Influence of tip mass on dynamic behavior of cracked cantilever pipe conveying fluid with moving mass

In this paper, we studied about the effect of the open crack and a tip mass on the dynamic behavior of a cantilever pipe conveying fluid with a moving mass. The equation of motion is derived by using Lagrange’s equation and analyzed by numerical method. The cantilever pipe is modelled by the Euler-Bernoulli beam theory. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The influences of the crack, the moving mass, the tip mass and its moment of inertia, the velocity of fluid, and the coupling of these factors on the vibration mode, the frequency, and the tip-displacement of the cantilever pipe are analytically clarified.     

Model study and active control of a rotating flexible cantilever beam

For a dynamic system of a rotating flexible cantilever beam, the traditional model assumes the small deformation in structural dynamics where axial and transverse displacements at any point in the beam are uncoupled. This traditional hybrid coordinate model is referred as the zero-order approximation coupling model in this paper, which may result in divergence to the dynamic problem of a flexible cantilever beam with a high rotational speed. In this paper, a first-order approximation coupling model is presented to analyze the dynamics of rotating flexible beam system, which is based on the Hamilton theory and the finite element discretization method. The proposed model for the system considers the second-order coupling quantity of the axial displacement caused by the transverse displacement of the beam. The dynamic characteristics of the rotating beam system when using the zero-order approximation coupling model are compared with those when using the first-order approximation coupling models through numerical simulations. In addition, the applicability of the two dynamic models for control design are studied by using the classical optimal control method. Simulation and comparison studies show that, for the case without control for the system, there exists big difference between the result using the zero-order approximation coupling model and that using the first-order approximation coupling model even for the case of small angular velocity of the system. The larger is the angular velocity, the bigger is the difference. Vibration frequency of the beam by using the first-order approximation coupling model is higher than that by using the zero-order approximation coupling model. When the angular velocity of the system is close to or is larger than the fundamental frequency of the beam without rotation motion, the zero-order approximation coupling results in a wrong result, while the first-order approximation coupling model is valid. For the case with control for the system, the applicability of the zero-order approximation coupling model can be much broadened. The critical angular velocity of the system for validity of the zero-order approximation coupling model is much larger than that without control for the system. The first-order approximation coupling model is available not only for the case of small angular velocity but also for the case of large angular velocity of the system, and is applicable to the cases with or without control for the system.     

弹性支承输流管道的动力学特性

研究两端弹性支承输流管道横向振动的动力学特性。根据梁模型横向弯曲振动模态函数,由两端弹性支承的边界条件得到其模态函数的一般表达式。根据特征方程具体分析弹性支承刚度、质量比、流体压力和流速、管截面轴向力等主要参数对管道固有特性及失稳临界流速的影响。数值计算结果表明,管道固有频率随弹性支承刚度、管截面轴向拉力的增加而增大,随流体流速、流体压强和管截面轴向压力的增加而下降;静态失稳临界流速则随弹性支承刚度、流体压强、管截面轴向压力的增加而下降,随管截面轴向拉力的增加而上升。     

考虑附加质量的中心刚体-柔性悬臂梁系统的动力特性研究

对考虑附加质量的中心刚体-柔性悬臂梁系统的动力特性进行研究.首先采用Hamilton原理和有限元离散化方法,在计入柔性梁由于横向变形而引起的轴向变形的二阶耦合量的条件下,给出该系统的刚柔耦合动力学方程(即一次近似耦合模型),以及相应的非惯性系下的动力学模型,然后通过数值仿真对系统的动力特性进行研究.仿真结果显示,即使是小的附加质量也会对系统动力特性产生重要影响,附加质量使得梁的响应幅值变大和响应频率降低,且会影响柔性梁和中心刚体的终点位置.附加质量的影响随系统大范围运动的角速度的增大而变大.当系统大范围运动为低速时,传统的混合坐标模型仍然会导致较大误差;当系统大范围运动为高速时,传统的混合坐标模型存在失效的可能.     

Dynamic behavior of cracked pipe conveying fluid with moving mass based on timoshenko beam theory

In this paper we studied about the effect of the open crack and the moving mass on the dynamic behavior of simply supported pipe conveying fluid. The equation of motion is derived by using Lagrange’s equation and analyzed by numerical method. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments i.e. the crack is modeled as a rotational spring. The influences of the crack severity, the position of the crack, the moving mass and its velocity, the velocity of fluid, and the coupling of these factors on the vibration mode, the frequency, and the mid-span displacement of the simply supported pipe are depicted.     

