移动荷载作用下弹性半空间Timoshenko梁的临界速度

根据梁的波速和半空间波速的相对关系,将Timoshenko梁-半空问系统分成四种不同情况。在梁与半空间相互作用的等效刚度和Timoshenko梁-半空间的弥散方程的基础上。利用弥散曲线，研究了移动荷载的临界速度。这四种情况分别为：软梁-硬半空间系统。次软梁-硬半空间系统，次硬梁-软半空间系统，硬梁-软半空间系统。研究表明，Timoshenko梁在移动荷载作用下的临界速度取决于梁的波速和半空间波速的相对关系；半空间的Rayleigh波波速始终是一个临界速度，当荷载速度达到Rayleigh波波速时．系统响应会趋于无穷大；对软梁-硬半空间系统，梁的剪切波速和压缩波速也是临界速度；对次软梁-硬半空间系统，梁的剪切波速是临界速度，并且还存在一个最小临界速度；对（次）硬梁-软半空间系统．粱的波速不再是临界速度。但也存在一个最小临界速度。     

匀变速移动质量与简支梁耦合系统的振动分析

对受变速移动荷载作用的简支梁的动力响应分析过程中,同时考虑移动质量的牵连惯性力及其加速度对梁横向振动的影响。利用时变力学系统的求解方法,得到在移动质量的初速度和加速度两个运动参数变化情况下,梁的挠度变化规律。数值结果表明,移动质量的加速度对梁横向振动的影响不能忽略,否则将产生较大的误差,而它的牵连惯性力对梁的横向振动影响不大,在一般的计算中可以忽略其影响以简化运算。     

Numerical comparison of flexible pavement dynamic response under different axles

A three-dimensional finite element model was utilised to examine the flexible pavement dynamic response under single, tandem and tridem axles at different speeds. Using two different hot-mix asphalt (HMA) layer thicknesses, 15.2 and 25.4 cm, the dynamic effects of moving axles were investigated on critical responses. These responses include the tensile strain at the bottom of asphalt layer, compressive strain on the top of subgrade and tensile and compressive strain on the surface layer. In this study, the HMA layer and other layers were characterised as linear viscoelastic and elastic material, respectively. Since this research focuses specifically on the time and dynamic effects, considering the transient dynamic loading and inertia forces, implicit dynamic analysis was done. The important findings are as follows. (1) Strains induced by tridem axles could be greater than tandem axles or even equal at different speeds. (2) It cannot be stated that axles always induce greater critical response value to road systems at lower speed because at higher speed they can also induce greater critical response value in pavements than that at lower speed. (3) Changing trend and changing rate of strains with speed are strongly affected by pavement thickness. In general, the effects of different axle configurations are strongly affected by moving speed and surface layer thickness.     

基于振速测量单全息面直接声场分离方法

摘 要：为了更精确的分离质点振速,以波叠加法作为声场分离算法基础,提出单全息面测量振速直接声场分离方法。建立了单面振速测量声场分离模型,并推导了理论计算方法,通过数值仿真,分析算法的计算精度,验证了该方法可以有效分离声场。然后对比本文分离方法和单面声压测量声场分离方法分离简单源和脉动声源的误差,结果表明：单面振速测量的直接声场分离方法可以有效分离目标声源,而且可以获得更高的振速分离精度。     

航道边界形状对移动载荷激励冰层位移响应特性的影响研究

基于欧拉-拉格朗日流体与固体耦合算法,针对移动载荷激励冰层响应问题开展了数值模拟。对均匀水深条件下的冰层位移响应进行了数值计算并与实验结果进行对比分析,发现二者获得的临界速度值、冰层位移响应波形特征以及最大下陷值都吻合较好,说明所采用的数值计算方法是可靠、有效的。针对限制水域不同航道边界形状条件下移动荷载激励冰层位移响应和载荷临界速度进行了数值模拟,得到了航道边界形状对位移响应和临界速度的影响规律,结果表明:不同截面形状直航道条件下,当矩形截面变化到梯形截面时,临界速度变小,且各速度下冰层最大下陷位移也相应变小;矩形截面形状弯曲航道条件下,临界速度仍存在,且该临界速度对应的冰层最大下陷位移幅值比直航道条件下大。     

