A vertical coupling dynamic analysis method and engineering application of vehicle–track–substructure based on forced vibration

Purpose–This study aims to propose a vertical coupling dynamic analysis method of vehicle–track–substructure based on forced vibration and use this method to analyze the influence on the dynamic response of track and vehicle caused by local fastener failure.Design/methodology/approach–The track and substructure are decomposed into the rail subsystem and substructure subsystem,in which the rail subsystem is composed of two layers of nodes corresponding to the upper rail and the lower fastener.The rail is treated as a continuous beam with elastic discrete point supports,and spring-damping elements are used to simulate the constraints between rail and fastener.Forced displacement and forced velocity are used to deal with the effect of the substructure on the rail system,while the external load is used to deal with the reverse effect.The fastener failure is simulated with the methods that cancel the forced vibration transmission,namely take no account of the substructure–rail interaction at that position.Findings–The dynamic characteristics of the infrastructure with local diseases can be accurately calculated by using the proposed method.Local fastener failure will slightly affect the vibration of substructure and carbody,but it will significantly intensify the vibration response between wheel and rail.The maximum vertical displacement and the maximum vertical vibration acceleration of rail is 2.94 times and 2.97 times the normal value,respectively,under the train speed of 350 km$h
1.At the same time,the maximum wheel–rail force and wheel load reduction rate increase by 22.0 and 50.2%,respectively,from the normal value.Originality/value–This method can better reveal the local vibration conditions of the rail and easily simulate the influence of various defects on the dynamic response of the coupling system.

Study on Electromagnetic Force and Vibration of Turbogenerator End Windings under Impact Load(Ⅰ): Analysis of Electromagnetic Force of End Windings under Impact Load

In this paper, the boundary value problem (BVP) of 3 D transient eddy current field in the end region in the case that the generator is affected by impact load is specified. Besides, ways to implement discrete methods in both time domain and space domain during the solution of the problem are investigated. The Crank Nicolson scheme is utilized to attain the iterative format of time differential, after taking factors that can ensure both computation precision and stability into consideration. In this paper, the magnetic distribution in the end region of a turbogenerator in the case that the generator is affected by impact load is specified. As a result, it provides foundation for further study of electromagnetic force and electromagnetic vibration in the end region of the turbogenerator.

Transverse Vibration and Stability Analysis of Circular Plate Subjected to Follower Force and Thermal Load

Transverse vibration and stability analysis of circular plate subjected to follower force and thermal load are analyzed.Based on the thin plate theory in involving the variable temperature,the differential equation of transverse vibration for the axisymmetric circular plate subjected to follower force and thermal load is established.Then,the differential equation of vibration and corresponding boundary conditions are discretized by the differential quadrature method.Meanwhile,the generalized eigenvalue under three different boundary conditions are calculated.In this case,the change curve of the first order dimensionless complex frequency of the circular plate subjected to the follower force in the different conditions with the variable temperature coefficient and temperature load is analyzed.The stability and corresponding critical loads of the circular plate subjected to follower force and thermal load with simply supported edge,clamped edge and free edge are discussed.The results provide theoretical basis for improving the dynamic stability of the circular plate.

Experimental study on durability fracture behavior and vibration modal sweep for vehicle rear axle

In order to study the fatigue fracture behavior of the rear axle of certain China-made car, the strain loading spectrum near the rear axle fracture location is collected, the modified Neuber rule and the cyclic stress-strain hysteresis loop curve equation are used to convert the nominal strain his- tory into the local stress-strain response. The impact of mean stress on fatigue damage is corrected according to the Manson-Coffin model, and programming calculation of the fatigue damage of the fracture crack is conducted in the INFIELD software, the electromagnetic vibrators are used to sweep the vibration modal frequencies of the rear axle and car body. The enhancement test and fre- quency sweep results show that the rear axle fatigue damage mainly concentrates on the washboard road, and when the forced vibration excitation frequency is 24. 07 Hz, the vibration modal frequency of the rear axle is close to the excitation frequency of the washboard road, leading to resonance and making the rear axle subjected to large strain and fatigue damage, and then vibration fatigue fracture due to high stress concentration.

