FLUTTER INSTABILITY OF SUPPORTED PIPES CONVEYING FLUID SUBJECTED TO DISTRIBUTED FOLLOWER FORCES

In the past decades,it has been reported that divergence is the expected form of instability for fluid-conveying pipes with both ends supported.In this paper,the form of instability of supported pipes ...     

New method for oblique impact dynamics research of a flexible beam with large overall motion considering impact friction force

A flexible beam with large overall rotating motion impacting with a rigid slope is studied in this paper. The tangential friction force caused by the oblique impact is analyzed. The tangential motion of the system is divided into a stick state and a slip state. The contact constraint model and Coulomb friction model are used respectively to deal with the two states. Based on this hybrid mod-eling method, dynamic equations of the system, which include all states (before, during, and after the collision) are obtained. Simulation results of a concrete example are compared with the results obtained from two other models: a nontangential friction model and a modified Coulomb model. Differences in the results from the three models are discussed. The tangential friction force cannot be ignored when an oblique impact occurs. In addition, the results obtained from the model proposed in this paper are more consistent with real movement.     

The regions of flutter and divergence instability of a column subjected to Beck's generalized load, taking into account the torsional flexibility of the loaded end of the column

Investigations into a slender system subjected to Beck's generalized load taking into account two rotational springs situated at each end of the system are presented in the paper. One spring models the finite rigidity of the mounting, while the second restricts the rotation of the loaded end of the system. The regions of divergence and flutter instability of the considered system were determined using the kinetic criterion of the stability. The boundary value of the rigidity of the spring situated at the loaded end of the column was also determined. The boundary value of the rigidity separates the regions of divergence and flutter instability. In respect of the problem of vibrations, the characteristic curves in the plane: load - natural frequency were presented. All computations were carried out using the parameters of the considered system, including the rigidity of the springs and the follower coefficient of the load.     

非匀质地基上正交异性矩形厚板的动态稳定

本文把伽辽金法和富里哀级数相结合,用以分析非匀质地基上的自由边正交异性矩形厚板的动态稳定。在板的自由边上作用着均匀分布的非保守跟随力,力的方向受到控制,使其与加载边的转角成定比。分析基于理论,因此包括了剪切变形的影响。力是非保守的,会有颤振和发散两种形式的失稳,力是保守的,只会有发散形式的失稳。     

Comparison and analysis of two Coulomb friction models on the dynamic behavior of slider-crank mechanism with a revolute clearance joint

The objective of this study is to investigate the effects of the Coulomb dry friction model versus the modified Coulomb friction model on the dynamic behavior of the slider-crank mechanism with a revolute clearance joint. The normal and tangential forces acting on the contact points between the journal and the bearing are described by using a Hertzian-based contact force model and the Coulomb friction models, respectively. The dynamic equations of the mechanism are derived based on the Lagrange equations of the first kind and the Baumgarte stabilization method. The frictional force is solved via the linear complementarity problem (LCP) algorithm and the trial-and-error algorithm. Finally, three numerical examples are given to show the influence of the two Coulomb friction models on the dynamic behavior of the mechanism. Numerical results show that due to the stick friction, the slider-crank mechanism may exhibit stick-slip motion and can balance at some special positions, while the mechanism with ideal joints cannot.     

A dynamical interpretation of flutter instability in a continuous medium

Flutter instability in an infinite medium is a form of material instability corresponding to the occurrence of complex conjugate squares of the acceleration wave velocities. Although its occurrence is known to be possible in elastoplastic materials with nonassociative flow law and to correspond to some dynamically growing disturbance, its mechanical meaning has to date still eluded a precise interpretation. This is provided here by constructing the infinite-body, time-harmonic Green's function for the loading branch of an elastoplastic material in flutter conditions. Used as a perturbation, it reveals that flutter corresponds to a spatially blowing-up disturbance, exhibiting well-defined directional properties, determined by the wave directions for which the eigenvalues become complex conjugate. Flutter is shown to be connected to the formation of localized deformations, a dynamical phenomenon sharing geometrical similarities with the well-known mechanism of shear banding occurring under quasi-static loading. Flutter may occur much earlier than shear banding in a process of continued plastic deformation.     

基于LuGre摩擦模型的接触约束法旋转柔性梁斜碰撞研究

基于接触约束法和LuGre摩擦模型对在重力场作用下作大范围旋转运动的柔性梁系统和斜坡发生含摩擦斜碰撞的动力学问题进行研究.首先运用刚柔耦合的多体系统动力学理论对大范围运动的柔性梁进行离散化和动力学建模,在碰撞时采用冲量动量法求出跳跃速度,其次在法向上引入接触约束求解出碰撞力,在切向上采用LuGre摩擦模型分两种方式求解...     

