Effects of Damping and Circulatory Forces on Dynamic Instability of Gyroscopic Conservative Continuous Systems

ABSTRACT The title problem is studied, with emphasis on the small damping and circulatory force case. It is shown that small internal and/or external damping forces and/or smalt (as well as large) circulatory forces in general destabilize an otherwise stable gyroscopic conservative system. A condition for no destabilizing effects of these small forces is obtained, A concept of "perfect" system in elastic stability of nonconservative problems is also presented. An example problem is given for demonstration purposes.     

Experimental investigation of secondary steady flows in Faraday surface waves

It is shown that in the two-dimensional Faraday surface waves excited in a vertically oscillating rectangular water-filled vessel there is a system of secondary circulatory flows that occupies the entire fluid volume between the vessel bottom and the free surface. In parallel with the oscillations at the wave frequency, the fluid particles are slowly displaced in accordance with these circulatory flows. The secondary flow velocity field is measured and the trajectories of individual fluid particles in the standing wave are determined. The experimental data are compared with the Longuet-Higgins model. It is shown that the initial stage of formation of regular structures on the surface of a sediment layer on the vessel bottom may be related with the presence of secondary circulatory flows.     

Destabilization paradox due to breaking the Hamiltonian and reversible symmetry

Stability of a linear autonomous non-conservative system in the presence of potential, gyroscopic, dissipative, and non-conservative positional forces is studied. The cases when the non-conservative system is close to a gyroscopic system or to a circulatory one are examined. It is known that marginal stability of gyroscopic and circulatory systems can be destroyed or improved up to asymptotic stability due to action of small non-conservative positional and velocity-dependent forces. The present paper shows that in both cases the boundary of the asymptotic stability domain of the perturbed system possesses singularities such as “Dihedral angle” and “Whitney umbrella” that govern stabilization and destabilization. In case of two degrees of freedom, approximations of the stability boundary near the singularities are found in terms of the invariants of matrices of the system. As an example, the asymptotic stability domain of the modified Maxwell-Bloch equations is investigated with an application to the stability problems of gyroscopic systems with stationary and rotating damping.     

On the high-frequency response of unsteady lift and circulation: A dynamical systems perspective

In this paper, we consider the unsteady aerodynamics of a two-dimensional airfoil as a dynamical system whose input is the angle of attack (or airfoil motion) and output is the lift force. Based on this view, we discuss the evolution of lift and circulation from a purely dynamical perspective through step response, frequency response, transfer function, etc. In particular, we point to the relation between the high-frequency gain of the transfer function and the physics of the development of lift and circulation. Based on this view, we show that the circulatory lift dynamics is different from the circulation dynamics. That is, we show that the circulatory lift is not lift due to circulation. In fact, we show that the circulatory–non-circulatory classification is arbitrary. By comparing the steady and unsteady thin airfoil theory, we show that the circulatory lift possesses some acceleration (added-mass) effects. Finally, we perform simulations of Navier–Stokes equations to show that a non-circulatory maneuver in the absence of a free stream induces viscous circulation over the airfoil.     

Steady-state dynamics of a non-ideal rotor with internal damping and gyroscopic effects

A rotor driven by an ideal source, i.e., a source capable of delivering unlimited amount of power, becomes unstable beyond a certain threshold spin speed due to non-conservative circulatory forces. The circulatory forces considered in this paper arise out of rotating internal damping. If the drive is non-ideal then the rotor spin speed cannot exceed the stability threshold. This phenomenon is a type of the Sommerfeld effect. In this work, a DC motor driving four-degrees-of-freedom rotor with internal damping and gyroscopic effects is considered and the corresponding steady-state spin frequency and the whirl orbit amplitude are analytically derived as functions of the parameters of the drive and the rotor system.     

STRENGTH PROPERTIES OF ABDOMINAL AORTIC VESSELS: EXPERIMENTAL RESULTS AND PERSPECTIVES

Journal of Applied Mechanics and Technical Physics - The aorta is the main vessel in the human circulatory system which plays a critical role in oxygen and nutrient supply to all abdominal...     

