NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS

The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.

Improvement of the axial trapping effect using azimuthally polarised trapping beam

A dual optical tweezers system, which consists of a doughnut mode optical tweezer （DMOT） with the azimuthally polarised trapping beam and a solid mode optical tweezer （SMOT） with the Gauss trapping beam was constructed to compare the axial trapping effect of DMOT and SMOT. The long-distance axial trapping of ST68 microbubbles （MBs） achieved by DMOT was more stable than that of SMOT. Moreover the axial trapping force measured using the viscous drag method, was depended on the diameter of the particle, the laser power, and the numerical aperture （NA） of the objective lens. The measurement of the axial trapping force and the acquisition of CCD images of trapping effect confirmed that the DMOT showed excellent axial trapping ability than SMOT. A simple and effective method is developed to improve axial trapping effect using the azimuthally polarized beam as trapping beam. This is helpful for the long-distance manipulating of particles especially polarised biological objects in axial direction.

Dynamic stability of parametrically-excited linear resonant beams under periodic axial force

The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied. It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory. The governing equations of motion are derived by using the Rayleigh-Ritz method and transformed into Mathieu equations, which are formed to determine the stability criterion and stability regions for parametricallyexcited linear resonant beams. An improved stability criterion is obtained using periodic Lyapunov functions. The boundary points on the stable regions are determined by using a small parameter perturbation method. Numerical results and discussion are presented to highlight the effects of beam length, axial force and damped coefficient on the stability criterion and stability regions. While some stability rules are easy to anticipate, we draw some conclusions： with the increase of damped coefficient, stable regions arise; with the decrease of beam length, the conditions of the damped coefficient arise instead. These conclusions can provide a reference for the robust design of parametricallyexcited linear resonant sensors.

Asymptotic analysis on weakly forced vibration of axially moving viscoelastic beam constituted by standard linear solid model

The weakly forced vibration of an axially moving viscoelastic beam is inves- tigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved. The nonlinear equations governing the transverse vibration are derived from the dynamical, constitutive, and geometrical relations. The method of multiple scales is used to determine the steady-state response. The modulation equation is derived from the solvability condition of eliminating secular terms. Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response are derived from the modulation equation. The stability of non- trivial steady-state response is examined via the Routh-Hurwitz criterion.

Modal and Fatigue Life Analysis on Beam with Multiple Cracks Subjected to Axial Force

Based on the transfer matrix method and Forman equation,a new method is proposed to conduct the modal and fatigue life analysis of a beam with multiple transverse cracks.In the modal analysis,the damping loss factor is introduced by the complex elastic modulus,bending springs without mass are used to replace the transverse cracks,and the characteristic transfer matrix of the whole cracked beam can be derived.In the fatigue life analysis,considering the interaction of the beam vibration and fatigue cracks growth,the fatigue life of the cracked beam is predicted by the timing analysis method.Numerical calculation shows that cracks have a significant influence on the modal and fatigue life of the beam.

Vibration of axially moving beam supported by viscoelastic foundation

In this paper, transverse vibration of an axially moving beam supported by a viscoelastic foundation is analyzed by a complex modal analysis method. The equation of motion is developed based on the generalized Hamilton＇s principle. Eigenvalues and eigenfunctions are semi-analytically obtained. The governing equation is represented in a canonical state space form, which is defined by two matrix differential operators. The orthogonality of the eigenfunctions and the adjoint eigenfunctions is used to decouple the system in the state space. The responses of the system to arbitrary external excitation and initial conditions are expressed in the modal expansion. Numerical examples are presented to illustrate the proposed approach. The effects of the foundation parameters on free and forced vibration are examined.