The destabilizing effect of external damping: Singular flutter boundary for the Pflüger column with vanishing external dissipation

Elastic structures loaded by non-conservative positional forces are prone to instabilities induced by dissipation: it is well-known that internal viscous damping destabilizes the marginally stable Ziegler's pendulum and Pflüger column (of which the Beck's column is a special case), two structures loaded by a tangential follower force. The result is the so-called ‘destabilization paradox’, where the critical force for flutter instability decreases by an order of magnitude when the coefficient of internal damping becomes infinitesimally small. Until now external damping, such as that related to air drag, is believed to provide only a stabilizing effect, as one would intuitively expect. Contrary to this belief, it will be shown that the effect of external damping is qualitatively the same as the effect of internal damping, yielding a pronounced destabilization paradox. Previous results relative to destabilization by external damping of the Ziegler's and Pflüger's elastic structures are corrected in a definitive way leading to a new understanding of the destabilizating role played by viscous terms.     

Leaf flutter by torsional galloping: Experiments and model

When wind blows on trees, leaves flutter. The induced motion is known to affect biological functions at the tree scale such as photosynthesis. This paper presents an experimental and theoretical study of the aeroelastic instability leading to leaf flutter. Experiments in a wind tunnel are conducted on ficus leaves (Ficus Benjamina) and artificial leaves. We show that stability and flutter domains are separated by a well-defined limit depending on leaf orientation and wind speed. This limit is also theoretically predicted through a stability analysis of the leaf motion.     

Instability of frictional contact states in infinite layers

The research reported in this paper is focused on the instability of equilibrium and steady sliding states of elastic orthotropic layers in the presence of unilateral obstacles with Coulomb friction with emphasis on a divergence type instability called directional instability of frictional contact states that cannot occur in isotropic layers. Analytic expressions and numerical solutions are provided for the instability mode and for the coefficient of friction at the onset of instability. A parametric study is done to investigate how this coefficient of friction and the instability mode vary with changes of the system parameters. For certain combinations of material data, significantly low coefficients of friction were required for the onset of instability. A finite element model that approximates the continuum and a lumped model that captures some of the features of the continuum are presented.     

非保守力作用下FGM矩形板的稳定性分析

对受均布随从力作用的功能梯度材料(FGM)矩形板,引入应力函数,得到了以应力函数和挠度函数表示的耦合运动微分方程组。用Fourier级数法研究了四边简支FGM非保守矩形板的稳定性,给出了不同边长比和不同梯度指标下频率和发散载荷的变化曲线,以及梯度指标变化对频率和发散载荷的影响。     

Vibrational self-alignment of a rigid object exploiting friction

In this paper, one-dimensional self-alignment of a rigid object via stick-slip vibrations is studied. The object is situated on a table, which has a prescribed periodic motion. Friction is exploited as the mechanism to move the object in a desired direction and to stop and self-align the mass at a desired end position with the smallest possible positioning error. In the modeling and analysis of the system, theory of discontinuous dynamical systems is used. Analytic solutions can be derived for a model based on Coulomb friction and an intuitively chosen table acceleration profile, which allows for a classification of different possible types of motion. Local stability and convergence is proven for the solutions of the system, if a constant Coulomb friction coefficient is used. Next, near the desired end position, the Coulomb friction coefficient is increased (e.g. by changing the roughness of the table surface) in order to stop the object. In the transition region from low friction to high friction coefficient, it is shown that, under certain conditions, accumulation of the object to a unique end position occurs. This behavior can be studied analytically and a mapping is given for subsequent stick positions.     

A flexible rod in annular leakage flow: Influence of turbulence and equilibrium offset,and analysis of instability mechanisms

The linear stability of a flexible, cylindrical rod subjected to annular leakage flow is studied. The mathematical models developed by Li, Kaneko, and Hayama in 2002 and Fujita and Shintani in 2001 are bridged and extended, to account for a flexible rod with equilibrium offset (eccentricity) in laminar or turbulent leakage flow. Stability characteristics are analyzed numerically for a variety of configurations. It is found that simply supported rods may become unstable at a certain critical flow speed by either divergence or flutter, depending on dimensions and fluid/solid properties. It is furthermore found that the critical flow speed is quite insensitive to use of a laminar friction model at high Reynolds numbers in cases of divergence, but sensitive to it in cases of flutter. These findings are verified analytically though analysis of an energy equation. This equation shows that (i) divergence instability is independent of fluid friction; (ii) flutter instability is caused solely by fluid friction. It also suggests a possible explanation to the question of why a ‘wrong’ fluid friction assumption gives a too large critical flow speed in cases of flutter instability at a high Reynolds number.     

