Behavior of Vortex-Induced Vibration of A Circular Cylinder Near A Deformable Wall with Two Degrees of Freedom in Steady Flow

The behavior of vortex-induced vibration of a two-degree-of-freedom cylinder near a deformable wall in steady flow is investigated experimentally. The typical phenomenon of the two-degree-of-freedom cylinder＇s VIV is discussed. The influences of initial gap between the cylinder and the wall on the dynamic responses of the cylinder are analyzed. The comparison is made about dynamic responses of the cylinder with one and two degrees of freedom. Experimental results show that the vibration of the cylinder near a deformable wall with a small value of initial gap-to-diameter ratios can generally be divided into two phases. The initial gap-to-diameter ratios have a noticeable influence on the occurrence of transverse vibration. The transverse maximum amplitude of the cylinder with two degrees of freedom is larger than that of the cylinder with one degree of freedom under the condition with the same values of other parameters. However, the vibration frequency of the cylinder for the two degrees of freedom case is smaller than that for the one degree of freedom case at the same value of Vr number

Physical Modeling and Parametric Study on Two-Degree-of-Freedom VIV of A Cylinder near Rigid Wall

Unlike most previous studies on the transverse vortex-induced vibration（VlV） of a cylinder mainly under the wallfree condition （Williamson ＆ Govardhan, 2004）, this paper experimentally investigates the vortex-induced vibration of a cylinder with two degrees of freedom near a rigid wall exposed to steady flow. The amplitude and frequency responses of the cylinder are discussed. The lee wake flow patterns of the cylinder undergoin^g VIV were visualized by employing the hydrogen bubble technique. The effects of the gap-to-diameter ratio （eo/D） and the mass ratio on the vibration amplitude and frequency are analyzed. Comparisons of VIV response of the cylinder are made between one degree （only transverse） and two degrees of freedom （streamwise and transverse） and those between the present study and previous ones. The experimental observation indicates that there are two types of streamwise vibration, i.e. the first streamwise vibration （FSV） with small amplitude and the second streamwise vibration （SSV） which coexists with transverse vibration. The vortex shedding pattern for the FSV is approximately syrmnetric and that for the SSV is ahernate. The first streamwise vibration tends to disappear with the decrease of eo/D. For the case of large gap-to-dianeter ratios （ e.g. eo/D = 0. 54 ～ 1.58）, the maximum amplitudes of the second streamwise vibration and transverse one increase with the increasing gap- to-diameter ratio. But for the case of small gap-to-diameter ratios （e. g. eo/D= 0. 16, 0.23）, the vibration amplitude of the cylinder increases slowly at the initial stage （i.e. at small reduced velocity Vr）, and across the maximum amplitude it decreases quickly at the last stage （i.e. at large Vr）. Within the range of the examined small mass ratio （m 〈 4）, both streamwise and transverse vibration amplitude of the cylinder decrease with the increase of mass ratio for the fixed value of Vr- The vibration range （ in terms of Vr） tends to widen with the decrease of the mass ratio. In the second streamwise vibration region, the vibration frequency of the cylinder with a small mass ratio （ e.g. mx = 1.44） undergoes a jump at a certain Vr＋ The maximum amplitudes of the transverse vibration for two-degree-of-freedom case is larger than that for one-degree-of-freedom case, but the transverse vibration frequency of the cylinder with two degrees of freedom is lower than that with one degree of freedom（transverse）.

OPTIMAL CONTROL OF THE FLEXI-BLE LINK MANIPULATOR WITH CONTROLLABLE LOCAL DEGREES OF FREEDOM

Although flexible manipulators own many potential advantages, one of their major disadvantages is the deterioration of the end-effector accuracy due to the flexibility. Therefore, how to reduce vibration is a significant problem. Inspired by the observation on the motion behaviors of animals, a new idea of decreasing motion deflection of the flexible manipulator is suggested. The concept of controllable local degrees of freedom is proposed and analyzed. By way of optimizing local motion provided by the controllable local degrees of freedom, the end-effector deflection of the flexible manipulator can be effectively decreased through dynamic coupling. The corresponding optimal method for vibration control of the flexible manipulator is put forward. The kinematic simulation is carried ant on a three-link flexible manipulator The corresponding results verify the feasibility of this method.

Long-Term Effect of TMD on Vibration Control of An MDOF Offshore Fixed Platform

A three-dimensional fixed offshore platform in deep water modeled by the finite element method is studied in this paper. Analysis of the dynamic response of the MDOF structure is realized taking the non-linearity of the wave drag force and the wave-structure interaction into account. The structural response statistics, which have Gaussian distributions, are used to evaluate the vibration effect of the structure without TMD and with TMD. And an optimal method to design TMD controlling the first mode of the multi-mode structure is proposed. Moreover, the probabilities of occurrence of sea states at the platform site are considered for prediction of the long-term effect of a TMD. Simulation results demonstrate that the long-term effect of a well-designed TMD is good and the practical use is possible due to the good stability of its optimal parameters under different sea states.