移动谐振荷载作用下浮置板轨道的动力响应

在移动谐振荷载作用下,依据周期结构响应的性质,将无限长浮置板轨道响应的问题求解转化到在一块浮置板长度范围内进行,并通过浮置板的位移影响矩阵在频域内实现了钢轨和不连续浮置板的耦合,求得了该范围内钢轨的动力响应,进而以此为基础求得了轨道结构上任意一点的动力响应。结果表明:移动谐振荷载作用下,在移动荷载自身激振频率附近,浮置板轨道位移响应频谱达到峰值;随着移动谐振荷载速度的增大,在频谱上,荷载自身激振频率附近很窄的频段位移响应会有所下降,而在其他大部分频段位移响应会有显著增加;当谐振荷载激振频率与浮置板轨道的固有频率一致时,发生共振现象,在频谱上位移响应的峰值远远大于其他激振频率时响应的峰值;浮置板轨道在移动荷载作用下,存在由荷载周期通过不连续浮置板和扣件而引发的参数激励;当移动谐振荷载激振频率接近有限长浮置板形成驻波的频率时,轨道结构也会产生较大的位移响应。     

Dynamics of the Moving Ring Load Acting in the System “Hollow Cylinder + Surrounding Medium” with Inhomogeneous Initial Stresses

This paper studies the influence of the inhomogeneous initial stress state in the system consisting of a hollow cylinder and surrounding elastic medium on the dynamics of the moving ring load acting in the interior of the cylinder. It is assumed that in the initial state the system is compressed by uniformly distributed normal forces acting at infinity in the radial inward direction and as a result of this compression the inhomogeneous initial stresses appear in the system. After appearance of the initial stresses, the interior of the hollow cylinder is loaded by the moving ring load and so it is required to study the influence of the indicated inhomogeneous initial stresses on the dynamics of this moving load. This influence is studied with utilizing the so-called three-dimensional linearized theory of elastic waves in elastic bodies with initial stresses. For solution of the corresponding mathematical problems, the discrete-analytical solution method is employed and the approximate analytical solution of these equations is achieved. Numerical results obtained within this method and related to the influence of the inhomogeneous initial stresses on the critical velocity of the moving load and on the response of the interface stresses to this load are presented and discussed. In particular, it is established that the initial inhomogeneous initial stresses appearing as a result of the action of the aforementioned compressional forces cause to increase the values of the critical velocity of the moving load.     

Dynamic behaviour of edge-cracked shear deformable functionally graded beams on an elastic foundation under a moving load

This paper studies the dynamic response of functionally graded beams with an open edge crack resting on an elastic foundation subjected to a transverse load moving at a constant speed. It is assumed that the material properties follow an exponential variation through the thickness direction. Theoretical formulations are based on Timoshenko beam theory to account for the transverse shear deformation. The cracked beam is modeled as an assembly of two sub-beams connected through a linear rotational spring. The governing equations of motion are derived by using Hamilton’s principle and transformed into a set of dynamic equations through Galerkin’s procedure. The natural frequencies and dynamic response with different end supports are obtained. Numerical results are presented to investigate the influences of crack location, crack depth, material property gradient, slenderness ratio, foundation stiffness parameters, velocity of the moving load and boundary conditions on both free vibration and dynamic response of cracked functionally graded beams.     

轴向变速黏弹性Rayleigh梁非线性参数振动稳态响应

研究非线性轴向运动黏弹性Rayleigh梁因速度周期变化产生的亚谐波共振。轴向运动速度在平均速度附近做简谐周期性脉动。通过取物质导数的Kelvin本构关系描述Rayleigh梁的黏弹性。运用多尺度近似解析方法,构建轴向运动Rayleigh梁的非线性偏微分方程的可解性条件,分析参数振动稳态响应的振幅与扰动速度频率关系。并运用微分求积方法直接离散非线性Rayleigh梁的控制方程,以验证近似解析方法分析。通过数值算例,分析了系统参数对稳态响应曲线的影响。     

