮各部位有良好的减振效果,以轮辋和踏面的减振效果最为显著;其中,6个制振阻尼片形式的降噪块对车轮的降噪效果最显著,径向激励下的降噪量为13.1 dB(A),轴向激励下的降噪量为11.1 dB(A),降噪频段主要集中在1000 Hz以上中高频。该文研究结果是对列车降噪研究领域的补充和发展。     

Semi-analytic solutions for the free in-plane vibrations of confocal annular elliptic plates with elastically restrained edges

A two-dimensional analytical model is developed to describe the free extensional vibrations of thin elastic plates of elliptical planform with or without a confocal cutout under general elastically restrained edge conditions, based on the Navier displacement equation of motion for a state of plane stress. The model has been simplified by invoking the Helmholtz decomposition theorem, and the method of separation of variables in elliptic coordinates is used to solve the resulting uncoupled governing equations in terms of products of (even and odd) angular and radial Mathieu functions. Extensive numerical results are presented in an orderly fashion for the first three anti-symmetric/symmetric natural frequencies of elliptical plates of selected geometries under different combinations of classical (clamped and free) and flexible boundary conditions. Also, the occurrences of “frequency veering” between various modes of the same symmetry group and interchange of the associated mode shapes in the veering region are noted and discussed. Moreover, selected 2D deformed mode shapes are presented in vivid graphical form. The accuracy of solutions is checked through appropriate convergence studies, and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data in the existing literature. The set of data reported herein is believed to be the first rigorous attempt to obtain the in-plane vibration frequencies of solid and annular thin elastic elliptical plates for a wide range of plate eccentricities.     

Vibration analysis of a wheel composed of a ring and a wheel-plate modelled as a three-parameter elastic foundation

The free in-plane vibrations of circular rings with wheel-plates as generalised elastic foundations are studied using analytical methods and numerical simulations. The three-parameter Winkler elastic layer is proposed as a mathematical model of the foundation. The effects of rotary inertia and shear deformation are included in the analytical model of the system. The motion equations of systems are derived on the basis of the thin ring theory and Timoshenko?s theory. The separation of variables method is used to find general solutions to the free vibrations. Elaborated analytical models are used to determine the natural frequencies and the natural mode shapes of vibrations of an arbitrarily chosen set of simplified models of aviation gears and railway wheels. The eigenvalue problem is formulated and solved by using a finite element representation for each simplified model. The results for these models are discussed and compared. The proposed solutions are verified by experimental investigation. It is important to note that the solutions proposed here could be useful to engineers dealing with the dynamics of aviation gears, railway wheels and other circular ring systems.     

瓦状阻尼橡胶块对高铁车轮减振降噪的影响分析

依据声学测试标准,为了评价某型高铁车轮在安装不同形式橡胶块装置后的减振降噪效果,在半消声室内基于B&K振动噪声测试分析系统,对裸轮和橡胶块车轮开展振动声辐射室内测试实验,并基于有限元方法对车轮模态进行了仿真分析。测试结果可知:相比裸轮,WA、WB车轮模态阻尼比显著增加,车轮的减振效果明显,其中WA车轮的减振效果略优于WB车轮。径向激励下,WA车轮声功率级降低了8 dB(A),WB车轮声功率级降低了5.5 d B(A);轴向激励下,WA车轮声功率级降低了8.2 dB(A),WB车轮声功率级降低了6.2 dB(A)。分析可知橡胶块装置能有效抑制车轮的滚动噪声和曲线啸叫,对车轮的减振降噪有积极作用。     

On the vibration transmission of a rolling tire on a suspension system due to periodic tread excitation

Several methods of modeling the vibration excitation of an automotive tire by its tread pattern were developed, ranging from a very simplified approach with an equivalent single point, single line scanning procedure to multi-point, multi-line scanning. This results in a periodic model, since even for a so called random tread pattern there is a periodicity corresponding to one tire revolution. Various tread profiles are explored and response spectra for forces and displacement at the suspension point are obtained and discussed. Receptances formulated in terms of the free tire shell modes are utilized. To contrast the force input type models of the tread excitation with the displacement type input of long road waves, the latter is also discussed briefly.     

阻尼贴片式高速列车车轮振动声辐射试验分析

为了研究辐板不同阻尼贴片装置对高速列车车轮的减振降噪效果,在半消声室内进行标准车轮与阻尼贴片式车轮自由状态下的振动声辐射试验研究,并基于有限元法对车轮模态进行了仿真计算。研究结果表明：施加辐板阻尼贴片后,两种阻尼贴片车轮的固有频率与标准车轮相比变化不大,但对于频率在1600Hz以上各阶模态阻尼比显著增加。径向与轴向激励下的降噪效果均达到10dB(A)以上,可见两种阻尼贴片装置均具有良好的降噪效果。其中在多了0.3mm铝合金薄板的情况下,W2车轮的降噪效果要略优于W1车轮,轴向激励下更加明显。     

A HYBRID MODEL FOR THE NOISE GENERATION DUE TO RAILWAY WHEEL FLATS

A numerical model is developed to predict the wheel/rail dynamic interaction occurring due to excitation by wheel flats. A relative displacement excitation is introduced between the wheel and rail that differs from the geometric form of the wheel flat due to the finite curvature of the wheel. To allow for the non-linearity of the contact spring and the possibility of loss of contact between the wheel and the rail, a time-domain model is used to calculate the interaction force. This includes simplified dynamic models of the wheel and the track. In order to predict the consequent noise radiation, the wheel/rail interaction force is transformed into the frequency domain and then converted back to an equivalent roughness spectrum. This spectrum is used as the input to a linear, frequency-domain model of wheel/rail interaction to predict the noise. The noise level due to wheel flat excitation is found to increase with the train speed V at a rate of about 20 log₀V whereas rolling noise due to roughness excitation generally increases at about 30 log₀V. For all speeds up to at least 200 km/h the noise from typical flats exceeds that due to normal levels of roughness. When the wheel load is doubled the predicted impact noise increases by about 3 dB.     

