Dynamic response of multi-scale structure in flexible pavement to moving load

In order to study the dynamic responses in the microstructures of the pavement structure, the multi-scale modeling subjected to moving load is analyzed using the discrete element method （DEM）. The macro-scale discrete element model of the flexible pavement structure is established. The stress and strain at the bottom of the asphalt concrete layer under moving load are calculated. The DEM model is validated through comparison between DEM predictions and the results from the classical program. Based on the validated macro-scale DEM model, the distribution and the volumetric fraction of coarse aggregate, mastics and air voids at the bottom of the asphalt layer are modeled, and then the multi-scale model is constructed. The dynamic response in the microstructures of the multi-scale model are calculated and compared with the results from the macro model. The influence of mastic stiffness on the distribution of dynamic response in the microstructures is also analyzed. Results show that the average values and the variation coefficient of the tensile stress at the aggregate-mastic interface are far more than those within the mastics. The dynamic response including stress and strain distributes non-uniformly in both mastics and the interface. An increase in mastic stiffness tends to a uniform distribution of tensile stress in asphalt concrete.

Dynamic response of a beam on a Pasternak foundation and under a moving load

The dynamic response of an infinite beam placed on a Pasternak foundation when the system was subjected to a moving load was investigated.We used the double Fourier transform and its inversion to solve the formulations of the problem.A closed form analytic solution of the beam was obtained by the theorem of residues.We selected a numerical example to illustrate the dynamic response of the beam on Pasternak and Winkler foundations,respectively.We discuss the effect of the moving load velocity on the dynamic displacement response of the beam.The maximum deflection of the beam increases slightly with increased load velocity but increases significantly with reduced shear modulus of subgrade at a given velocity.The maximum deflection of a beam resting on a Pasternak foundation is much smaller than that of a beam on a Winkler foundation.

Dynamic Response of Curved Beam under Moving Load

In this paper an integral transform method is used to analyze the dynamic response of simple supported curved beam under single moving load with constant speed, and some parameters are defined. These parameters, such as radius of curvature, ratio of stiffness, velocity, warping stiffness, which may influence the response, are also discussed.

High-precision solution to the moving load problem using an improved spectral element method

In this paper, the spectral element method(SEM)is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem.In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases.Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.

Vibration characteristics of frozen soil under moving track loads

Vibration due to moving traffic loads is an important factor which induces frozen soil damage; this paper analyzed these vibration characteristics of frozen soil foundation under track loads. Firstly, seismic observation array （SOA） technology was applied to monitor the three dimensional dynamic characteristics of frozen soil under movable track load in a per- mafrost region and seasonal frozen soil area. Secondly, a numerical simulation for the response of frozen soil under movable track load was performed based on finite element analysis （FEA）, The results show that dynamic characteristics of frozen soil in perpendicular and parallel direction of the track are obviously different. In the direction perpendicular to the track, the vertical acceleration amplitude had an abrupt increase in the 9-10 m from the track line. In the direction parallel to the track, the acceleration in vertical and horizontal direction had a quick attenuation compared to the other direction. Lastly, various parameters were analyzed for the purpose of controlling the dynamic response of frozen soil and the vibration attenuation in frozen soil layer.

Numerical Simulation-Based Analysis of the Impact of Overloading on Segmentally Assembled Bridges

Segmentally assembled bridges are increasinglyfinding engineering applications in recent years due to their unique advantages,especially as urban viaducts.Vehicle loads are one of the most important variable loads acting on bridge structures.Accordingly,the influence of overloaded vehicles on existing assembled bridge structures is an urgent concern at present.This paper establishes thefinite element model of the segmentally assembled bridge based on ABAQUS software and analyzes the influence of vehicle overload on an assembled girder bridge struc-ture.First,afinite element model corresponding to the target bridge is established based on ABAQUS software,and the load is controlled to simulate vehicle movement in each area of the traveling zone at different times.Sec-ond,the key cross-sections of segmental girder bridges are monitored in real time based on the force character-istics of continuous girder bridges,and they are compared with the simulation results.Finally,a material damage ontology model is introduced,and the structural damage caused by different overloading rates is compared and analyzed.Results show that thefinite element modeling method is accurate by comparing with on-site measured data,and it is suitable for the numerical simulation of segmental girder bridges;Dynamic sensors installed at 1/4L,1/2L,and 3/4L of the segmental girder main beams could be used to identify the dynamic response of segmental girder bridges;The bottom plate of the segmental girder bridge is mostly damaged at the position where the length of the precast beam section changes and the midspan position.With the increase in load,damage in the direction of the bridge develops faster than that in the direction of the transverse bridge.Thefindings of this study can guide maintenance departments in the management and maintenance of bridges and vehicles.

