A novel approach to the dynamic response analysis of Euler-Bernoulli beams resting on a Winkler soil model and subjected to impact loads

This work presents a novel approach to the dynamic response analysis of a Euler-Bernoulli beam resting on a Winkler soil model and subjected to an impact loading.The approach considers that damping has much less importance in controlling the maximum response to impulsive loadings because the maximum response is reached in a very short time,before the damping forces can dissipate a significant portion of the energy input into the system.The development of two sine series solutions,relating to different types of impulsive loadings,one involving a single concentrated force and the other a distributed line load,are presented.This study revealed that when a simply supported Euler-Bernoulli beam,resting on a Winkler soil model,is subject to an impact load,the resulting vertical displacements,bending moments and shear forces produced along the span of the beam are considerably affected.In particular,the quantification of this effect is best observed,relative to the corresponding static solution,via an amplification factor.The computed impact amplification factors,for the sub-grade moduli used in this study,were in magnitude greater than 2,thus confirming the multiple-degree-of-freedom nature of the problem.

Experimental study on dynamic load magnification factor for ballastless track-subgrade of high-speed railway

The magnitude of dynamic load produced by high-speed trains depends on many factors,of which train speed is the most critical one.However,it is quite difficult to determine the effect of train speed on dynamic load using the theoretical methods due to the complexity of the interaction between vehicle and track-subgrade.Thus large-scale model test has gradually become an important approach for studying dynamic responses of ballastless track-subgrade of high-speed railway.In this study,a full-scale model of ballastless track-subgrade was constructed in accordance with the design and construction standards for Shanghai-Nanjing intercity high-speed railway line firstly.Then,the dynamic strain of slab and the dynamic earth pressure of subgrade were measured by conducting single wheel axle excitation test.In addition,the relationship between the dynamic load magnification factor（DLF） and the train speed was obtained.Finally,the DLF of track-subgrade under different train speeds was proposed,similar to that given by German Railway Standard.

EFFECT OF GEAR WIDTH AND HELIX ANGLE ON FACTOR OF DYNAMIC LOAD OF DOUBLE CIRCULAR ARC HELICAL GEARING

Based on theory of mechanical dynamics, meshing characteristic as well as thedynamic model of double circular arc helical gearing, an analysis approach and a computer programhave been developed for studying the state of dynamic load and factor of dynamic load of thegearing, the changing situation of dynamic load and dynamic load factor vs some affecting factorssuch as gear width, helix angle and accuracy grade etc are investigated. A series of conclusions areobtained: ①With the increasing in the values of gear width, the dynamic load factor appears slowdecreasing tendency in most region of gear width. ②When the accuracy grades of the gearing areimproved, the values of dynamic load factor decrease. ③The value of dynamic load factor appears adecreasing tendency with the increasing of value of helix angle at the same ratio of criticalrotational speed.

Dynamic caustics test of blast load impact on neighboring different cross-section roadways

Using digital laser dynamic caustics experimental system and conducting simulation experiment researched the influence rule of blasting excavation of a new roadway on neighboring existed different cross-section roadways. The experimental results show that the influence of blast load on adjacent roadway has a good relationship with the cross-section of roadway. The expansion distance of precrack existed in circular, arch-wall, rectangular roadway is respectively 1.76, 1.61 and 0 cm under blast load.At the same time, the direct-blast side of rectangular roadway has more obvious damage compared with circular and arch-wall roadway. It explains that plane reflects more stress wave than arc, so that it exerts more tensile failure in the direct-blast side, which leads to less stress wave diffracting to the precrack in the back-blast side. When the precrack extends, higher value dynamic stress intensity factor in circular roadway works longer than that of arch-wall roadway. Indirectly, it explains that plane's weakening function on stress wave is significantly stronger than arc. Stress wave brings about self-evident influence on the upper and bottom endpoints of the rectangular roadway, and it respectively extends 1.03, 2.06 cm along the line link direction of the center of the blasthole and the upper and bottom endpoints on the right wall.