Seismic Behavor of RC Beam-Column Joint with Additional Bars under Cyclic Loading

The behavior of Beam-Column Joints in moment resisting frame structures are susceptible to damage caused by seismic effects due to poor performance of the joint.A good number of researches were carried out to understand the complex mechanism of RC joints which are considered in seismic design code practices presently adopted.The traditional construction detailing of transverse reinforcement have shown serious joint failure. This paper introduces a new design philosophy involving the use of additional diagonal bars within the joint particularly suitable for low to medium seismic effects in earthquake zones throughout the world.In lieu to this study,ten(10) full-scale interior beam-column specimens were constructed with various additional reinforcement details and configurations as will be discussed in the later.The experiment provided adequate results to proof the idea of additional bars as suitable approach in reinforced concrete structures where earthquake is eminent.While compared with overall cracking observation during the test,the specimen with additional bars (diagonal and straight) had shown few cracks on the column than the ones without.Furthermore,concrete confinement is certainly an important design method as recommended by certain international codes.

考虑轴力与底板约束的埋入式钢柱脚刚度模型

为准确预测埋入式(特别是浅埋)钢柱脚节点的初始转动刚度,将柱脚的埋入段简化为地基梁,基于初参数法完善考虑轴力影响的Winkler地基上的Timoshenko梁理论,提出受锚栓和混凝土约束的柱脚底板转动刚度的计算方法,进而建立可以综合反映柱脚埋深、埋入段剪切变形、钢柱轴力、底板约束影响的埋入式钢柱脚转动刚度模型。基于已验证的有限元模型进行参数分析,研究埋深比、轴力和锚栓布置对柱脚转动刚度的影响。与有限元结果的对比表明,提出的刚度模型较过往文献中理论模型具有更高的精度和更好的适用性,尤其是对于埋深比为0.5~1.5的浅埋柱脚节点。理论与有限元结果表明:埋深比较小时,柱脚转动刚度随埋深比的增加快速增大,而埋深比增加到一定程度后,其对转动刚度几乎无影响;柱脚转动刚度随钢柱轴压力增加呈增大的趋势;对于浅埋柱脚节点,底板约束对其转动刚度的影响较大,而随着埋深的增大,其影响逐渐减小;底板转动约束对埋深比小于1.5的节点刚度具有显著影响,当埋深比增大至2.5,其影响可以忽略。

热轴力对双层微梁谐振器热弹性阻尼的影响分析

近年来,已有不少关于复合材料层合梁/板谐振器热弹性阻尼的研究论文发表.然而,在这些研究中热轴力(热薄膜力)对热弹性阻尼的贡献都被忽略了.众所周知,若梁/板的材料性质分布关于几何中面不对称则其物理中面将偏离几何中面.于是,热-弹耦合振动引起的变温场不但会形成热弯矩,还会产生热轴力(热薄膜力),二者将共同产生热弹性阻尼.文章基于Euler-Bernoulli梁理论和经典热传导理论,建立了双层矩形截面微梁热-弹耦合振动数学模型,精确考虑了热轴力对微结构内能耗的贡献.然后,采用解析方法求得了用变形几何量表示的热轴力和热弯矩,进而求得了系统自由振动的复频率以及用逆品质因数表示的热弹性阻尼解析解.作为数值算例,选取由均匀的银(Ag)和氮化硅(Si_(3)N_(4))分层组成的双层微梁,通过大量的数值实验定量分析了分层体积分数变化对热弹性阻尼的影响规律,考察了热轴力对热弹性阻尼的影响程度.结果表明,忽略热轴力将会低估层合梁谐振器的热弹性阻尼.在金属银的体积分数为70%(氮化硅体积分数为30%)时,忽略热轴力后对热弹性阻尼的低估最大可达16.3%.