Nonlinear dynamic analysis of cantilever tube conveying fluid with system identification

The vibration of a flexible cantilever tube with nonlinear constraints when it is subjected to flow internally with fluids is examined by experimental and theoretical analysis. These kinds of studies have been performed to find the existence of chaotic motion. In this paper, the important parameters of the system leading to such a chaotic motion such as Young’s modulus and the coefficient of viscoelastic damping are discussed. The parameters are investigated by means of system identification so that comparisons are made between numerical analysis using the design parameters and the experimental results. The chaotic region led by several period-doubling bifurcations beyond the Hopf bifurcation is also re-established with phase portraits, bifurcation diagram and Lyapunov exponent so that one can define optimal parameters for system design.     

Experimental determination of time lag due to phase shift on a flexible pipe conveying fluid

A finite element model of a flexible tube conveying fluid is developed in MATLAB^© based on the principle of virtual work, using a three-node isoparametric beam element. Finite element equations are formulated by applying Galerkin technique on the coupled equations of pipe conveying fluid. The present element developed is capable to model three-dimensional flexible tubes by including curved geometry, effects of damping, velocity and gyroscopic effects. The external excitation applied at the middle of the tube in the lateral direction produced a time lag between the lateral responses, which were measured at two equidistant points from the excitation point. This is due to the Coriolis effect, and the same is simulated using the developed code. An experiment, supported with a robust error analysis, is also conducted on a straight polyurethane tube conveying water, subjected to a sinusoidal excitation at the center between the clamped supports. The measured time responses are compared with the numerical values predicted by the code. The time lags for both cases are obtained from the temporal shift along the time axis, between the zero crossing points of the time–response curves. The results obtained agreed well. The code can be used to predict the time lag, which is correlated to the mass flow rate. The proposed method will help to design Coriolis mass flow meters for existing pipelines, without altering the system.     

Dynamic analysis of rotating damped beams with an elastically restrained root

The vibration of a rotating damped blade with an elastically restrained root is investigated. The effects of viscous damping and the translational and rotational damping at the root of blade are considered. The flow-indued force and moment between the tip of a blade and the casing are simulated by using the time-dependent boundary conditions. A simple and efficient algorithm for deriving the semi-analytical steady state solution of the general system is proposed. The governing equation is divided into two coupled real differential equations. The two coupled equations are uncoupled into an eighth-order characteristic differential equation. The eight corresponding boundary conditions are obtained. The eight linearly independent homogenous semi-analytical solutions of the eighth-order characteristic differential equation are derived. If the coefficients of the uncoupled governing differential equation are constant, the exact fundamental solutions are obtained. The exact steady state solution is obtained by using Green's function in terms of the eight homogenous solutions. Moreover, the influence of the translational, rotational and viscous damping constants on the frequency response curves of a rotating beam are investigated. The opposite influence of the transverse viscous damping constant and the root damping constants on the frequency of resonance is revealed.     

Kinetostatic model of spring constant ratios for an AFM cantilever with end extended mass

In previous work we showed that the kinetostatic method is very effective in computing the increase in value of the spring constants of an AFM free (with or without added mass) and supported rectangular cantilever for higher mode oscillations relative to their values for natural vibration. We have considered in all previous cases that added mass is a concentrated one. However, the additional mass may be an extended one particularly in the case of a V-shaped cantilever. In this article we consider the influence of the constituent beam’s (leg’s) mutual skew and the altered position of the nodal points in the case when the attached extended triangular (trapezoid) mass of the V-shaped cantilever has a significant moment of rotational inertia and a center of this mass gravity located beyond the constituent beam end. We show that considering these effects in using the kinetostatic model yields results for the ratios of the spring constants at higher modes of oscillation and their values at the first frequency natural vibration for a V-shaped cantilever which are in good agreement with the thermomechanical noise amplitudes obtained by other researchers. This should prove helpful for the proper calibration of V-shaped cantilevers whose application with higher modes oscillation provides increased measurement sensitivity.     

Free vibration of Timoshenko beam with finite mass rigid tip load and flexural–torsional coupling

In this paper, the free vibration of a cantilever Timoshenko beam with a rigid tip mass is analyzed. The mass center of the attached mass need not be coincident with its attachment point to the beam. As a result, the beam can be exposed to both torsional and planar elastic bending deformations. The analysis begins with deriving the governing equations of motion of the system and the corresponding boundary conditions using Hamilton's principle. Next, the derived formulation is transformed into an equivalent dimensionless form. Then, the separation of variables method is utilized to provide the frequency equation of the system. This equation is solved numerically, and the dependency of natural frequencies on various parameters of the tip mass is discussed. Explicit expressions for mode shapes and orthogonality condition are also obtained. Finally, the results obtained by the application of the Timoshenko beam model are compared with those of three other beam models, i.e. Euler–Bernoulli, shear and Rayleigh beam models. In this way, the effects of shear deformation and rotary inertia in the response of the beam are evaluated.     