双层弹性支撑板的水下宽带隔声

为实现水下宽带隔声,提出了一种由弹性元件支撑两块刚性端板构成的双层弹性支撑板结构。采用弹簧振子振动分析法和声传播理论,建立了平面波入射的水下隔声理论模型,分析了结构参数对隔声量的影响规律,结果表明足够小的弹性元件单位面积弹性系数或足够大的端板单位面积质量都可以连续一致地提高隔声量.仿真分析了双层弹性支撑板的振动位移和声输入阻抗,比较了双层弹性支撑板与连续介质层的隔声特性,结果表明,降低弹性元件质量,有助于在低频段消除半波全透射现象.在同厚度、同质量、同静态压缩率条件下,双层弹性支撑板能更好的降低两侧流体的振动及声耦合,隔声频带更宽,带内一致性更好,隔声量更大.     

某型振动轮噪声数值模拟及优化分析

空中声源的辐射噪声谱包括宽带连续谱和窄带线谱,线谱能量高于连续谱。与水下声源相比,空中声源的运动速度普遍较高,线谱多普勒频移明显,可用于进行水下对空中声源的运动参数估计。首先通过时频分析提取接收信号的瞬时频率,而后利用非线性最小二乘法将瞬时频率提取值与预测值相拟合,进而估计声源的运动参数(声源的运动速度、静止频率、与接收器最小水平距离及经过最近点时刻)。仿真与实验均能较为准确地估计出声源运动参数,同时在实验中实现了水下对空中运动声源的测距和定位,测距误差小于15.8%。在满足一定信噪比和保证足够多普勒信息的情况下,该参数估计方法具有很好的适用性。     

Vibration analysis of automobile tire due to bump impact

The improvement of car driving comfort is requested according to development of automobile manufacturing technology. Therefore, many experts have been studying automotive vibration of normally driving cars to improve automotive driving comfort. In this paper, vibration characteristics of an automobile tire that passes a cleat are analyzed. The model for automobile tire is verified through numerical analysis and experimental method. The automobile tire is assumed to 7-degree of freedom system, and the effect on the proposed tire design factor is considered. This analysis result proved that the proposed tire design factor reduced tire and wheel vibration energy.     

旋转超声磨削平行砂轮复合变幅器设计与试验

为了获得大负载平行砂轮复合变幅器的设计方法,将复合变幅器简化为复合变幅杆与多阶环盘组成.利用Mindlin中厚板理论,求解了各振动环盘的位移、转角、弯矩和剪力解析表达式,通过复合变幅杆各振动单元间的力、位移的边界条件和连续条件,以及复合变幅杆和环盘两者结构间力与位移的耦合条件,建立了复合变幅器的数学模型和频率方程.针对...     

基于I-DEAS的某汽车车轮建模与分析

运用I-DEAS对某汽车车轮进行实体建模，并通过对汽车车轮的几何模型进行网格划分、确定边界条件，最后得到受力情况下的应力分布及变形特点。结果表明利用I-DEAS可以有效的对车轮进行受力分析。     

基于薄层单元与弹簧单元的滚动直线导轨副动力学建模

针对某大型光机装置中使用的LM型直线导轨-滑块的结合面,采用薄层单元与弹簧单元模拟其接触面,建立了大行程传输结构模拟件的有限元模型。通过模型修正方法,根据模态试验结果对薄层单元弹性模量以及弹簧刚度进行了识别。模型修正后,结构前三阶模态频率计算结果与试验结果最大差别为2.23%,地脉动载荷下各测点位移响应计算结果与试验结果最大差别为7.61%。计算结果与试验结果具有较好的一致性,验证了模型的有效性。     

Finite element modeling of heating phenomena of cracks excited by high-intensity ultrasonic pulses

A three-dimensional thermo-mechanical coupled finite element model is built up to simulate the phenomena of dynamical contact and frictional heating of crack faces when the plate containing the crack is excited by high-intensity ultrasonic pulses.In the finite element model,the high-power ultrasonic transducer is modeled by using a piezoelectric thermal-analogy method,and the dynamical interaction between both crack faces is modeled using a contact-impact theory.In the simulations,the frictional heating taking place at the crack faces is quantitatively calculated by using finite element thermal-structural coupling analysis,especially,the influences of acoustic chaos to plate vibration and crack heating are calculated and analysed in detail.Meanwhile,the related ultrasonic infrared images are also obtained experimentally,and the theoretical simulation results are in agreement with that of the experiments.The results show that,by using the theoretical method,a good simulation of dynamic interaction and friction heating process of the crack faces under non-chaotic or chaotic sound excitation can be obtained.     

厚圆盘弯曲振动研究

当厚跨比大于五分之一时,研究板弯曲振动中的剪切应力及由此引起的剪切、扭转变形等就不能忽略,经典的薄板理论将失效.从声学应用的角度,基于Mindlin板理论,本文推导了厚圆盘弯曲振动径向位移和横向位移的解析表达式,并得到了自由、简支、固定边界条件下的频率方程.解析方法计算得到的前几阶振型对应的频率与有限元方法计算的结果基本相符,与实验测试结果基本一致.本文的结果对厚圆盘弯曲振动辐射器的设计提供了理论参考. 关键词： 厚圆盘 弯曲振动 频率方程