考虑翘曲影响的Bernoulli-Euler薄壁梁的弯扭耦合振动

通过直接求解均匀薄壁梁单元弯扭耦合振动的运动偏微分方程，推导其自由振动时的精确动态传递矩阵。采用考虑翘曲影响的Bernoulli-Euler梁理论，且假定薄壁梁单元的横截面是单对称的。动态传递矩阵可以用于计算薄壁梁集合体的精确固有频率和模态形状。针对两个薄壁梁算例，采用自动Muller法和结合频率扫描法的二分法求解频率特征方程，并讨论翘曲刚度对弯扭耦合：Bernoulli-Euler薄壁梁固有频率的影响。数值结果验证了本文方法的精确性和有效性，并指出翘曲刚度可以显著改变薄壁开口截面梁的固有频率。     

[BIM模型与智能设计]中低速磁浮系统起浮阶段的振动特性分析

为了研究电磁悬浮（EMS）中低速磁浮系统在起浮阶段的悬浮稳定性问题,建立了“车辆-电磁-轨道梁”耦合系统动力学模型。利用仿真模型分析了EMS中低速磁浮系统在起浮阶段的振动响应特性,对比分析了弹性梁与刚性梁的振动差别,仿真分析了单级悬浮控制与双级悬浮控制的效果差异。结果表明：EMS中低速磁浮列车在弹性轨道梁上起浮时,容易发生悬浮失稳的异常振动现象,原因是单级悬浮控制模式的悬浮架自激振动频率激发了弹性轨道梁的固有频率,从而诱发了车轨剧烈耦合共振;提高轨道梁刚度或采用双级悬浮控制器模式,可以缓解EMS中低速磁浮系统起浮阶段异常振动引起的悬浮失稳现象。     

Bending and vibration of a discontinuous beam with a curvic coupling under different axial forces

The transverse stiffness and vibration characteristics of discontinuous beams can significantly differ from those of continuous beams given that an abrupt change in stiffness may occur at the interface of the former. In this study, the equations for the deflection curve and vibration frequencies of a simply supported discontinuous beam under axial loads are derived analytically on the basis of boundary, continuity, and deformation compatibility conditions by using equivalent spring models. The equation for the deflection curve is solved using undetermined coefficient methods. The normal function of the transverse vibration equation is obtained by separating variables. The differential equations for the beam that consider moments of inertia, shearing effects, and gyroscopic moments are investigated using the transfer matrix method. The deflection and vibration frequencies of the discontinuous beam are studied under different axial loads and connection spring stiffness. Results show that deflection decreases and vibration frequencies increase exponentially with increasing connection spring stiffness. Moreover, both variables remain steady when connection spring stiffness reaches a considerable value. Lastly, an experimental study is conducted to investigate the vibration characteristics of a discontinuous beam with a curvic coupling, and the results exhibit a good match with the proposed model.

     

基于固有频率的呼吸式裂纹梁损伤识别方法

将呼吸裂纹梁简化为由扭转弹簧连接的两段弹性梁,在假定振动响应随振幅变化的基础上推导出呼吸裂纹梁的固有频率方程;考虑振动过程中呼吸裂纹的开合情况,假定裂纹梁的刚度是振幅的非线性函数,建立了呼吸裂纹梁的多项式刚度模型;结合等高线裂纹识别理论和方法,提出了一种基于固有频率的呼吸裂纹梁损伤识别方法,算例验证了方法的可行性与有效性。研究表明,该方法的识别精度取决于实验固有频率的精度。     

Improved flexural–torsional stability analysis of thin-walled composite beam and exact stiffness matrix

A simple but efficient method to evaluate the exact element stiffness matrix is newly presented in order to perform the spatially coupled stability analysis of thin-walled composite beams with symmetric and arbitrary laminations subjected to a compressive force. For this, the general bifurcation-type buckling theory of thin-walled composite beam is developed based on the energy functional, which is consistently obtained corresponding to semitangential rotations and semitangential moments. A numerical procedure is proposed by deriving a generalized eigenvalue problem associated with 14 displacement parameters, which produces both complex eigenvalues and multiple zero eigenvalues. Then the exact displacement functions are constructed by combining eigenvectors and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently exact element stiffness matrices are evaluated by applying member force–displacement relationships to these displacement functions. As a special case, the analytical solutions for buckling loads of unidirectional and cross-ply laminated composite beams with various boundary conditions are derived. Finally, the finite element procedure based on Hermitian interpolation polynomial is developed. In order to verify the accuracy and validity of this study, the numerical, analytical, and the finite element solutions using the Hermitian beam elements are presented and compared with those from ABAQUS's shell elements. The effects of fiber orientation and the Wagner effect on the coupled buckling loads are also investigated intensively.     