含动脉分支的体循环模拟实验系统

本文首先建立了含分支动脉的血液体循环集中参数模型，在计算机仿真研究的基础上，设计、研制出含主要动脉分支的体循环模实验系统，系统由微机实施控制，数据采集与处理。实验结果表明它既可较好地模拟左心室、主动脉弓附近的血流动力学特性，同时又可较好地模拟左锁骨下动脉、挠动脉处的血流压力脉搏波基本特征。     

Analysis of squeal noise and mode coupling instabilities including damping and gyroscopic effects

This paper deals with an audible disturbance known as automotive clutch squeal noise from the viewpoint of friction-induced mode coupling instability. Firstly, an auto-coupling model is presented showing a non-conservative circulatory effect originating from friction forces.Secondly, the stability of an equilibrium is investigated by determining the eigenvalues of the system linearized equations. The effects of the circulatory and gyroscopic actions are examined analytically and numerically to determine their influence on the stability region. Separate and combined effects are analyzed with and without structural damping and important information is obtained on the role of each parameter and their interactions regarding overall stability. Not only is structural damping shown to be of primary importance, as reported in many previous works, this article also highlights a particular relationship with gyroscopic effects.A method of optimizing both the stability range and its robustness with respect to uncertainty on system parameters is discussed after which practical design recommendations are given.     

基于大鼠背部视窗显微观测的微血管网的三维重建

微循环是循环系统中最基层的结构和功能单位,它在保持人体正常生理功能中占有突出地位,许多疾病的发生也是从微循环开始. 因此,利用脊背视窗技术,并通过体视显微镜观察视窗内的血管结构, 进一步对所获血管图像进行一系列图像处理,得到了血管边界和中心线等结构信息. 同时,根据血管分叉处相贯线的信息确定分叉血管的连接方式. 在网格划分时,采用了改进的超限插值算法,构建了三维血管网的有限元网格模型,实现了对任意分支血管网的三维重建. 为微循环的体外实验和数值分析奠定基础.      

The blood flow and the motion of vessel wall

The correlation problem between the blood flow and the motion of vessel wall in the mammalian circulatory system is discussed in this paper. Supposing the blood flow is under the stable oscillatory condition, a set of formulas for velocity distribution, pressure distribution, displacement of vessel wall and constraining stress are obtained. Kuchar’s formulas are extended from steady flow to unsteady oscillatory flow by means of the formulas obtained in this paper. The problem of elasticity effect of vessel wall is also discussed.     

On the levitation of a charged body in an electrostatic field

The possibility of levitation of a body bearing a point electric charge in the electric field of a fixed point charge of the same sign is demonstrated. Stabilization of the unstable equilibrium state of the body in which the body weight is balanced by the Coulomb force is provided by gyro forces due to body rotation. The conservative stability of the levitating body corresponds to a finite range of angular velocities. It is shown that dissipative and circulatory forces considered together can improve the stability of the system to asymptotic stability. The attraction domain of the stable equilibrium position is studied numerically as a function of system parameters.     

Flow in a permeable tube surrounded by porous material. Application to the capillaries of the circulatory system

Unsteady problems are solved numerically for the system of one-dimensional quasilinear equations describing the flow in the capillaries of the circulatory system and the mass transfer between a capillary and the surrounding tissue. The effect of oscillations of the entrance pressure and the passage of a protein concentration jump on the characteristics of the system is investigated. The influence of the degree and nonuniformity of capillary wall permeability and lymphatic drainage factors is also examined. The sphere of applicability of the equations and the possibility of an analytical investigation of capillary flow are discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 14–20, July–August, 1986.     

A note on internal damping induced self-excited vibration in a rotor by considering source loading of a DC motor drive

It is well known that rotors become unstable beyond a certain threshold spinning speed due to the non-conservative circulatory forces, which arise out of rotating internal damping. In this note, it is shown that if the source loading of the non-ideal drive is considered then this instability manifests itself as a constant rotor spinning speed and a constant amplitude whirl orbit about an unstable equilibrium. A DC motor drive is considered and the corresponding steady-state spinning frequency and whirl orbit amplitude are analytically derived as functions of the drive and the rotor system parameters.     

Three-dimensional gas flow in a rotating cylinder with a retarding cover

The study of rotating flows is of interest due to both the development of the centrifugal method of separation of gas and isotope mixtures and the possibility of astrophysical applications. An analytical nonlinear model for calculating the hydrodynamic characteristics of the viscous incompressible fluid flow in a rotating cylinder in the presence of a retarding cover is presented. The cases of stationary and rotating covers are considered. The analysis is performed on the basis of the system of hydrodynamic Navier-Stokes equations. The flow domain is divided up into the main flow and end boundary layers at the cylinder bottom and at the rotating cover. In its turn, the main flow is divided up into an inviscid quasi-rigid core and a lateral layer within which almost the entire upward circulatory flow is concentrated. The equations of the boundary layers at the end surfaces are analyzed by the approximate Slezkin-Targ method. The solutions in the boundary and lateral layers are “stitched” together with the velocity distribution in the main flow core. The unknown angular velocity ω ₁ and radial boundary R ₁ of the core are determined from the balance of the moments of the friction forces acting on the main rotating flow and the continuity condition for the circulatory flow. The experimental and calculated data are compared.     

