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

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.

ON THE HOMOCLINIC ORBITS IN A CLASS OF TWO-DEGREE-OF-FREEDOM SYSTEMS UNDER THE RESONANCE CONDITIONS

A class of two-degree-of-freedom systems in resonance with an external, parametric excitation is investigated, the existence of the periodic solutions locked to Omega is proved by the use of the method of multiple scales. This systems can be transformed into the systems of Wiggins under some conditions. A calculating formula which determines the existence of homoclinic orbits of the systems is given.

Experimental Study on Interaction Between Degrees of Freedom in a Wave Buoy

Increasing degrees of freedom(DOFs)is a useful way to raise the power capture efficiency of oscillating wave energy converters.Thus,this study proposes a buoy with three DOFs,which are surge,heave,and pitch.The hydrodynamic performance and power capture efficiency of the buoy is physically modeled.Amplitudes of unidirectional and coupled motions are compared to analyze the interaction effect between freedoms under conditions with and without power take-off damping.The capture width ratio and corresponding growth rates are also calculated.Results show that the buoy makes a periodic sinusoidal(or approximate)movement in every DOF.Coupling effect can cause an increase in the amplitude in one DOF and a decrease in the amplitudes of the others.This phenomenon shows that the kinematic energy of the buoy redistributes to all DOFs compared with the unidirectional conditions.Adding DOFs can improve the power absorption of the buoy in most cases,but the number of DOFs is not the more the better.

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）.

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.

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.

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.

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.

Vibration Reduction of Open-chain Flexible Manipulators by Optimizing Independent Motions of Branch Links

In order to suppress vibration in flexible manipulators, a new type of manipulator mechanism with controllable local degrees of freedom is proposed. This mechanism consists of a main chain and some branch links. The main chain is of a flexible open-chain configuration with an end-effector installed at its tip, and the rigid branch links are able to perform active movements. It is proved by kinematics and dynamic analysis that, the branch links bear no direct kinematic relation to the main chain, but their independent motions can strongly affect the dynamic behavior and performance of the flexible manipulator. Then comes a new idea of suppressing vibration, in which independent motions of the branch links are used to suppress the undesired vibration of the flexible main chain through dynamic coupling. On this basis, an optimal method for reducing vibration of flexible manipulators is proposed. Finally, the effectiveness of this method is verified by numerical simulations.

Study on 6-DOF active vibration-isolation system of the ultra-precision turning lathe based on GA-BP-PID control for dynamic loads

The vibration disturbance from an external environment affects the machining accuracy of ultra-precision machining equipment.Most active vibration-isolation systems(AVIS)have been developed based on static loads.When a vibration-isolation load changes dynamically during ultra-precision turning lathe machining,the system parameters change,and the efficiency of the active vibration-isolation system based on the traditional control strategy deteriorates.To solve this problem,this paper proposes a vibration-isolation control strategy based on a genetic algorithm-back propagation neural network-PID control(GA-BP-PID),which can automatically adjust the control parameters according to the machining conditions.Vibration-isolation simulations and experiments based on passive vibration isolation,a PID algorithm,and the GA-BP-PID algorithm under dynamic load machining conditions were conducted.The experimental results demonstrated that the active vibration-isolation control strategy designed in this study could effectively attenuate vibration disturbances in the external environment under dynamic load conditions.This design is reasonable and feasible.

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.

THEORETICAL AND EXPERIMENTAL RESEARCH ON DYNAMIC BEHAVIOR OF GUYED MASTS UNDER WIND LOAD

A frequency-domain algorithm is presented for the dynamic analysis of guyed masts. By introducing a four-degrees-of-freedom model of a suspended cable, guyed masts are simpli?ed as an equivalent cable-beam model. Then, based on the discrete random vibration theory, recurrence formulas for the statistical moments of the wind-induced behavior of guyed masts are developed with the wind load treated as ?ltered white noise excitation. The dynamic analysis of a two-level guyed mast has been illustrated. Finally, results from a wind-tunnel experiment of guyed mast are used to testify the theory developed in this paper.

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.

半无限介质多自由度频响函数离散时间有理近似的稳定参数识别

离散时间有理近似函数是将半无限土频响函数转化为时域模型的重要工具,离散时间有理近似函数和时域模型具有相同的稳定性和精度。目前关于离散时间有理近似函数的研究只针对于单自由度系统。该文基于线性控制理论,给出了多自由度有理近似系统的稳定条件。将稳定性条件与遗传-序列二次算法相结合,开发了多自由度频响函数参数辨识方法,保证了多自由度系统的稳定性和精度。不同维度的多自由度有理近似系统的数值仿真验证了该文方法可以保证多自由度有理近似系统的稳定性和精度。

激光测距仪多自由度集成可调装置的研制

基于测距仪激光轴竖直向上和向下两个方向的定位装夹及多自由度调节需要,设计了模块化的集成可调装置:(1)零点定位装夹模块,方便测距仪的快速固定和装配;(2)摇臂式角度调节模块,在调节过程中,确保测距仪测量基准面不变;(3)落地式和吊顶式二维移动及调平模块,适应不同工作现场的检定需要;在此基础上完成实物样机的制造装配和测试,结果表明,该装置各模块组装便捷、调节精度高,结构设计独特紧凑、重心低稳定性好,可以较好地满足大量程液位计现场校准的快速定位和多自由度调节。

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。

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%.