山地地铁小半径曲线路段车辆/轨道参数对钢轨波磨的影响

针对山地地铁小半径曲线轨道钢轨波磨频发问题,根据现场调研建立车辆-轨道系统的动力学模型,探究车辆通过小半径曲线时轮轨间的接触特性。根据动力学分析结果建立半车车体-转向架-轨道系统的有限元模型,采用复特征值分析法研究半车车体-转向架-轨道系统摩擦自激振动特性,并研究车辆悬挂参数和轨道扣件参数对整体系统摩擦自激振动的影响规律。采用神经网络结合遗传算法对影响整体系统摩擦自激振动的关键参数进行多参数拟合,并求得车辆/轨道结构关键参数的优化解。结果表明：小半径曲线路段轮轨间的饱和蠕滑力导致半车车体-转向架-轨道系统的摩擦自激振动,从而引起钢轨波磨;车辆结构参数中一系悬挂横向刚度以及轨道结构参数中扣件垂向刚度、扣件横向刚度、扣件垂向阻尼对整个系统的摩擦自激振动具有明显影响。设置一系悬挂横向刚度为5.34 MN/m,扣件垂向刚度为25.45 MN/m,扣件横向刚度为6.9 MN/m,扣件垂向阻尼为6.06 kN·s/m时,能够有效抑制山地地铁小半径曲线轨道上钢轨波磨的产生。     

双层欧拉梁声子晶体弯曲振动带隙特性研究

为了探究新型低频减振结构,建立局域共振型声子晶体双层欧拉梁简化模型,基于平面波展开法计算其能带结构,通过有限元仿真得到振动传输曲线并验证其带隙特性。结果表明,反对称振动和对称振动能带形成带隙,两能带耦合导致部分非带隙频段仍存在振动衰减,这是单层梁不具备的优势。根据固有振型给出带隙起始、截止频率的计算公式,并研究了弹簧刚度等对带宽的影响。     

高速轨道结构振动及传递特性

高速列车的快速发展使板式无砟轨道得以广泛应用。利用有限元分析软件ANSYS和多体动力学软件SIMPACK,建立车辆-弹性轨道耦合动力学模型,分析车辆运行的安全性和平稳性,研究轨道系统的位移、加速度、加速度功率谱密度、载荷特性,以及不同速度对轨道系统的振动影响,并对系统振动的主要影响因素进行初步探究。结果表明,轨道结构的垂向振动位移、加速度及载荷在由上至下传递过程中呈递减趋势,且钢轨到轨道板的衰减幅度大于轨道板到底座;轨道系统的振动能量主要集中在0～150Hz范围内,大于300Hz的钢轨振动能量经扣件衰减后基本未被向下传递,且速度升高,功率谱密度峰值出现的位置向右移动;速度为300km/h时,钢轨垂向加速度功率谱密度小于100Hz的峰值频率主要与钢轨固有模态有关,大于100Hz的峰值频率呈倍频关系,且与轨道系统固有属性相关。联合仿真提高了研究效率,揭示了车辆-轨道系统的垂向振动特性及传递规律,为工程应用提供了参考依据。     

Characteristics of Vibration and Sound Radiation of Metro Resilient Wheel

Resilient wheels are extensively used in urban rail transit, especially for tramway systems, owing to its advantages in noise reduction. A new type of resilient wheel for a metro is designed, and its characteristics of vibration and sound radiation, including the rolling noise of a resilient single wheel coupled with a track, are studied in this paper. A two-step research is presented. Firstly, laboratory experiments were conducted to obtain the vibration response of the designed resilient wheel under the radial excitation on its tread. Secondly, the rolling noise model of the resilient wheel coupled with a slab track used in a metro line is developed. The wheel model is based on the 3 D finite elementand boundary element methods and verified by using the experimental results obtained from the laboratory. The track vibration model is based on the wavenumber finite element method, and the track sound radiation is calculatedby using an e cient frequency-domain Rayleigh method. The interaction of the resilient wheel and the slab track is analyzed considering the measured wheel/rail roughness of the metro. The contribution of the resilient wheel to the reduction of wheel/rail system noise is analyzed. The results show that the resilient wheel can e ectively reduce the wheel/rail rolling noise by approximately 2 dB(A) to 3 dB(A), mainly because the radiated noise by the rail is reduced. In addition, the elastic modulus of the rubber has an important influence on the noise reduction of resilient wheels.     