挤压油膜阻尼器支承的柔性转子的双稳态响应特性

分析了同心型挤压油膜阻尼器的流体惯性力对柔性转子的双稳态响应的影响。研究表明，雷诺数越大（即惯性力的影响越大），则挤压油膜阻尼器的刚度力越小，阻尼力越大，从而导致系统稳态响应的峰值转速降低，且在大多数转速区轴颈的振幅减小。盘心的振幅变化有类似的趋势。流体惯性力对系统在亚临界及超临界的双稳态响应具有明显的抑制作用，随惯性力增大，系统的双稳态响应特性得到改善。     

移动荷载列作用下简支梁振动响应参数研究

推导了移动荷载列作用下简支梁位移响应的精确解,在此基础上引入3个无量纲参数,研究了荷载移动速度、荷载频率及结构阻尼对桥梁响应的影响,分析了简支梁在一定荷载速度下的共振和消振现象发生机理。结果表明:桥梁跨中的最大位移响应并非随着荷载速度的增大而单调地增大,而是表现出一种类似正弦但波幅逐渐变大的方式;当移动荷载列以消振速度通过桥梁时,引起的桥梁余振响应趋近于零;简支梁的共振速度与移动荷载列的间距有直接关系,当共振速度同时又是消振速度时,共振现象被抑制;当简谐荷载移动速度较低时,梁体位移在荷载频率等于梁体第一阶自振频率时达到最大响应,随着荷载移动速度的增大,梁体位移达最大响应不再发生于荷载频率等于梁体第一阶自振频率的情况。     

插值振型函数法求解移动荷载作用下等截面连续梁的动态响应

根据哈密顿原理,应用插值振型函数法,分析了多跨连续梁在移动荷载作用下的车桥耦合振动动态响应。经实例讨论分析,给出了多跨等截面连续梁在不同速度移动荷载作用下的数值结果。实例分析表明,该方法具有很好的收敛性和很高的精度。具通过对结果的分析讨论,得到了多跨连续梁在移动荷载作用下的一些规律。     

An accurate solution for the responses of circular curved beams subjected to a moving load

In this paper, an accurate and effective solution for a circular curved beam subjected to a moving load is proposed, which incorporates the dynamic stiffness matrix into the Laplace transform technique. In the Laplace domain, the dynamic stiffness matrix and equivalent nodal force vector for a moving load are explicitly formulated based on the general closed‐form solution of the differential equations for a circular curved beam subjected to a moving load. A comparison with the modal superposition solution for the case of a simply supported curved beam confirms the high accuracy and applicability of the proposed solution. The internal reactions at any desired location can easily be obtained with high accuracy using the proposed solution, while a large number of elements are usually required for using the finite element method. Furthermore, the jump behaviour of the shear force due to passage of the load is clearly described by the present solution without the Gibb's phenomenon, which cannot be achieved by the modal superposition solution. Finally, the present solution is employed to study the dynamic behaviour of circular curved beams subjected to a moving load considering the effects of the loading characteristics, including the moving speed and excitation frequency, and the effects of the characteristics of curved beams such as the radius of curvature, number of spans, opening angles and damping. The impact factors for displacement and internal reactions are presented. Copyright © 2000 John Wiley & Sons, Ltd.     

电磁轨道发射状态下导轨的动态响应

当导轨通入电流时,电枢受到推力作用沿轨道移动;同时,电枢经过的导轨受到安培力和电枢压力的作用。由于导轨外部的外包层将对导轨起到弹性支撑的作用,因此,可将导轨简化为弹性地基梁。应用二维Fourier积分变换,导出了导轨在移动荷载作用下动态挠度的一般解。根据电磁场理论、传热学,以及弹性力学的基本方程,可以得到电枢受到的推力、导轨相互作用的斥力和电枢作用在导轨上的压力的表达式,从而得到了电磁轨道发射状态下导轨挠度解的具体形式,并且分析了通入电流、导轨尺寸、外包层刚度等参量对导轨动态响应的影响     

Dynamics of elastically connected double-functionally graded beam systems with different boundary conditions under action of a moving harmonic load