A comprehensive review on coupling vibrations of train-bridge systems under external excitations

In recent years,high-speed railways in China have developed very rapidly,and the number and span of the railway bridges are keeping increasing.Meanwhile,frequent extreme disasters,such as strong winds,earthquakes and floods,pose a significant threat to the safety of the train–bridge systems.Therefore,it is of paramount importance to evaluate the safety and comfort of trains when crossing a bridge under external excitations.In these aspects,there is abundant research but lacks a literature review.Therefore,this paper provides a comprehensive state-of-the-art review of research works on train–bridge systems under external excitations,which includes crosswinds,waves,collision loads and seismic loads.The characteristics of external excitations,the models of the train–bridge systems under external excitations,and the representative research results are summarized and analyzed.Finally,some suggestions for further research of the coupling vibration of train–bridge system under external excitations are presented.

Forced vibration analysis of nano-composite rotating pressurized microbeam reinforced by CNTs based on MCST with temperature-variable material properties

In this study, free and forced vibration analysis of nano-composite rotating pressurized microbeam reinforced by carbon nanotubes （CNTs） under magnetic field based on modify couple stress theory （MCST） with temperature-variable material propertiesis presented. Also, the boundary conditions at two ends of nano-composite rotating pressurized microbeam reinforced by CNTs are considered as simply supported. The governing equations are obtained based on the Hamilton＇s principle and then computed these equations by using Navier＇s solution. The magnetic field is inserted in the thickness direction of the nano-composite microbeam. The effects of various parameters such as angular velocity, temperature changes, and pressure between of the inside and outside, the magnetic field, material length scale parameter, and volume fraction of nanocomposite microbeam on the natural frequency and response systemare studied. The results show that with increasing volume fraction of nano-composite microbeam, thickness, material length scale parameter, and magnetic fields, the natural frequency increases. The results of this research can be used for optimization of micro-structures and manufacturing sensors, displacement fluid, and drug delivery.

ITERATIVE COMPUTATION METHOD FOR NONLINEAR FORCED VIBRATION EQUATION ON HELICOPTER MAIN ROTOR LOAD

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Effect of Coupled Torsional and Transverse Vibrations of the Marine Propulsion Shaft System

In this study,the coupled torsional-transverse vibration of a propeller shaft system owing to the misalignment caused by the shaft rotation was investigated.The proposed numerical model is based on the modified version of the Jeffcott rotor model.The equation of motion describing the harmonic vibrations of the system was obtained using the Euler-Lagrange equations for the associated energy functional.Experiments considering different rotation speeds and axial loads acting on the propulsion shaft system were performed to verify the numerical model.The effects of system parameters such as shaft length and diameter,stiffness and damping coefficients,and cross-section eccentricity were also studied.The cross-section eccentricity increased the displacement response,yet coupled vibrations were not initially observed.With the increase in the eccentricity,the interaction between two vibration modes became apparent,and the agreement between numerical predictions and experimental measurements improved.Given the results,the modified version of the Jeffcott rotor model can represent the coupled torsional-transverse vibration of propulsion shaft systems.

An isogeometric analysis approach for dynamic response of doubly-curved magneto electro elastic composite shallow shell subjected to blast loading

For the first time, the isogeometric analysis(IGA) approach is used to model and analyze free and forced vibrations of doubly-curved magneto-electro-elastic(MEE) composite shallow shell resting on the visco-Pasternak foundation in a hygro-temperature environment. The doubly-curved MEE shallow shell types include spherical shallow shell, cylindrical shallow shell, saddle shallow shell, and elliptical shallow shell subjected to blast load are investigated. The Maxwell equation and electromagnetic boundary conditions are used to determine the vary of the electric and magnetic potentials. The MEE shallow shell's equations of motion are derived from Hamilton's principle and refined higher-order shear theory. Then, the IGA method is used to derive the laws of natural frequencies and dynamic responses of the shell under various boundary conditions. The accuracy of the model and method is verified through reliable numerical comparisons. Aside from this, the impact of the input parameters on the free and forced vibration of the doubly-curved MEE shallow shell is examined in detail. These results may be useful in the design and manufacture of military structures such as warships, fighter aircraft, drones and missiles.