地铁钢轨短波长波磨形成原因分析

国内某地铁线路运营后曲线轨道出现了短波长钢轨波磨现象,通过力锤敲击法对不同扣件轨道动态特性进行了测试。利用ABAQUS建立了轮轨三维实体有限元模型,分析了轮轨耦合模态特性以及白噪声激励时轨道频响特性。结合试验和仿真结果,分析了轮轨结构动态特性与短波长钢轨波磨之间的相关性。研究结果表明：普通扣件和减振扣件轨道钢轨波磨主波长分别为30~63 mm和40~50 mm;白噪声激励下,两种轨道分别在450~920 Hz和570~720 Hz范围内的敏感共振频率与列车通过钢轨波磨频率(454~954 Hz和572~715 Hz)相吻合;线路轨道短波长波磨的产生主要与轨道结构高频固有特性相关,轨道短波长波磨通过频率与轮轨耦合模态频率相近,其模态振型表现为轮对弯曲扭转的同时,伴随钢轨相对轨道板的垂向弯曲振动,轮轨耦合高频模态特征加剧短波长波磨的发展。     

Flexural-torsional coupled vibration of slewing beams using various types of orthogonal polynomials

Dynamic behavior of flexural-torsional coupled vibration of rotating beams using the Rayleigh-Ritz method with orthogonal polynomials as basis functions is studied. Performance of various orthogonal polynomials is compared to each other in terms of their efficiency and accuracy in determining the required natural frequencies. Orthogonal polynomials and functions studied in the present work are : Legendre, Chebyshev, integrated Legendre, modified Duncan polynomials, the special trigonometric functions used in conjunction with Hermite cubics, and beam characteristic orthogonal polynomials. A total of 5 cases of beam boundary conditions and rotation are studied for their natural frequencies. The obtained natural frequencies and mode shapes are compared to those available in various references and the results for coupled flexural-torsional vibrations are especially compared to both previously available references and with those obtained using NASTRAN finite element package. Among all the examined orthogonal functions, Legendre orthogonal polynomials are the most efficient in overall CPU time, mainly because of ease in performing the integration required for determining the stiffness and mass matrices.     

Flexural–torsional coupled vibration and buckling of thin-walled open section composite beams using shear-deformable beam theory

A general analytical model based on shear-deformable beam theory has been developed to study the flexural–torsional coupled vibration and buckling of thin-walled open section composite beams with arbitrary lay-ups. This model accounts for all the structural coupling coming from the material anisotropy. The seven governing differential equations for coupled flexural–torsional–shearing vibration are derived from Hamilton's principle. The resulting coupling is referred to as sixfold coupled vibration. Numerical results are obtained to investigate effects of shear deformation, fiber orientation and axial force on the natural frequencies, corresponding mode shapes as well as load–frequency interaction curves.     

Investigation on dynamic behavior of railway track in transition zone

Railway track transition zone is a zone where track stiffness changes abruptly. This change occurs where the slab track connects to a conventional ballasted track, at the abutments of open-deck bridges, at the beginnings and ends of tunnels, at road and railway level crossings, and at locations where rigid culverts are placed close to the bottom of sleepers. In this paper, ballasted and slab tracks are simulated by two-dimensional model with two-layer masses. The transition zone is divided into three segments, each having a length of 6 meters with different specification and stiffness. The model of track consists of a Timoshenko beam as a rail and slab, lumped mass as sleepers, and spring and damper as ballast, sub-grade, and rail pad. The results of the dynamic analysis are presented and compared in two circumstances — one considering the transition zone and the other its absence.     

Effect of axial force on free vibration of Timoshenko multi-span beam carrying multiple spring-mass systems

The situation of structural elements supporting motors or engines attached to them is usual in technological applications. The operation of machine may introduce severe dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli–Euler single-span beams carrying a number of spring-mass system and Bernoulli–Euler multi-span beams carrying multiple spring-mass systems are plenty, but that of Timoshenko multi-span beams carrying multiple spring-mass systems with axial force effect is fewer. This paper aims at determining the exact solutions for the first five natural frequencies and mode shapes of a Timoshenko multi-span beam subjected to the axial force. The model allows analyzing the influence of the shear and axial force effects and spring-mass systems on the dynamic behavior of the beams by using Timoshenko Beam Theory (TBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1–4 span beams are studied. The calculated natural frequencies of Timoshenko multi-span beam by using secant method for non-trivial solution for the different values of axial force are given in tables. The mode shapes are presented in graphs.     