DYNAMIC RESPONSE OF A DOUBLE-LAYERED SUBGRADE WITH ROCK SUBSTRATUM TO A MOVING POINT LOAD

In this paper, an analytical solution for the dynamic response of a double-layered subgrade with rock substratum to a moving point load is derived. The subgrade profile is divided into two layers. The upper layer is modeled by an elastic medium and the lower layer by a fully saturated poroelastic medium governed by Biot’s theory. In the meanwhile, the subgrade is resting on the rock substratum. The analytical solutions for stress, displacement and pore pressure are derived by using the Fourier transform. Numerical results obtained by using the inverse fast Fourier transform (IFFT) are used to analyze the influence of the moving load velocity, the thickness of an elastic medium layer and a fully saturated poroelastic medium layer on the dynamic response.

Numerical modelling of vibration response in loess hills due to a high-speed train on railway viaduct

In order to accurately analyze vibration characteristics and site effects of loess hills under moving load of a highspeed train,four types of loess hill models under railway viaduct was established by ABAQUS of finite element analysis software by field test.The dynamic response and stability of loess hills under two different vibration sources under high-speed train load were studied by using two-dimensional equivalent linear response timehistory analysis,and the influence of the mechanical parameters of loess on the vibration of different types of loess hill was analyzed.Results show that there are obvious differences between peak displacement cloud maps of loess hills under the railway viaduct under gravity and train load action.We analyzed the influence of the change of elastic modulus on vibration propagation of soil of foundation and loess knoll,and found that the change of elastic modulus of soil in different position of foundation has more effect on vibration propagation than that of loess knoll soil.At the same time,the vertical acceleration cloud maps of the four types of loess hills are obviously different.

移动荷载下考虑钢筋作用的混凝土裂缝梁动力响应分析

由于钢筋的约束作用,混凝土梁裂缝截面的局部柔度与无筋时不同。建立了移动荷载作用下考虑钢筋影响的混凝土裂缝梁动力方程,基于力平衡和钢筋与混凝土变形协调对裂缝截面的局部柔度进行修正,采用无质量弹簧模拟裂缝,得到计入钢筋作用的裂缝梁自振特性,通过Newmark方法求解控制方程获取钢筋混凝土梁的动力响应。以受移动车辆荷载的简支梁为例,分析不同荷载速度、裂缝深度、裂缝位置、配筋率等条件下的钢筋混凝土裂缝梁响应。研究结果表明,裂缝处钢筋的约束作用可以显著地影响梁的动力响应,计入钢筋提供的刚度后裂缝梁的位移响应总体减小,且随着开裂损伤程度的增加钢筋的影响呈现变大的趋势。移动荷载下裂缝梁的共振现象较无损梁更为不利,考虑钢筋作用后裂缝梁的共振速度有所提高,共振响应则有一定程度的降低。由于钢筋混凝土裂缝梁和无损梁的共振速度存在差异,在某些荷载速度下无损梁的位移响应大于裂缝梁。

基于切比雪夫拟谱法的移动荷载作用下简支梁动力响应计算

采用切比雪夫拟谱法求解移动荷载作用下简支梁的动力响应问题,该方法通过重新选取插值点的方式并借助转换矩阵对边界条件进行施加,对集中荷载采用高斯函数法进行正则化处理。将本文方法计算结果与解析解和有限元解进行比较,结果表明,在划分较少单元数量时,采用本文方法计算结果与解析解吻合良好,求解效率高于有限元方法。采用本文方法对Dirac函数的正则化参数σ_(n)进行敏感性分析,结果表明,当在±3σ_(n)范围内布置配点数6~10个时,计算结果能取得较好的精度。

埋置移动荷载作用下三维黏弹性半空间的动力响应

采用积分变换方法对埋置移动荷载作用下三维黏弹性半空间地基振动的衰减规律进行了理论研究。首先,基于理想弹性介质的动力Navier方程,利用Helmholtz分解定理及傅里叶变换方法,在直角坐标系中求得了变换域内弹性介质动力响应分量的表达式。结合相应的边界条件及连续条件,得到了埋置移动荷载作用下黏弹性半空间地基动力响应的积分形式解。当荷载埋深为零时,埋置移动荷载退化为地表移动荷载,对比发现退化解结果与已有结果吻合较好。最后,采用IFFT法对地基土体动力响应进行数值求解,分析了移动荷载埋深、速度等因素对地基振动的分布衰减规律以及频谱分布的影响。