Analytic solution for size-dependent behaviors of micro-beam under forced vibration

This paper focuses on the size-dependently mechanical behaviors of a micro-beam under forced vibration.Governing equations of a micro-beam under forced vibration are established by using the modified couple stress theory,Bernoulli-Euler beam theory and D’Alembert’s principle together.A simply supported micro-beam under forced vibration is solved according to the established governing equations and the method of separation of variables.The dimensionless deflection,amplitude mode and period mode are defined to investigate the size-dependently mechanical behaviors of a micro-beam under forced vibration.Results show that the performance of a micro-beams under forced vibration is distinctly size-dependent when the ratio of micro-beam height to material length-scale parameter is small enough.Both frequency ratio and loading location are the important factors that determine the sizedependent performance of a micro-beams under forced vibration.

Dynamic performance analysis of a seismically isolated bridge under braking force

In order to study the dynamic performance of seismically isolated bridges under the most unfavorable loads in the longitudinal direction, a dynamic equation for vehicle braking in the longitudinal direction is established. A four or five- order Runge-Kutta method is adopted to obtain the time-history response of a wheel set under braking force. The quadratic discretization method is then used to transform this time-history into a braking and bending force time-history of a structural fixed node, and a dynamic response analysis of the seismically isolated bridge under the vehicle＇s braking force is carried out using ANSYS, a universal finite element analysis software. According to the results, seismic isolation design results in a more rational distribution of braking force among piers; the influence of the initial braking velocity on the vehicle braking force is negligible; the location where the first wheel set leaves the bridge is the most unfavorable parking location; a seismic isolation bridge bearing constructed according to typical design methods enters into a yield stage under the braking force, while the shearing force at the bottom of the pier declines as the isolation period is extended; the design requirements can be met when the yield displacement of the seismic isolation bearing is less than 5 mm and the yield strength is greater than the braking force.

Characteristics of Pore Water Pressure of Saturated Silt Under Wave Loading

The characteristics of dynamic stress in the seabed under wave loading are constant principal stress and continuous rotation of the principal stress direction. Cyclic triaxial-torsional coupling shear tests were pefformed on saturated silt by the hollow cylinder apparatus under different relative densities, deviator stress ratios and vibration frequencies to study the development of pore water pressure of the saturated silt under wave loading. It was found that the development of pore water pressure follows the trend of ＂fast - steady - drastic＂. The turning point from fast to steady stage is not affected by relative density and deviator stress ratio. However, the turning point from steady to drastic stage relies on relative density and deviator stress ratio. The vibration cycle for the liquefaction of saturated silt decreases with increasing deviator stress ratio and increases with relative density. The vibration cycle for the liquefaction of the saturated silt increases with vibration frequency and reaches a peak value, after which it decreases with increasing vibration frequency for the relative density of 70%. But the vibration cycle for the liquefaction of saturated silt increases with vibration frequency for the relative density of 30%. The development of pore water pressure of the saturated silt is influenced by relative density and vibration frequency.

NON-LINEAR DYNAMIC BEHAVIOR OF THERMOELASTIC CIRCULAR PLATE WITH VARYING THICKNESS SUBJECTED TO NONCONSERVATIVE LOADING

The non-linear dynamic behaviors of thermoelastic circular plate with varying thickness subjected to radially uniformly distributed follower forces are considered. Two coupled non-linear differential equations of motion for this problem are derived in terms of the transverse deflection and radial displacement component of the mid-plane of the plate. Using the Kantorovich averaging method, the differential equation of mode shape of the plate is derived, and the eigenvalue problem is solved by using shooting method. The eigencurves for frequencies and critical loads of the circular plate with unmovable simply supported edge and clamped edge are obtained. The effects of the variation of thickness and temperature on the frequencies and critical loads of the thermoelastic circular plate subjected to radially uniformly distributed follower forces are then discussed.