随从力作用下热弹耦合轴向运动梁的稳定性

研究了切向均布随从力作用下热弹耦合轴向运动梁的稳定性问题。建立了热弹耦合轴向运动梁 在随从力作用下的运动微分方程,采用归一化幂级数法,推导出了2种边界条件下热弹耦合轴向运动梁在随 从力作用下的特征方程。计算了系统的前3阶量纲一复频率,分析了量纲一运动速度、量纲一热弹耦合系数 和量纲一随从力等参数对梁的稳定性的影响。     

Multiple impacts with friction in rigid multibody systems

An impact model for two-dimensional contact situations is developed which contains the main physical effects of a compliance element in the normal direction and a series of a compliance and Coulomb friction elements in the tangential direction. For systems with multiple impacts a unilateral formulation based on Poisson's hypothesis is used to describe the impulses which are transferred in the normal direction. The event of an impact is divided into two phases. The phase of compression ends with vanishing approaching velocity if normal impulses are transferred and is equivalent to a completely inelastic collision. The phase of expansion allows the bodies to separate under the action of the normal impulses whenever they are large enough. The absolute values of the tangential impulses are bounded by the magnitudes of the normal impulses, due to the Coulomb friction relationship on the impulse level. One part of the transferred tangential impulse during compression is assumed to be partly reversible which may be regarded as an application of Poisson's law. The remaining part is completely irreversible and considered friction. This formulation contains the special case of completely elastic tangential impacts as well as the situation when only Coulomb friction acts. It is proven that the presented impact model is always dissipative or energy preserving. The evaluation of the problem is done by solving one set of complementarity conditions during compression and a nearly identical set of equations during expansion. The theory is applied to some basic examples which demonstrate the difference between Newton's and Poisson's hypotheses.     

受限颗粒体对制动系统非线性振动的影响

制动系统在工作时,往往受到沙粒、尘土以及磨屑等受限颗粒体的影响,这些受限颗粒体在摩擦副中的高度分布具有较强的随机性,一定程度诱发了制动系统的非线性振动. 本文中基于制动片切向振动模型,引入了新的受限颗粒体摩擦模型,提出了用波动系数来描述受限颗粒体高度分布随机性的强弱. 发现在特定参数下,当此系数为0时,制动片切向振动为周期运动;但是当此系数不为0时,制动片切向振动呈现拟周期或混沌运动,此时的切向振动分岔特性图的稳定轨道也会出现数量或分布的变化,甚至表现出混沌特性. 同一时变信号内,受限颗粒体引发制动片切向非线性振动包括发散、收敛以及拟周期运动等多种形式.      

自由正交异性矩形厚板的动态稳定

对在一条边上作用着均匀分布的非保守跟随力的四边自由正交异性矩形厚板的动态稳定进行了分析，通过把位移和剪力展成重傅立叶级数解，把微分方程简化成了代数方程。计算表明厚度的微小变化会引起颤振载荷明显的减小。这个明显减小是因为存在剪切变形。     

Non-conservative stability of intermediate spring supported columns with an elastically restrained end support

The non-conservative stability of an intermediate spring supported uniform column clastically restrained at one end and subjected to a follower force at the other unsupported end is studied. It is found that when the intermediate spring support is far from the unsupported end, the instability mechanism is flutter. As the intermediate spring support approaches the unsupported end, the instability mechanism is changed from flutter to divergence with the increase of intermediate spring stiffness. For the hinged-intermediate and guided-intermediatc spring supported columns, the critical buckling load of flutter instability will first decrease, then increase as the intermediate spring stiffness is increased. Nevertheless, when the instability mechanism is divergence, the critical buckling load depends on the location of the intermediate spring support only, whereas for the clamped-intermediate spring supported column the critical buckling load of divergence instability decreases monotonically to a fixed value as the intermediate spring stiffness is increased. Finally, the influence of elastic end restraints on the stability of the column is also investigated.     

Dynamics of spatial structure-varying rigid multibody systems

Summary Couplings in machines and mechanisms exhibiting backlash and friction phenomena can be modeled as multibody systems with unilateral constraints and Coulomb friction. The structure of the differential-algebraic equations describing the system depends on the state of the constraints. The contact forces occurring at active constraints are taken into account in the equations of motion as Lagrange multipliers. Additionally, the kinematic conditions of all active constraints are formulated on the acceleration level. Contact and friction laws are sufficient conditions for state transitions of active constraints, and are represented by nonsmooth characteristics. Several formulations, like the linear complementarity problem, and two different nonlinear systems of equations are presented together with their solution method. The theory is applied to a mechanical system containing three-dimensional and coupled unilateral constraints with friction. Received 14 May 1998; accepted for publication 5 January 1999     

Physical mechanism of the destabilizing effect of damping in continuous non-conservative dissipative systems

The paper attempts to give a physical explanation of the mechanism behind the so-called destabilizing effect of small internal damping in the dynamic stability of Beck's column. Both internal (material) and external (viscous fluid) damping are considered. An energy equation is derived for the balance between the work done by the non-conservative ‘follower force’ and the energy dissipated by the internal and external damping forces. Evaluated at the critical load, where a flutter instability is initiated, this equation explicitly shows the influence of damping upon flutter frequency, phase angle, and vibration amplitude. The gradient of the phase angle, evaluated at the free end of the column, is found to be the ‘valve’, which controls how much work the follower force can do on the column during each period of oscillation. And a large change in this gradient with increasing—but still small—internal damping is found to be responsible for the destabilizing effect.