Dynamic fracture behavior of rock under impact load using the caustics method

We studied the dynamic fracture mechanical behavior of rock under different impact rates. The fracture experiment was a three-point bending beam subjected to different impact loads monitored using the reflected caustics method. The mechanical parameters for fracture of the three-poim bending beam specimen under impact load are analyzed. The mechanism of crack propagation is discussed. Experimental results show that the dynamic stress intensity factor increases before crack initiation. When the dynamic stress intensity factor reaches its maximum value the crack starts to develop. After crack initiation the dynamic stress intensity factor decreases rapidly and oscillates. As the impact rate increases the cracks initiate earlier, the maximum value of crack growth velocity becomes smaller and the values of dynamic stress intensity factor also vary less during crack propagation. The results provide a theoretical basis for the study of rock dynamic fracture.

Dynamic amplification factors for a system with multiple-degrees-of-freedom

It is well-known that the responses of a structure are different when subjected to a static load or a sudden step load.The dynamic amplification factor(DAF),which is defined as the ratio of the amplitude of the vibratory response to the static response,is normally used to depict the dynamic effect.For a single-degree-of-freedom system(SDOF)subjected to a sudden dynamic load,the maximum value of DAF is 2.Many design guidelines therefore use 2 as an upper bound to consider the dynamic effect.For a civil engineering structure,which is normally a multiple-degrees-of-freedom(MDOF)system,the DAF may exceed 2 in certain circumstances.The adoption of 2 as the upper bond as suggested by the design guidelines therefore may lead to unsafe structural design.Very limited studies systematically investigate the DAF of a MDOF sysCorrespondence to:Bi Kaiming,Centre for Infrastructure Monitoring and Protection,School of Civil and Mechanical Engineering,Curtin University,Kent Street,Bentley WA 6102,Australia Tel:(+61)892665139 E-mail:kaiming.bi@curtin.edu.autem.This study theoretically investigates the DAF of a MDOF system when it is subjected to a step load based on the fundamental theory of structural dynamics.The condition on which the DAF may exceed 2 is defined.Two numerical examples and one experimental study of a cable-stayed bridge subjected to sudden cable loss are presented to illustrate the problem.

Evaluation of vertical impact factor coefficients for continuous and integral railway bridges under high-speed moving loads

In the railway bridge analysis and design method,dynamic train loads are regarded as static loads enhanced by an impact factor(IF).The IF coefficients for various railway bridges have been reported as a function of span length or frequency of the bridges in Eurocode(2003).However,these IF coefficient values neglect the effects of very high speeds(>200 km/h)and soil-structure interaction(SSI).In this work,a comprehensive study to assess the impact factor coefficients of mid-span vertical displacements for continuous and integral railway bridges subjected to high-speed moving loads is reported.Three different configurations,each for the three-dimensional(3D)continuous and integral bridge,are considered.Also,single-track(1-T)and two-track(2-T)“real train”loading cases for both these bridge types are considered.Subsequently,finite element analysis of the full-scale 3D bridge models,to identify their IF values,considering the effects of SSI for three different soil conditions,is conducted.The IF values obtained from the study for both bridge types are comparable and are greater than the values recommended by Eurocode(2003).The results reveal that with a loss of soil stiffness,the IF value reduces;thus,it confirms the importance of SSI analysis.

CONVOLUTION OF THE IMPACT THREE-DIMENSIONAL ELASTO-DYNAMICS AND DYNAMIC STRESS INTENSITY FACTOR FOR AN ELLIPTIC CRACK

This paper presents a formulation for three-dimensional elasto-dynamics with an elliptic crack based on the Laplace and Fourier transforms and the convolution theorem. The dynamic stress intensity factor for the crack is determined by solving a Fredholm integral equation of the first kind. The results of this paper are very close to those given by the two-dimensional dual integral equation method.

Analysis of dynamic stress intensity factors of three-point bend specimen containing crack

A new formula is obtained to calculate dynamic stress intensity factors of the three-point bending specimen containing a single edge crack in this study. Firstly, the weight function for three-point bending specimen containing a single edge crack is derived from a general weight function form and two reference stress intensity factors, the coefficients of the weight function are given. Secondly, the history and distribution of dynamic stresses in uncracked three-point bending specimen are derived based on the vibration theory. Finally~ the dynamic stress intensity factors equations for three-pointing specimen with a single edge crack subjected to impact loadings are obtained by the weight function method. The obtained formula is verified by the comparison with the numerical results of the finite element method （FEM）. Good agreements have been achieved. The law of dynamic stress intensity factors of the three-point bending specimen under impact loadings varing with crack depths and loading rates is studied.