RADIAL VIBRATIONS OF AXISYMMETRICALLY LOADED STEPPED PRESSURE VESSELS

Differential equations of free/forced radial vibrations of axisymmetrically loaded stepped pressure vessels are established by using singular functions. Furthermore, their general solutions are solved, the expression of vibration mode function and frequency equations on usual supports are derived with W operator and the forced response of such vessels are calculated.

Simulation of Reciprocating Compressor Start-up and Shut-down under Loaded and Unloaded Conditions

During the start-up and shut-down phase of reciprocating compressors, the loads on all components of driven train system are very high. In this paper a method for calculating the forces on coupling, e-motor, crank shaft as well other components of the system will be described. The modelling of the electrical induction motor, coupling, crank shaft, damper as well as the compressor resistance torque are extremely important in simulating start-up and shut-down of reciprocating compressor. Furthermore the switching torque of the electrical motor and the instantaneous moment of inertia of the reciprocating compressor crank gear are important as well. The transient start-up and shut-down process under loaded and unloaded conditions is described using a non-linear differential equation for driven train system： E-motor--coupling--flywheel--reciprocating compressor--damper. Shaft torsional moments on the drive train and especially on the coupling, whether elastic or stiff, can then only be calculated using numerical simulation. This paper will describe some of the key elements in modelling, simulating and measurements of drive train start-up and shut-down carried out on already operational piston compressor units.

特高压并联电抗器铁芯振动及噪声特征研究

特高压并联电抗器因其铁芯是以铁芯饼与气隙垫块交替堆叠而成的结构特点,导致其运行过程中振动强度远超同电压等级的变压器,易出现振动超标等问题,现有计算方法对特高压并联电抗器铁芯振动特征还无法准确表征。鉴于此,该文针对1台特高压并联电抗器的铁芯振动机理及产生的噪声进行研究,结合磁-结构-声多场耦合分析,对铁芯所受麦克斯韦力及磁致伸缩力进行仿真计算,将结构场计算结果进行快速傅里叶变换后作为载荷激励进而计算由电抗器振动产生的噪声,并单独分析磁致伸缩力和麦克斯韦力对电抗器铁芯振动造成的影响。结果表明:电抗器运行过程中电抗器铁芯旁轭中部产生的振动最剧烈,电抗器周围产生的噪声最大。对比麦克斯韦力与磁致伸缩力对电抗器铁芯振动的影响发现,同时考虑两个力时铁芯振动小于未考虑磁致伸缩力的情况,证明影响电抗器铁芯振动的两个力存在相互衰减作用。

浮式风力机若干特征动力学问题综述

总结浮式风力机类型及其对应的特征动力学问题,针对浮式风力机气动荷载、水动荷载的计算方法以及结构动力学、控制动力学典型问题进行论述。讨论了气动—水动—结构—伺服耦合分析的难点,重点分析了二阶波浪力、畸形波等非线性波浪荷载、流荷载及涡激运动对浮式风力机特征动力响应的影响。阐述了浮式风力机动力学研究的试验方法、数值仿真方法、样机测试方法,并对模型试验技术的相似理论、气动模型的实现和难点以及数值仿真的频域方法、时域方法和分析工具进行了归纳对比。研究表明:浮式风力机多场、多体耦合动力分析机理及相关技术仍不成熟,气动荷载、高阶非线性波浪荷载耦合模型的建立是动力学问题研究的重点,数值仿真及模型试验是浮式风力机动力响应研究的主要方法,样机测试技术的积累将促进设计标准的完善及浮式风电的产业化发展。