Asynchronous free oscillations of linear mechanical systems: A general appraisal and a digression on a column with a follower force

The concept of asynchronous oscillatory response of mechanical systems in free vibrations is addressed as an introduction to a definition of asynchronous modes of vibration. Connection of the asynchronous modes with the localization and other dynamical phenomena is discussed. Then, conditions for the occurrence of asynchronous modes are investigated in depth. It is seen that a non-conservative system, with an asymmetric stiffness matrix – caused, for instance, by circulatory loads, may have an asynchronous mode. Yet, it is also seen that non-conservativeness is not actually mandatory. Two- to four-degree-of-freedom models of a column with a follower force are addressed, allowing for a mathematical modelling and phenomenological discussion.     

On possible mechanisms of generation of a support by fishes at explosive accelerations

Methods of creating large specific supports during the explosive motion of a model profile, which are related with the generation of both self-similar flow with a closed dead zone of maximum possible volume and a circulatory flow, are considered. Possible mechanisms of using by birds and marine animals of the vortex energy of both the surrounding medium and a system of Π-shaped vortex bunches for facilitating their motion are discussed.     

Secondary flows and particle centrifugation in slightly tilted rotating pipes

A theoretical analysis is presented of viscous incompressible laminar flow in a pipe which rotates around an axis held at small angle with respect to its symmetry-axis. Analogous to the results of Barua and Benton [1, 2], solutions in closed-form are given for circulatory flows in the cross-sectional plane of the pipe due to Coriolis forces in combination with Hagen-Poiseuille flow through the pipe. The solutions are used to derive analytical expressions for trajectories of solid or liquid particles entrained in the gas and being subject to centrifugation and the said secondary flows. It is shown that despite centrifugation, particles can be locked into circulatory trajectories thus remaining suspended in the gas flowing through the pipe.     

导管对动脉中脉动流生理参数的影响

导管在循环生理学和临床医学中已得到广泛的应用。血管中介入导管后必然会影响测量的准确性和受检者的正常生理状态。许多学者讨论过导管的介入对压力测量结果的影响,但还未见有讨论导管介入对正常生理状态影响的文章报导。本文基于动脉中血液流的刚性管分析模型,从理论上讨论了血流量和纵向阻抗等生理状态参数在导管介入前后的变化情况,为进一步全面分析导管介入对动脉中血液脉动流的影响提供了理论基础。     

Convective instability of a homogeneous fluidized bed

Convective motions of the phases in a homogeneous fluidized bed are considered. The motions of the phases are described by a simple model of two ideal interpenetrating interacting fluids. The model admits an increasing concentration of the solid particles with the height, which leads to circulatory flows. Approximate equations of motion of the liquid and the solid particles are obtained, and these are analogous to the Boussinesq approximation in the case of natural convection in a pure liquid. The equations contain a parameter which is analogous to the Rayleigh number and characterizes the stability of the layer. An approximate analytic solution to the corresponding eigenvalue problem is found. The spectrum of Rayleigh numbers and the sizes of the convective cells are determined. The obtained results provide an explanation for the existence of the multicenter circulatory motions of the phases frequently observed in a fluidized beds and make it possible to determine the sizes of the circulatory regions. Information about the Rayleigh number spectrum and the sizes of the regions is needed to solve the problem of the scale transition and also to enable the choice of measures to suppress or intensify the displacement processes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 39–46, July–August, 1982.     

On the minimal model for the low frequency wobbling instability of friction discs

An analytical and numerical study of the wobbling dynamics of friction disks is presented. Of particular interest is the excitation mechanism taking into account two contrarian effects both originating in dry friction: the circulatory terms describing the energy input due to the sliding contacts and the friction induced damping which stabilizes the system. Balance of these terms determines the instability domain in the parameter space. It is shown that there is a slip threshold so that, if the slip is under this limit, the system remains stable. If the slip is larger than this limit, then the criterion of stability is determined by the relation between the friction coefficient and the internal damping. The limit cycle appearing in the unstable domain is also investigated. It is shown that the limit cycle can be described as a kind of a regular reverse precession of the wobbling disc. Its amplitude is limited by the geometric nonlinearity and partial contact loss. Analytic results are compared with numeric simulations.