基坑圈梁轴力施工监测分析

某工程在某半地下储罐基坑周围区域布设了6个监测点用以监测圈梁轴力。文中整理分析此监测数据,并根据监测数据对圈梁轴力的监测结果进行了分析,结果表明,在圈梁钢筋的围护下,钻孔咬合灌注桩处于安全状态,针对半地下式储罐设计的环形咬合灌注桩基坑支护结构合理可行,对基坑变形的控制效果显著。

巷道全生命周期锚杆轴力规律研究

巷道锚杆轴力监测可作为判断围岩稳定性的依据。以某矿工作面辅运顺槽为研究对象,采用锚杆无损检测技术和锚杆测力计相结合的手段,获得了巷道全生命周期锚杆轴力的变化规律,结果表明:在巷道掘进初期,受巷道围岩应力重分布的影响,锚杆轴力呈上升趋势;随着巷道的不断掘进,进入稳定期后,锚杆轴力趋于稳定;在工作面采动期间,锚杆轴力再次呈上升趋势,且随着工作面的不断推进,上升趋势也逐渐明显。通过锚杆轴力的变化情况可以获取巷道围岩稳定性,以此来为巷道支护参数优化提供依据。

丹江口水库特大桥跨中无轴力连接装置施工关键技术

丹江口水库特大桥为主跨760 m的双塔双索面部分地锚式混合梁斜拉桥,边中跨比为0.2,采用梁塔分离、梁台固结的结构体系。根据主桥结构体系受力需要,主梁在跨中位置断开,设置跨中无轴力连接装置+伸缩装置构造。无轴力连接装置由导梁、外部大箱梁(H梁段和H′梁段)、竖向及横向支座系统组成,导梁长13.68 m。无轴力连接装置现场安装采用导梁跨中分段(2×6.84 m)拼装、外部大箱梁逐缝合龙的施工方法。首先在总拼场地进行无轴力连接装置工厂化预拼装,并安装竖向及横向支座系统,拼装完成后将导梁断开,回位至H梁段和H′梁段进行转运;然后现场吊装匹配连接H梁段,并将H梁段内部导梁向岸侧拖动固定;之后起吊H′梁段并与前置G梁段软连接;再进行H梁段和H′梁段导梁匹配连接;导梁匹配连接完成后进行H′梁段匹配连接;最后进行斜拉索放张、桥面吊机拆除。

Forced vibration control of an axially moving beam with an attached nonlinear energy sink

This paper investigates a highly efficient and promising control method for forced vibration control of an axially moving beam with an attached nonlinear energy sink（NES）.Because of the axial velocity,external force and external excitation frequency,the beam undergoes a high-amplitude vibration.The Galerkin method is applied to discretize the dynamic equations of the beam–NES system.The steady-state responses of the beams with an attached NES and with nothing attached are acquired by numerical simulation.Furthermore,the fast Fourier transform（FFT）is applied to get the amplitude–frequency responses.From the perspective of frequency domain analysis,it is explained that the NES has little effect on the natural frequency of the beam.Results confirm that NES has a great potential to control the excessive vibration.

轴向力影响下大阻尼梁高频能量流响应解析模型

针对轴向力作用下大阻尼梁的高频振动问题,基于能量流分析方法构建高频动响应解析预报模型。推导梁结构的能量传递方程和能量损失方程,结合功率平衡方程构建轴向力影响下大阻尼梁的能量密度控制方程。以简支梁为典型算例,分析结构的能量密度响应,研究轴向力和结构阻尼损耗因子对高频能量流响应的影响。数值结果表明:提出的能量流响应解析模型渐进一致逼近基于波动分析法的经典模型解,可以准确预示轴向力作用下大阻尼梁的高频弯曲振动响应。随着梁结构轴向载荷和阻尼损耗因子的增加,能量密度自激励点向两端约束边界衰减速度提高。但是,梁结构的弯曲振动总能量随轴向载荷单调增加,而随阻尼损耗因子单调减小。

基于弹性梁理论的在役拉杆轴向载荷测量方法与应用

基于弹性梁理论,建立了横向加载条件下在役拉杆轴力理论计算模型及预加应力梁的三维有限元模型,对在役支吊架拉杆轴力测量方法进行了研究,讨论了不同长径比和横向载荷对拉杆中点挠度的影响。研究结果表明,理论预测结果与有限元计算结果吻合较好;在工程应用方面给出了以横向载荷容差度及挠度容差值为指标的固支段拉杆长径比的优选方案。该方法可用于快速测量不卸载拉杆的轴向载荷。