简支矩形薄壁箱梁受不确定移动偏载作用的竖向振动响应研究

针对工程中薄壁箱梁受不确定移动偏载作用的振动问题,给出了一种基于区间过程的求解简支矩形薄壁箱梁结构竖向振动响应边界的方法.基于修正Timoshenko梁理论、乌氏第二理论和箱梁畸变理论,求得了移动偏载作用下考虑截面扭转和畸变的简支矩形薄壁箱梁受迫竖向振动解析解,通过引入区间过程描述移动偏载的不确定性,推导了简支矩形箱梁竖向振动响应边界的计算过程,分析了不确定性参数的相关性和荷载速度对简支矩形薄壁箱梁竖向振动响应的影响,与有限元计算结果对比验证了本文方法的正确性.

移动砰击载荷作用下的加筋板动力响应参数分析

针对高海况下船舶结构遭受的砰击载荷问题,该文采用Abaqus有限元软件,模拟了不同移动方向的砰击载荷对5块加筋板动力响应的影响。研究中,砰击载荷被等效为线性上升、指数衰减的脉冲时历形式,通过改变载荷参数(峰值压力、低压值、上升段长度、下降段长度和移动速度),并分析这些参数对加筋板动力响应的具体影响。研究发现,加筋板的动力响应与载荷参数紧密相关,特别是移动速度对动力响应的影响最为显著。此外,通过引入移动动荷系数DLFm和进行无因次化分析,文中深入探讨了动力响应与砰击载荷无因次参数间的变化规律及其敏感度,为船舶结构设计和优化提供了重要的理论依据。

基于非局部Biot理论的矩形移动荷载下饱和土动力响应

为进一步研究矩形移动荷载下饱和土路基中动力响应问题,首先,基于非局部Biot理论,以饱和土地基为研究对象,建立了考虑孔隙尺寸效应和矩形荷载作用下的非局部孔隙弹性计算模型;然后,考虑路基表面的透水边界条件,采用二次傅里叶逆变换得到饱和土体在矩形移动荷载下的时域内动力响应解析解;最后,分析了在不同模态和不同非局部参数的取值下,矩形荷载移动速度和荷载自振频率的变化对饱和土竖向和水平位移响应的影响。结果表明:在低模态时,非局部参数对饱和土位移响应影响不大,而在高模态时,其影响较大,并且位移响应主要取决于低模态。非局部参数与竖向位移成正比,而与水平位移成负相关关系。当荷载自振频率增大时,位移受到非局部参数的影响,随着非局部参数增大,位移响应峰值会在更低的荷载自振频率处出现,位移响应峰值向左移动。当荷载自振频率增大时,位移受到荷载移动速度的影响,在较低荷载移动速度下会出现位移响应峰值。当荷载移动速度增大时,位移受到荷载自振频率的影响,位移响应峰值出现对应的荷载自振频率减小。

移动荷载作用下悬浮隧道管体TMD减振分析及优化布置

为减小悬浮隧道管体在移动荷载作用下的动力响应,采用TMD作为振动控制措施并对减振效果进行了分析。将悬浮隧道管体简化为弹性地基梁,采用移动简谐力模拟汽车荷载,通过Morison方程计算管体振动过程中的流体附加惯性效应和阻尼效应,推导建立了移动荷载作用下管体-TMD系统振动控制方程组。采用Newmark-β法进行数值求解,分析了TMD对悬浮隧道管体的减振效果。针对悬浮隧道管体振动特征,提出采用分布式TMD的布置形式,并对移动速度、TMD阻尼比的影响进行了讨论。结论表明:TMD对移动简谐荷载作用下的悬浮隧道管体具有显著减振效果,最大位移减振率在50%以上。由于多阶模态参与振动,单一TMD的有效减振范围有限。在保持总质量不变的情况下,采用分布式TMD可以获得较好的整体减振效果。提高TMD质量比和降低移动荷载速度有助于提高TMD的减振效果。增大阻尼比会减弱TMD的效果,应综合考虑减振效果和工作空间的要求确定。