基于同频弯扭耦合强迫振动的桥梁断面颤振导数识别方法改进

为拓展强迫振动法在桥梁断面颤振导数识别领域中的应用能力,采取让断面做2次同频异相的弯扭耦合简谐运动模式,理论推导出任意非零相位差条件下的桥梁断面颤振导数识别公式。以理想平板的Theodorsen解为气动力数据源,对该方法的识别能力进行数值验证,并在此基础上研究弯扭耦合运动相位差、高斯白噪声、整数倍频有色噪声对平板颤振导数识别结果的影响规律。基于Fluent软件,将该方法与计算流体动力学(Computational Fluid Dynamics,CFD)技术结合,识别得到丹麦大带东桥主梁断面的颤振导数。研究结果表明:当平板气动力不包含噪声时,在任意非零相位差取值条件下,按照该方法识别所得颤振导数结果与理论值完全吻合;当平板气动力含有高斯白噪声时,在考察的3个低水平噪声条件下(5%、10%、15%),颤振导数识别误差与高斯白噪声比例水平、折算风速均成正相关,但不同颤振导数对高斯白噪声敏感程度各异;当平板气动力包含整数倍频有色噪声时,3倍频、4倍频噪声对颤振导数的识别精度影响显著,其他低倍频噪声和超高倍频噪声的影响较小,在8个颤振导数的识别结果中,H_(2)^(*)、H_(4)^(*)、A_(2)^(*)、A_(4)^(*)对倍频有色噪声更敏感。应用该方法结合CFD数值模拟识别得到的大带东桥主梁颤振导数与既有文献结果吻合良好,经计算得到的颤振临界风速也较为接近。研究结果可满足同类桥梁颤振设计的工程计算需求。

公轨合建盾构隧道振动荷载的动力响应特性

为了探究汽车-列车振动荷载对公轨合建盾构隧道内部结构及周围土体的动力响应特性,采用有限元软件ABAQUS对某公轨合建盾构隧道内部结构及周围土体进行数值模拟,通过ABAQUS软件的Dload子程序对汽车、列车振动荷载进行耦合,分别将单一振动荷载及汽车-列车振动荷载作用引入公轨合建盾构隧道,分析公轨合建盾构隧道内部结构及周围土体在不同工况时加速度、位移、应力、应变的变化。结果表明:汽车、列车振动荷载频率不同,共同作用后产生拍频现象,导致相同方向合成荷载的振幅可能小于分荷载的振幅,当频率相同时所合成荷载的振幅最大;管片上方的土体以及非封闭弧形内衬外侧土体发生较大的应变,最大塑性应变发生于拱顶偏右侧,达到7.032×10^(-6);公轨合建盾构隧道内部结构中的预制箱涵牛腿柱、顶板处出现较大拉、压应变,在长期运营期间需要对预制箱涵牛腿柱、顶板位置进行定期检查和必要支护。

耦合索股系统自振特性与索力全局识别算法

索是缆索承重结构重要的受力构件,索力直接影响结构的服役状态与使用寿命。对于局部刚性耦合的索股结构,索股振动具有独立性和耦联性,系统呈现的整体振动与完全独立或完全耦合的索股系统振动特性均不同。为了对局部刚性耦合的索股系统的索力进行有效识别,首先建立耦合多索股模型并推导了系统的振动方程,根据系统的频率方程对系统的自振特性进行参数分析;然后将填充函数法和最优化理论相结合,构建了耦合索股系统索力识别算法,实现了索力全局识别;最后通过试验和有限元仿真验证了算法的正确性和可靠性。结果表明:刚性耦合使各索股振动同频,索股系统的自振频率在整数倍频之间出现了分数倍频,在整体振型之间出现局部振型;该文所提出的基于全局最优化理论的索力识别算法对迭代初值要求低,计算精度和收敛效率高,可扩展到其他参数识别问题中。