Existence of Solutions for Boundary Value Problems of Vibration Equation with Fractional Derivative

In this paper, we investigate the solvability of boundary value problems for a class of vibration differential equation describing the fractional order damped system with signal stimulus. By presenting kernel function through the Laplace transform, and using the eigenvalue and the improved Leray-Schauder degree, the existence of solutions for boundary value problems is established.

Dynamic analysis of new type elastic screen surface with multi degree of freedom and experimental validation

A feasible method was proposed to improve the vibration intensity of screen surface via application of a new type elastic screen surface with multi degree of freedom(NTESSMDF). In the NTESSMDF, the primary robs were coupled to the main screen structure with ends embedded into the elastomers, and the secondary robs were attached to adjacent two primary robs with elastic bands. The dynamic model of vibrating screen with NTESSMDF was established based on Lagrange's equation and the equivalent stiffnesses of the elastomer and elastic band were calculated. According to numerical simulation using the 4th order Runge-Kutta method, the vibration intensity of screen surface can be enhanced substantially with an averaged acceleration amplitude increasing ratio of 72.36%. The primary robs and secondary robs vibrate inversely in steady state, which would result in the friability of materials and avoid stoppage. The experimental results validate the dynamic characteristics with acceleration amplitude rising by62.93% on average, which demonstrates the feasibility of NTESSMDF.

A new single degree-of-freedom resonance device

A new single degree-of-freedom(1 DOF) resonance device was developed.It mainly comprises a linear motor,a vibrating screen,a supporting spring set,a supporting frame and a damper set.Forces acting on the vibrating screen were found.A differential equation for describing the forces was set up.Equations that were used to evaluate the exciting force and exciting frequency in resonance were derived from the solution to the differential equation.In addition,an equation for evaluating the deformed magnitude of the damping springs in the damper set was presented so that the suitable damping may be obtained.Finally,a Matlab/Simulink model of the new 1 DOF resonance device was also built.Displacement?time curves of the vibrating screen under four conditions were obtained in the use of the Matlab/Simulink simulation.The curves indicate that it can shorten the time for the vibrating screen to be into the stable resonance with increasing the damping,and it can lengthen the time with increasing the vibrated mass or amplitude,but every given angular frequency cannot acquire the desired amplitude value of resonance.

Nonlinear dynamics of two degree of freedom systems with linear and nonlinear stiffnesses

In this study, a new analytical approach is developed to analyze the free nonlinear vibration of conservative two-degree-of-freedom （TDOF） systems. The mathematical models of these systems are governed by second--order nonlinear partial differential equations. Nonlinear differential equations were transferred into a single equation by using some intermediate variables. The single nonlinear differential equations are solved by using the first order of the Hamiltonian approach （HA）. Different parameters, which have a significant impact on the response of the systems, are considered and discussed. Some comparisons are presented to verify the results between the Hamiltonian approach and the exact solution. The maximum relative error is less than 2.2124 % for large amplitudes of vibration. It has been established that the first iteration of the Hamiltonian approach achieves very accurate results, does not require any small perturbations, and can be used for a wide range of nonlinear problems.

An experimental investigation of one-and two-degree of freedom VIV of cylinders

In the paper,an experiment investigation was conducted for one-and two-degree of freedom vortex-induced vibration（VIV） of a horizontally-oriented cylinder with diameter of 11 cm and length of 120 cm.In the experiment,the spring constants in the cross-flow and in-line flow directions were regulated to change the natural vibration frequency of the model system.It was found that,in the one-degree of freedom VIV experiment,a ＂double peak＂ phenomenon was observed in its amplitude within the range of the reduced velocities tested,moreover,a ＂2T＂ wake appeared in the vicinity of the second peak.In the two-degree of freedom VIV experiment,the trajectory of cylinder exhibited a reverse ＂C＂ shape,i.e.,a ＂new moon＂ shape.Through analysis of these data,it appears that,besides the non-dimensional in-line and cross-flow natural vibration frequency ratios,the absolute value of the natural vibration frequency of cylinder is also one of the important parameters affecting its VIV behavior.

INCREASING PROPERTY OF SPECTRUM IN THE VIBRATIONS OF A CYCLIC CHAIN OF MASSES DISTRIBUTED ACCORDING TO THE GTM SEQUENCE

Generalized Thue-Morse sequences were introduced into the vibrational problem of a chain of masses linked by springs of constant strength, and the increasing property of spectrum of linear operator about the vibrational model was proved.