Investigation into the vibration of metro bogies induced by rail corrugation

The current research of rail corrugation mainly focuses on the mechanisms of its formation and development. Compared with the root causes and development mechanisms, the wheel–rail impacts, the fatigue failure of vehicle-track parts, and the loss of ride comfort due to rail corrugation should also be taken into account. However, the influences of rail corrugation on vehicle and track vibration, and failure of vehicle and track structural parts are barely discussed in the literature. This paper presents an experimental and numerical investigation of the structural vibration of metro bogies caused by rail corrugation. Extensive experiments are conducted to investigate the effects of short-pitch rail corrugation on the vibration accelerations of metro bogies. A dynamic model of a metro vehicle coupled with a concrete track is established to study the influence of rail corrugation on the structural vibration of metro bogies. The field test results indicate that the short-pitch rail corrugation generates strong vibrations on the axle-boxes and the bogie frames, therefore, accelerates the fatigue failure of the bogie components. The numerical results show that short-pitch rail corrugation may largely reduce the fatigue life of the coil spring, and improving the damping value of the primary vertical dampers is likely to reduce the strong vibration induced by short-pitch rail corrugation. This research systematically studies the effect of rail corrugation on the vibration of metro bogies and proposes some remedies for mitigating strong vibrations of metro bogies and reducing the incidence of failure in primary coil springs, which would be helpful in developing new metro bogies and track maintenance procedures.     

Stiffness matrix of thin-walled curved beam for spatially coupled stability analysis

The exact stiffness matrix for the spatially coupled stability analysis of thin-walled curved beam with non-symmetric cross-section subjected to uniform compression is newly presented. For this, the elastic strain energy including the axially/flexurally/torsionally coupled terms and the potential energy due to the initial stress resultant are introduced. Then, equilibrium equations and force–deformation relationship are derived from the energy principle and explicit expressions for displacement parameters are derived based on power series expansions of displacement components. Next, the exact element stiffness matrix is determined using force–deformation relationships. In order to verify the accuracy of this study, the numerical solutions are presented and compared with the finite element solutions using the Hermitian curved beam elements. In addition, the coupling of symmetric and anti-symmetric modes at the buckling load crossover with change in curvature of beam is investigated.     

Free vibration analysis of sandwich beam carrying sprung masses

In this paper, free vibration of three-layered symmetric sandwich beam carrying sprung masses is investigated using the dynamic stiffness method and the finite element formulation. First the governing partial differential equations of motion for one element are derived using Hamilton’s principle. Closed form analytical solution of these equations is determined. Applying the effect of sprung masses by replacing each sprung mass with an effective spring on the boundary condition of the element, the element dynamic stiffness matrix is developed. These matrices are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by the use of numerical techniques and the well known Wittrick–Williams algorithm. Free vibration analysis using the finite element method is carried out by increasing one degree of freedom for each sprung mass. Finally, some numerical examples are discussed using the dynamic stiffness method and the finite element formulation. After verification of the present model, the effect of various parameters such as mass and stiffness of the sprung mass is studied on the natural frequencies.     

动力总成悬置系统基于ANSYS的参数化优化设计

在有限元分析软件ANSYS中以质量矩阵单元、刚性梁单元以及弹簧单元为基本单元,用APDL程序语言对动力总成悬置系统进行参数化建模,基于能量法解耦进行模态分析,并对隔振器三向刚度进行优化配置使悬置系统各阶模态尽可能解耦。结果表明,悬置系统的模态频率与解耦度均达到满意的要求。     

十自由度车-轨耦合仿真分析

文章以十自由度车轨耦合模型为例,探究由轨道不平顺所导致车-轨耦合垂向振动的问题,由功率谱密度计算确定了轨道不平顺并以此作为激励源,计算分析车辆与轨道之间的垂向耦合振动响应.通过MATLAB仿真结果图分析得出,轨下的高底不平顺主要影响的是构架和轮对的振动频率,对车体的影响并不大,因此要减轻车-轨系统的振动主要从一系悬挂和...     

汽车仪表板横梁系统固有振动特性研究

测量了横梁系统在车身安装状态下的固有振动特性,并通过有限元计算得出横梁系统的模态参数,结果确定了横梁系统刚度较差的原因与横梁骨架和车身前围板刚度不足有关;然后基于有限元模型分析了横梁系统主要零件的板厚对固有频率、质量的灵敏度,发现不同零件对横梁系统的固有频率和质量影响程度存在差异;最后在OptiStruct中建立数学模型并优化零件板厚,使横梁系统总质量、固有频率和刚度之间得到了较好的平衡,改善了横梁系统的固有振动特性。