移动荷载作用下底部局部脱空地基梁力学响应研究

目的针对地基由于塑性变形、雨水冲蚀等引起混凝土路面底部产生的脱空效应,方法 将底部局部脱空混凝土路面简化为跨越空洞的弹性地基梁,采用Kelvin地基模型模拟路基对路面的作用,建立移动荷载作用下局部脱空地基梁动力响应控制方程,运用振型叠加法推导地基梁动力响应解析解。通过与既有理论方法计算结果对比,验证本文方法的正确性。然后采用推导出的理论解析解探讨荷载移动速度、地基弹性系数、地基梁抗弯刚度和脱空区宽度对地基梁动力响应的影响。结果 分析表明:忽略地基梁底部局部脱空的影响,将导致地基梁动力响应理论计算值偏小。地基梁底部局部脱空对脱空区正上方梁的振动位移影响较大,而对脱空区外侧地基梁的振动位移影响较小。地基梁抗弯刚度越小,脱空区宽度对地基梁中点振动位移最大值的影响越显著。当地基梁底部脱空区宽度与梁计算长度的比值为2/9时,地基梁中点振动位移最大值约为不考虑地基梁底部脱空影响时的5倍。增大地基梁抗弯刚度和地基弹性系数可以减小跨越空洞区地基梁中点振动位移,但当地基梁底部脱空区宽度大于1/3梁的计算长度时,提高既有地基弹性系数的控制效果反而较差。结论 混凝土路面底部脱空会加剧车辆荷载下的动力响应。

公路交通荷载对公路路基的稳定性影响

路基是路面的基础,只有稳定、坚实、耐久的路基才能保证路面的质量。因此,理解交通荷载如何影响路基的稳定性并采取相应的改良措施,对于提升公路质量和耐用性至关重要。文章结合某公路工程,采用有限元软件Plaxis 3D建立公路交通荷载作用下的路基动力响应模型,通过对路基的动力响应进行分析,得到公路交通荷载作用下路基动力响应规律。研究表明:移动荷载的移动速度和激振频率是影响路基稳定性的主要因素,移动荷载作用下的路基动力响应随着荷载移动速度的增大先迅速增大,在达到峰值后迅速减小;竖向位移、竖向加速度和动应力的关键速度分别为1.1倍、0.9倍和1.0倍的剪切波速;随着激振频率的增大,移动荷载作用下的路基动力响应总体呈现上涨的趋势,在激振频率超过约30 Hz后缓慢减小,且动力响应时程曲线表现出更显著的动力性。研究成果对于路基路面施工、路用材料的选择、路面抗车辙研究及养护工程具有重要的参考和借鉴价值。

基于Chebyshev-Ritz法分析两端固支梁在移动荷载下的动力响应

基于小变形、二维弹性力学理论,采用Chebyshev-Ritz法分析两端固支梁在移动集中简谐荷载下的动力响应.利用第一类Chebyshev多项式与边界特征函数的积作为梁位移的试函数,给出求解梁任意阶自振频率的方法,采用Newmark-β法求解振动控制方程得到梁位移响应的数值解.由收敛性分析可知本文方法求解的数值稳定、收敛快速且精度较高,与有限元软件ANSYS建模分析结果对比一致性较好.分析加速、减速和匀速运动下不同速度、荷载频率对于位移响应的影响,可为桥梁损伤检测和计算提供数据支撑和理论参考.

移动荷载作用下地铁轨道梁振动影响因素分析

城市轨道交通产生的振动问题随着城市化的快速发展已越来越不可忽略。为了更好地分析解决振动带来的影响,本文建立了连续弹性支承无限长轨道梁的模型,研究了它在变速移动荷载下的振动现象。首先建立了连续弹性支承Euler-Bernoulli梁的运动控制方程,然后通过Laplace变换结合Fourier变换把四阶非线性微分方程解的问题转化为常数解的问题,再通过Laplace和Fourier的反变换得到了关于时间和空间上梁振动的解析解,最后利用Mathematica、Matlab软件编程计算其变化规律。计算结果表明,在恒定速度、系统无阻尼下,无限长Euler梁不同位置处的动力响应相同;荷载移动的加速度会对梁的挠度产生影响;增大系统的支承刚度和支承阻尼可以有效减小梁的最大挠度。

桥梁受移动荷载动力响应的一种精细积分法

迄今为止,精细积分法都是应用于荷载作用位置固定不变的问题。本文将精细积分法推广到荷载作用点位置随时间而变化的情形,按有限元方法计算了桥梁受移动荷载作用时的动力响应,并与常规的Newmark方法、解析解做了比较。数值结果表明,精细积分法按本文的策略推广后,计算精度和效率均比通常的数值积分方法得到显著的提高。