This paper studies the dynamic responses of an elastically connected double-functionally graded beam system (DFGBS) carrying a moving harmonic load at a constant speed by using Euler–Bernoulli beam theory. The two functionally graded (FG) beams are parallel and connected with each other continuously by elastic springs. Six elastically connected double-functionally graded beam systems (DFGBSs) having different boundary conditions are considered. The point constraints in the form of supports are assumed to be linear springs of large stiffness. It is assumed that the material properties follow a power-law variation through the thickness direction of the beams. The equations of motion are derived with the aid of Lagrange’s equations. The unknown functions denoting the transverse deflections of DFGBS are expressed in polynomial form. Newmark method is employed to find the dynamic responses of DFGBS subjected to a concentrated moving harmonic load. The influences of the different material distribution, velocity of the moving harmonic load, forcing frequency, the rigidity of the elastic layer between the FG beams and the boundary conditions on the dynamic responses are discussed.     

轴压作用下自由-自由运动梁振动特性研究

针对轴向压力作用下的两端自由运动梁的振动问题,根据Timoshenko梁理论和Hamilton原理建立了梁的横向振动控制方程,通过解析法和微分求积法(DQM)求解了梁的振动特性,分析了轴向压力和运动效应以及轴向力导数和运动加速度对梁固有特性的影响,并对临界载荷、临界速度等的影响因素进行了比较研究。结果表明:轴向压力和运动效应都使得固有频率降低,压力和运动速度的特定组合会导致超临界现象和耦合模态颤振的出现;压力导数和加速度效应都会使得梁的基础频率产生不稳定性;梁的临界载荷随着运动速度增大而变小,临界速度随轴向压力增大而降低。     

Critical velocity for rails in hypervelocity launchers

This paper is related to the dynamic and strength analysis and optimized design of hypervelocity electromagnetic launchers. Projectile motion along the rails at critical velocity is associated with damaging resonant regimes. These regimes reveal increased displacements and stress that can lead to failure of a launcher. To calculate critical velocity and to visualize dynamic deformations of the launcher we have developed two alternative approaches utilizing analytical and finite element models. The first approach employs a closed form analytical solution for critical velocity that is based on the Bernoulli–Euler model of a beam resting on an elastic foundation and subjected to a moving load. The critical velocity is expressed as a function of geometric and material parameters of the rail and equivalent stiffness of the supporting structure. The stiffness of the supporting structure is found from a 2D finite element model. In the second approach, we employed beam finite element and 3D solid finite element models to visualize and measure the “natural” and “forced” bending waves traveling along the rails. These approaches helped to better understand the transient resonant dynamic processes and offered insight on how to alter the launching device materials and geometry to reduce the critical-velocity effects.     

The coupled vibration characteristics of a spinning and axially moving composite thin-walled beam

This article focuses on the coupled vibration characteristics of a spinning and axially moving composite thin-walled beam. Dynamic equations of the coupled vibration problem are built by Hamilton's principle. Galerkin's method is employed to solve the equations. The combined effects of spinning angular speeds and axial speeds on natural frequencies of the beam are studied specifically. Some interesting conclusions about the critical axial speed and critical spinning angular speed are proposed. Numerical simulations are performed to discuss the influences of spinning angular speeds, axial speeds, length- and thickness-to-radius ratios and fiber orientation angles on vibration characteristics of the beam.     

轴向载荷作用下无限长连续梁振动研究

研究了轴向静载荷作用下无限长等间距支承梁的横向振动问题。通过所建立的理论模型，分析了不同轴向载荷包括拉压对梁振动特性的影响，着重讨论了共振频率和对应幅值的变化规律；模型中，振动激励载荷为一作用于梁中的正弦变化的集中横向力，并考虑了梁横向变形阻尼系数、应变阻尼系数以及支承刚度对梁振动特性影响等因素。     

高速轴向运动梁横向受迫振动的稳态分析

在两端简支边界条件下,研究超临界速度范围内轴向运动梁横向非线性受迫振动的稳态响应。考虑Kelvin本构关系,通过坐标变换建立一个积分偏微分方程,以此描述高速轴向运动梁受到一个周期的外激励后所作的微幅振动。用8阶Galerkin方法截断标准控制方程,然后使用有限差分法计算受迫振动稳定的稳态响应。结果表明,在超临界速度范围,当激励频率接近前两阶固有频率时存在共振现象。