射流管伺服阀前置级的动态流场分析

射流管电液伺服阀的喷嘴到接收孔间的流场较为复杂,尤其在射流管偏转及阀芯运动的动态情况下,会存在回流、漩涡等现象。以某型射流管电液伺服阀结构为模型,结合射流管偏转时的阀芯力平衡关系,得到阀芯的运动方程,应用雷诺平均方程和标准两方程模式的封闭方程,通过流体动力学软件FLUENT建立射流管伺服阀喷嘴到阀芯两腔的三维可视化模型,仿真分析了喷嘴到接收孔的前置级瞬态流场及阶跃响应。仿真结果表明:接收孔中的涡量强度会影响射流管电液伺服阀的阶跃响应,涡量强度越大、振荡越大、阶跃响应越慢,并通过试验测试阀芯位移验证了数值计算的正确性,同时对比了不同接收孔间夹角的同时刻涡量及阶跃响应,得到接收孔间夹角为45°的最优设计。研究方法和结果对于提高射流管电液伺服阀的动态响应有重要参考价值。     

Optimization of structural parameters for spatial flexible redundant manipulators with maximum ratio of load to mass

1Introduction Inrecentyears,therehasbeenawidespread interestinthelight weightmechanismsandma nipulatorswithflexiblemembersbecauseadvan tagesoverrigidbodysuchas:smalleractuators,lowerpowerrequirements,higheroperation speed,highloadtomassratioandmorecompact linkdesignetc.Thesehavebeendemonstrated byanumberofpaperspublishedinmanyareas concerningelasticmechanismsandflexiblema nipulators.Muchadvancementhasbeen made[13].Themostadvancementinflexiblemecha nismsandmanipulatorsconcentratedondynamic mode…     

具有响应与强度约束的凸轮机构动态设计

以滚子从动件平面凸轮机机构为分析对象,结合从动件相对变形理论,提出了输出响应限制与构件强度约束相结合的凸轮机构动态设计与修改方法,并从理论上进行了阐述。最后,通过一实例对不同频率比λ、不同摆臂截面形状及截面积下的摆臂最大变形、最大弯应力及凸轮与转子间最大压应力进行了数值计算,为凸轮机构动态设计与修改,提供了一种理论依据及具体的实现方法。     

Development of dynamic response analysis algorithm for beam structures using transfer of mass coefficient

The authors developed the transfer mass coefficient method (TMCM) in order to compute effectively the dynamic response of a beam structure. In this paper, the algorithm for the dynamic response analysis of a three-dimensional beam structure is formulated. Through the computation results of numerical models, which are plane and space beam structures, obtained by the transfer mass coefficient method and the direct integration method, we verify that the transfer mass coefficient method can remarkably decrease the computation time of the direct integration method without the loss of accuracy in spite of using small computer storage. This paper was recommended for publication in revised form by Associate Editor Hong Hee Yoo Myung-Soo Choi received his B.S. and M.S. degrees from National Fisheries University of Pusan, Korea, in 1992 and 1994, respectively. He then received his Ph.D. degree from Pukyong National University in 1999. Dr. Choi is currently an Assistant Professor at the Department of Maritime Police Science at Chonnam National University in Yeosu, Korea. His research interests include mechanical vibration, structural dynamics, and optimum design. Jung-Joo Suh received his B.S., M.S. and Ph.D. degrees from National Fisheries Uni-versity of Pusan, Korea, in 1972, 1985 and 1995, respec-tively. Dr. Suh is currently a Professor at the Faculty of Marine Technology at Chonnam National University in Yeosu, Korea. His research interests include internal combustion engines and numerical analysis. Dong-Jun Yeo received his B.S., M.S. and Ph.D. degrees from National Fisheries University of Pusan, Korea, in 1981, 1985 and 1996, respectively. Dr. Yeo is currently a Professor at the Faculty of Marine Technology at Chonnam National University in Yeosu, Korea. He serves as an Academic Director of the Korean Society for Power System Engineering. His research interests include structural dynamics, vibration, and analytic techniques. Jung-Kyu Yang received his B.S. degree from Pusan Fisherise College, Korea, in 1973. He then received his M.S. and Ph.D. degrees from Chungnam National University in 1985 and 1996, respectively. Dr. Yang is currently a Professor at the Faculty of Marine Technology at Chonnam University in Yeosu, Korea. His research interests include combustion engineering, air flow characteristics, and numerical analysis. Jung-Hwan Byun received his B.S. and M.S. degrees from National Fisheries University of Pusan, Korea, in 1992 and 1995, respectively. He then received his Ph.D. degree from Pukyong National University in 1997. Dr. Byun is currently an Associate Professor at the Faculty of Marine Technology at Chonnam National University in Yeosu, Korea. His research interests include numerical analysis and synchronous control.