Flow-Induced Stream-Wise Vibration of Circular Cylinders

Results from a series of studies on the stream-wise vibration of a circular cylinder verifying Japan Society of Mechanical Engineers Standard S012-1998, Guideline for Evaluation of Flow-induced Vibration of a Cylindrical Structure in a Pipe, are summarized and discussed in this paper. Experiments were carried out in a water tunnel and in a wind tunnel using a two-dimensional cylinder model elastically supported at both ends of the cylinder and a cantilevered cylinder model with a finite span length that was elastically supported at one end. These cylinder models were allowed to vibrate with one degree of freedom in the stream-wise direction. In addition, we adopted a cantilevered cylinder model that vibrated with two degrees of freedom in both the stream-wise and cross-flow directions under the same vibration conditions as an actual thermocouple well. The value of the Scruton number (structural damping parameter) was changed over a wide range, so as to evaluate the value of the critical Scruton number that suppressed vibration of the cylinder. For the two-dimensional cylinder, two different types of stream-wise excitations appeared in the reduced velocity range of approximately half of the resonance-reduced velocity. For the stream-wise vibration in the first excitation region, due to a symmetric vortex flow, the response amplitudes were sensitive to the Scruton number, while the shedding frequency of alternating vortex flow was locked-in to half of the Strouhal number of vibrating frequency of a cylinder in the second excitation region. In addition, the effects of the aspect ratio of a cantilevered cylinder on the flow-induced vibration characteristics were clarified and compared with the results of a two-dimensional cylinder. When a cantilevered circular cylinder with a finite length vibrates with one degree of freedom in the stream-wise di-rection, it is found that acylinder with a small aspect ratio has a single excitation region, whereas a cylinder with a large aspect ratio has two excitation regions. Furthermore, the vibration mechanism of a symmetric vortex flow was investigated by installing a splitter plate in the wake to prevent shedding of alternating vortices. The vibration amplitude of acylinder with a splitter plate increased surprisingly more than the amplitude of a cylinder without a splitter plate. For a cantilevered cylinder vibrating with two degrees of freedom, the Lissajous figure of vibration of the first excitation region shows the trajectories of elongated elliptical shapes, and in the second excitation region, the Lissajous trajectories draw a figure “8”. The results and information from these experimental studies proved that Standard S012-1998 provides sufficient design methods for suppressing hazardous vibrations of cylinders in liquid flows.

Vibration Characteristics of Mistuned Bladed Disks

The finite element models of blade, disk and bladed disk are built up by finite element software ANSYS. The natural frequencies of the single blade, the whole bladed disk and the bladed disk with only one sector by cyclic symmetry boundary have been calculated. Then, based on the results above, a structure dynamic model of multiple degree-of-freedom （MDOF） systems is established to simulate the bladed-disk assembly. Solve the motion equation by using the Runge-Kutta Method （Gill Method）. The dynamic response of the MDOF system is achieved. As for the given mistuning patterns, the vibration responses of bladed disks are calculated. The results have been compared and analyzed, and the optimum pattern is selected.

PE管道的爆破振动响应规律及灰色关联度分析

为了降低隧道爆破施工对既有埋地PE管道造成的振动危害,有必要在施工前了解影响管道振动效应的各种因素。根据现场实测数据,采用MIDAS GTS NX软件建立岩土体-隧道-PE管道三维数值模型,并将现场监测结果和数值模拟结果进行对比分析,验证数值模型的可靠性。分析得出:爆破振动作用下土体弹性模量、泊松比和管径的增加会使管道的最大振速增大;因为地表自由面叠加作用的原因,管道埋深的增加使管道最大振速先减小后增大。运用灰色关联度理论,确定了4种不同因素对管道振动效应的影响程度,主次关系为:土体弹性模量>管道埋深>土体泊松比>管道直径。准确地了解各因素对管道振动的影响程度能够更好的对隧道爆破施工时PE管道的安全性进行评估,为工程实际施工提供参考。

双自由度D形截面柱体流致振动的二维数值模拟

本文研究了D形截面柱体在顺流向和横流向两个自由度下的流致振动特性,迎流角为90°,质量比为2.6,雷诺数为370~3685,应用RANS方程采用SST k-ω湍流模型和Newmark-β法求解水流运动和柱体运动,入口流速采用匀加速法,检验了数值模型的网格和时间步长敏感性,并与相关文献的实验结果进行对比,验证了数值模型的可靠性。基于计算结果,系统分析了D形截面柱体的振幅、振动频率、水动力系数、尾涡脱落模式,以及平均位置偏移情况。结果表明,双自由度D形截面柱体在约化速度为8~14的区间内表现为涡激振动-驰振模式,尾涡多为2S和S+2S交替脱落,双自由度振幅比单自由度有显著的增大。升力主要偏向截面的直线边一侧,且升力出现了多个倍频。横流向和顺流向平均偏移量最大都可达到一倍特征长度以上。