THE THREE-DIMENSIONAL STRESS INTENSITY FACTOR UNDER MOVING LOADS ON THE CRACK FACES

The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body,with the crack faces subjected to a traction distribution consisting of two pairs of combined mode point loads that move in a direction perpendicular to the crack edge is considered.The analytic expression for the combined mode stress intensity factors as a function of time for any point along the crack edge is obtained.The method of solution is based on the application of integral transform together with the Wiener-Hopf technique and the Cagniard-de Hoop method. Some features of the solution are discussed and graphical results for various point load speeds are presented.

大重合度直齿轮动载特性分析

针对大重合度直齿轮啮合齿数与普通直齿轮间的差异性变化,以一对大重合度直齿轮和普通直齿轮为研究对象,通过有限元法求解齿轮时变啮合刚度,建立大重合度直齿轮啮合耦合型动力学模型,利用Newmark-β时域积分求解齿轮系统动态响应,对其进行时频域分析并与普通直齿轮进行对比,获得了大重合度直齿轮在不同转速、误差影响下的动载系数变化规律。结果表明,大重合度直齿轮啮合刚度与普通齿轮有较大差异,其动态响应结果波动幅值较普通直齿轮有明显降低,提升了系统稳定性;大重合度直齿轮动载系数与普通直齿轮相比有明显下降,并且随着转速的升高和误差的增大出现不同程度的增加,其中在共振转速区域范围内增幅明显。

风与地震作用下平面索网幕墙系统的动力性能研究

平面索网幕墙被广泛应用于大型公共建筑中,因具有阻尼小、刚度低、非线性强等特点,其在强风与地震作用下易出现索力突变、变形过大、面板损伤等不利现象。建立了索网幕墙系统的精细化数值模型,量化了风、地震作用下相邻主结构对幕墙动力性能的影响,分析了两种灾害共同作用下的索网动力响应及面板、密封胶安全状态,计算了幕墙的风振系数并与规范参考值进行对比。研究结果表明:考虑主结构影响的索网幕墙的频率平均减小了12%,地震作用下中部拉索的峰值位移比为6.5,远大于风致响应,计算索网幕墙的地震响应时不可忽略主结构的影响。两种灾害共同作用时,索网位移的增幅大于索力的增幅,位移响应对外部激励变化更加敏感,且位于幕墙顶部的玻璃面板与密封胶的应力均超过设计强度,应在运维过程中予以重点关注。此外,对索网幕墙风致响应结果进行数理统计,得到了可供工程设计参考的风振系数。

人群步行荷载等效动载因子及应用

人群步行荷载是大跨楼盖、人行桥等工程结构人致振动分析的基础。现有时域模型缺乏对人-人相互作用的考虑,频域模型形式复杂难以用于工程设计。对此,提出了一种简单有效的人群步行荷载等效动载因子模型,该模型基于二阶傅里叶级数,充分考虑人-人相互作用且适用于人群密度相关的多种交通状态。首先利用基于实测的人群步行荷载互功率谱模型进行了不同人数、主导步频、结构阻尼比下的单自由度系统响应模拟,进而依据结构响应等效的原则,由模拟结果拟合确定等效动载因子计算公式。利用已建成大跨结构的实测响应进行了验证,结果表明,该模型相比国内外现有规范方法具有更低的预测误差,可为大跨结构设计中人致振动舒适度和安全性评估提供参考。

循环荷载作用下土工格栅加筋黄土动力特性研究

【目的】由于黄土所具有的结构疏松、抗剪性低,以及对水、力及震动都十分敏感等工程特性,故探究采用双向土工格栅对西宁地区黄土加筋前后土体动力性能的改善效果。【方法】采用GDS双向动三轴测试系统开展不同加筋层间距、不同围压、不同动应力幅值工况条件下加筋黄土的动三轴试验,分析循环荷载作用下加筋层间距对黄土动强度、动剪切模量、阻尼比等动力响应特性的影响,探讨分析加筋黄土动力响应特性的演化规律。【结果】结果显示:黄土动应变随着动应力的增大而增大,骨干曲线呈现应变强化型,并且骨干曲线随加筋层间距的减小逐渐由曲线型过渡为直线型;随着加筋层间距的减小,黄土强度随之增大,随着围压和加筋层间距的增加,黄土幅值剪应力明显增大,动剪应变减小,阻尼比明显减小。【结论】结果表明:围压和加筋层间距对加筋黄土的动力特性具有显著的增强作用,且存在一个最优加筋层间距。研究成果可为西宁地区加筋黄土道路设计提供参考依据。