轴向运动形状记忆合金层合梁的参强联合共振

该研究探讨了轴向变速运动形状记忆合金(shape memory alloy,SMA)层合梁在简谐激励下的参强联合共振问题。基于SMA的Falk多项式本构模型,结合Timoshenko梁理论推导了轴向运动SMA层合梁的非线性振动方程。利用伽辽金积分法对其进行时间变量和空间变量的离散,用多尺度法以及坐标变换的方法推导系统参强联合共振的幅频响应方程。通过算例分析,得到不同物理参数变化时的幅频响应曲线图和振幅-参数曲线图,分析了轴向速度、温度及强迫激励对系统参强联合共振特性的影响。结果表明,系统呈现典型的非线性振动特征和复杂的动力学行为。

含轴力高频振动梁的能量辐射传递模型

为考察轴力对梁高频振动的影响,建立了轴力作用下梁的能量辐射传递模型。针对具有恒定轴力作用的Euler-Bernoulli梁,引入受轴力影响的波数和群速度,建立能量密度控制方程,推导轴力作用下梁的能量密度和能量强度的核函数。实源强度由导纳法计算得到的输入功率表示,虚源强度通过边界能量平衡方程确定,根据惠更斯原理,梁的能量响应由实源产生的直接场与虚源产生的反射场线性叠加得到。通过将能量辐射传递法(energy radiative transfer model,RETM)获得的结果与波传播法解析解进行比较,分析了轴力作用下无限结构导纳的适用性,验证所提RETM的正确性,同时分析了轴力对梁能量响应的影响。

轴向运动梁在横向裂纹作用下的Green函数解

为了研究轴向运动梁在横向裂纹作用下的振动问题,利用分离变量法、Laplace变换法和传递矩阵法得到了轴向运动裂纹梁的Green函数解。通过数值计算验证了解析解的有效性,并研究了轴向速度、裂纹深度、裂纹位置等各种重要物理参数对挠度的影响。当轴向速度从10 m/s增加到40 m/s时,无量纲Green函数g(ξ,0.5)由10减小到6,表明随着轴向速度的增加,梁的挠度相应减小。此外,还研究了两条裂纹的相互作用,发现其相互影响强度可通过曲线间的面积表示。分析结果可以为裂纹梁问题的数值模拟和实验研究提供参考。

连梁低屈服点钢剪切型阻尼器力学性能研究

连梁低屈服点钢剪切型阻尼器实际处于多种荷载组合作用下,针对连梁低屈服点钢剪切型阻尼器只考虑了剪力的现象,通过ABAQUS对阻尼器施加纯剪切作用、轴向–剪切作用、弯矩–剪切作用,改变阻尼器材料,将公式推导与有限元模拟相结合,研究轴力、弯矩对阻尼器力学性能的影响。研究结果表明:轴力会使阻尼器提前进入屈服,对阻尼器耗能能力影响较小;弯矩的存在会降低阻尼器的屈服荷载、极限荷载,增强阻尼器的耗能能力;材料改变对阻尼器力学性能影响不显著。

空间桁架门梁基于不同计算模型的比较分析

空间桁架门梁作为承担大门自重和承受墙面风荷载的受力构件,其计算通常与其下部混凝土门柱分开进行,然而,这样的简化计算并不能真实反映混合结构的实际受力状况。文章通过建立独立门梁模型和整体结构模型,对空间桁架门梁的跨中变形、杆件轴力和杆件强度利用率进行了比较分析,发现采用独立门梁模型计算的跨中位移及各类杆件的最大计算应力比均大于整体结构模型,结构偏安全,使用较普遍,但经济性不高。整体结构模型兼顾了准确计算与成本控制,是既安全又经济的选择。