平台运动对柔性立管涡激振动影响的实验研究

基于自循环实验水槽开展了存在平台纵荡和横荡运动时的悬链线型柔性立管涡激振动响应测试,模型立管的长径比为125,测试的平均约化速度范围为4.40~39.33.利用激光位移传感器和高速摄像机分别监测了平台运动和立管振动位移,从响应频率、振幅和振动形态等方面分析了平台运动对立管振动的影响.根据立管振动的主导频率与平台运动的主导频率是否相同,区分了强耦联和弱耦联现象,定义了强耦联的立管长度,其在立管振动的模态过渡组次相对较短.立管振动与平台运动存在两个方向均耦联、仅单一方向耦联和不耦联3种情形.其中,立管平面外振动受平台运动的影响较平面内振动小.以立管瞬时形态的波腹个数变化量化了模态竞争和平台运动对振动形态的影响.通过对比过滤平台固有频率前后的立管振幅、振形与主导频率的时空分布,用强耦合的时间权重和空间长度量化了平台对立管振动耦合的影响,发现高约化速度时,平台运动抑制了立管空间的频率竞争,也抑制了立管平面内与平面外振动的耦合响应.

地铁上盖建筑振动响应预测及舒适度分析——以南京地铁1号线停车维修库综合体上盖住宅项目为例

对南京市地铁1号线车库段上部待建住宅楼进行研究,探讨地铁上盖建筑受地铁出入库振动的影响。通过现场测试与数值模拟,预测不同工况下待建建筑的振动响应以及室内振动加速度限值范围。模拟结果表明,采用底部加速度法将所测轨道、混凝土柱的振动输入计算模型中,可以获得待建建筑三向位移变化,并进行结构易损部位及预警分析,判断建筑安全性。通过模拟8种工况,计算得到1~80 Hz频率范围内各建筑楼板1/3倍频程中心频率下的加速度响应有效值和加速度振级,获取了住宅舒适度影响较大区域的具体坐标。研究成果对结构减振及舒适度提升具有参考意义。

基于等效单自由度的涡轮扫频振动研究

针对有限元方法对扫频工况下涡轮振动求解出现的困难,提出了基于等效单自由度的涡轮结构振动扫频算法,并对涡轮扫频振动特征进行分析.建立了涡轮流固耦合计算模型,使用非线性谐波法得到了涡轮表面的气动激励,使用谐响应方法分析了涡轮的稳态振动特性.基于能量原理,建立了涡轮等效单自由度计算模型,通过与稳态振动结果的对比,验证了方法的可行性与正确性,并利用所建立模型分析了涡轮的扫频振动特征.结果表明,涡轮在扫频工况下响应峰值、半功率带宽以及响应曲线形状等特征与稳态工况存在差异.等效单自由度算法与有限元方法计算得到的涡轮响应误差小于10%,共振峰偏移率小于1%.

振动试验量级异常波动的机理及解决方法

针对振动试验行业内试验控制量级大幅波动的异常现象,进行了控制原理分析,根据分析结果进行了试验验证,试验完全复现了控制量级大幅波动现象,证实了特殊限制谱等导致的超低量级和信号干扰是导致大幅波动的两种直接原因。在确定直接原因的基础上分析了该现象的根本原因,据此提出了解决措施,并对措施进行了验证。结果表明解决措施有效,提高控制自由度和采用输出保持均能有效避免大幅波动情况。该问题的解决有助于提高振动试验控制的稳定性和安全性。

振杆密实法加固粗粒混合土模型试验

中国中西部地区粗粒混合土分布广泛,但其松散性和不均匀性导致这些散体材料难以作为构筑物的地基。以提高粗粒混合土地基的承载力和消除不均匀性为主要目标,提出使用振杆法处理粗粒混合土地基,以室内模型试验为主要研究手段,分别进行了振动加固试验、轻型动力触探试验和密度测量试验,并在试验过程中实时监测振动和沉降指标,探究了振杆密实法对粗粒土的加固效果,分析了k值(d90/振杆直径)和振动频率对加固效果的影响。结果表明:振动处理后,式样的轻型动力触探击数平均可达13击,较处理前提高了11击,试样底部的平均压实度可达81%,相应的承载力提高200 kPa以上,经振杆密实法处理后变为低压缩性地基土;当k值在1/2.0时,加固效果优于k值为1/10.0的情况,前者的地基承载力和沉降率比后者分别高出50 kPa和7%左右;粗粒混合土在14 Hz振动频率下的地表振动速度较大,可达36 mm/s,对采集到的振动数据进行了希尔伯特-黄变换(HHT),其HHT能谱图显示振动频率在14 Hz附近时,地震响应较大;以正三角型布置加固点位,群点作用可以有效地消除地基土的不均匀性,地基土的不均匀系数K从试验前的26.40减小到1.39。振杆密实法可为粗粒混合土地基处理提供新思路,也可为现场施工提供关键参数依据。