Nelson-Siegel模型中的时变载荷因子及其对提高经济形势预测的重要作用

现有文献中Nelson-Siegel模型大多将载荷因子λ提前固定为常数或作为待估静态参数,较少考虑载荷因子λ的时变化。本文基于得分驱动时变参数建模方法,在状态空间模型框架内考虑时变载荷因子λ,构建GAS-λ-DNS模型,并提取相应时变载荷因子。结果显示,时变载荷因子λ_(t)呈现出极强的波动性,同时与经济周期密切相关;将时变载荷因子λ_(t)应用于预测工业产出增速,发现载荷因子相比于传统宏观预测因子具有额外增量信息,引入λ_(t)可以显著提高模型预测精度。本文结论对Nelson-Siegel利率期限结构建模和宏观经济预测因子选取具有参考价值。

行星传动系统均载与动载系数试验测量改进设计

试验测量行星传动系统均载与动载系数的精准度是评价系统动态性能的基础。针对现有行星传动系统均载与动载系数测量方法存在灵敏度与精度欠佳、系数测试算法缺失、测试应力点存误等问题,本文提出了一种方便、实用且具有高精度的行星传动系统均载与动载系数测试方法,定义了系统系数的测试算法与概念,明确了精确应力测试位置点及不同位置间差异性,采用应变片电桥传感器串并联设计,实现了拉压应力叠加、温度补偿以及繁琐标定免除等优点,为精准测取行星传动系统均载与动载性能提供了重要的理论基础和技术手段。

安全阀排放的动响应分析

安全阀排放冲击与响应是振动工程中典型的瞬态响应问题。根据阀后直管段长度L与特征长*度L的关系,讨论了四种可能的冲击形式;利用Laplace变换和逆变换,给出了四种冲击的瞬态响应解析解,表明冲击响应的最大幅值是关于安全阀全开时间与系统自振周期之比的函数;据此对安全阀排放系统的动载系数DFL取值给了分析和建议。

相邻炮孔爆生裂纹相互作用试验研究

为了研究爆炸载荷作用下的相邻炮孔间爆生裂纹相互作用机理,采用新型数字激光动态焦散线试验系统,通过改变炮孔间距,调整药包装药结构,研究了不同间距、不同装药结构下爆生裂纹相向扩展作用机理。结果表明:2炮孔均为普通药包时爆生裂纹随机分布,切缝药包与普通药包相互作用时前期爆生裂纹独立扩展,后期相互吸引互为自由面。2炮孔均为切缝药包相互作用时,炮孔间距较小情况下爆生裂纹在炮孔中心轴线方向贯穿呈“直线型”分布,间距较大时裂纹在炮孔中心轴线方向呈“牵手型”分布。随着炮孔间距增大,裂纹相遇时能量损耗较大,动态应力强度因子峰值和裂纹速度峰值较小,振幅较低,炮孔周围形成的粉碎区面积及次裂纹长度越小,分形维数也越小。

曳引电梯轿厢垂直振动特性研究

对电梯垂直方向的振动研究是提高电梯运行性能的关键,基于曳引比为2∶1的电梯系统,建立垂直方向上的动力学模型,分析轿厢载重和提升高度等参数对轿厢振动的影响及参数变化时系统的谐响应和惯性力响应,并对电梯制动的动载系数变化进行研究。结果表明,曳引机也是电梯轿厢振动的重要振源,轿厢振动与载荷质量和提升高度呈正比。

车辆载荷作用下穿越公路管段动力响应仿真研究

重载车辆行驶在管道上方时会对管道产生较大轴向载荷,易导致管道的断裂失效。因此,文中以穿越公路管段为研究对象,利用多体动力学仿真软件ADAMS模拟并提取车轮力,建立了管道动力响应有限元模型,研究了整车质量、行车速度以及轮压位置对穿越管段动力响应的影响,并确定了影响管道动力响应的主控因素。研究结果表明:车辆载荷作用下管道轴线方向的应力和位移呈抛物线型分布,且在两车轮中点附近达到最大值。管道的应力与整车质量呈正相关,与行车速度呈负相关,影响管道力学行为的主控因素为整车质量。