On the Motion of Rigid Bodies in a Viscous Compressible Fluid

We prove the existence of global-in-time weak solutions to a model describing the motion of several rigid bodies in a viscous compressible fluid. Unlike most recent results of similar type, there is no restriction on the existence time, regardless of possible collisions of two or more rigid bodies and/or a contact of the bodies with the boundary. (Accepted September 23, 2002) Published online February 4, 2003 Communicated by Y. Brenier     

The nonlinear theory of electromagnetic wave attenuation in plasmas

The absorption of a circularly polarized electromagnetic wave which propagates in a plasma along a magnetic field is analyzed. The exact equations of particle motion in the resonance region are solved with aid of elliptic functions. It is shown that the nonlinear damping constant has an oscillatory form. For t→0, it coincides with the constant obtained on the basis of linear theory, while for t→∞, in the absence of collisions, it tends to zero. The influence of collisions on wave absorption is studied. It is shown that with allowance for collistions, the damping constant depends on the amplitude of both the H₁ and H₁ ^−3/2 waves. The analysis of slowly decaying waves may be based on a model proposed by Dawson [1] and later modified in [2,3]. According to this model, all plasma particles are grouped into resonant and nonresonant ones. The velocity distribution function of the nonresonant particles is assumed to be the same as in the case of undamped waves. The distribution function of resonant particles at the initial instant is assumed to be Maxwellian. The nonlinear equations of motion of the resonant particles are integrated exactly. The damping constant is defined as the ratio of the energy expended by the wave at the resonant particles to the total energy of the wave. In nonlinear formulation, resonant absorption appears to be nonstationary. After a time lapse on the order of several vibrational period of a particle captured by the wave, nonstationary absorption ceases, and stationary absorption, created by infrequent collisions, becomes essential. It is noteworthy that absorption of this type has been studied by V. E. Zakharov and V. I. Karpman [4] for the case of plasma waves. Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 9, No. 5, pp. 11–17, 1968.     

Impulsive motions of elastic pseudo-rigid bodies II: further results and examples

In this paper we study collisions of pseudo-rigid bodies. A new formulation of the problem is given which extends the results of our previous work. We specialize the general results to various particular cases, and we study two of these in detail.     

Dynamic modeling of a gear transmission system containing damping particles using coupled multi-body dynamics and discrete element method

Nonlinear Dynamics - The reduction in vibration in gear transmission systems is an engineering task. Particle damping technology attenuates vibration by means of friction and inelastic collisions...     

Damping of Forced Vibrations in Systems of Connected Rigid Bodies

The problem of damping forced vibrations in a system of bodies linked by one-degree-of-freedom elastic joints is considered. The vibrations are damped by introducing additional bodies into the system. The controlled motion of these bodies compensates the effect of the external perturbation. The motion of a system of three bodies is studied in detail. To determine the sensitivity of the perturbation compensation method to the damping parameters, a numerical simulation is carried out     

Energy dissipation mechanism and experiment of particle dampers for gear transmission under centrifugal loads

As a passive means of vibration reduction, particle damping is mainly applied to the horizontal or vertical steady field. However, it is seldom applied to centrifugal fields. Under high speed and heavy loading, the vibration of tooth surfaces of gear transmissions becomes more severe shortening gear service life and augmenting noise. Under centrifugal loading, the particle system exhibits different characteristics, for example, particles are extruded at the end farthest from the center. We investigated gears with drilled via holes filled with damping particles. Using the discrete-element method, we developed an energy dissipation model for the particle system accounting for friction and inelastic collisions. Energy dissipation and damping characteristics of this system were analyzed. Experiments were also conducted with the gear system having different particle filling rates. The results show that this filling rate is an important parameter associated with particle damping in a centrifugal field. An unsuitable filling rate would significantly reduce damping effectiveness. With changes in rotation speed and load, the gear transmission system has different optimal filling rates. The results provide guidelines for the application of particle damping in centrifugal fields of gear transmissions.     

Continuous contact force models for impact analysis in multibody systems

One method for predicting the impact response of a multibody system is based on the assumption that the impacting bodies undergo local deformations and the contact forces are continuous. In a continuous analysis, the integration of the system equations of motion is carried out during the period of contact; therefore, a model for evaluating the contact forces is required. In this paper, two such contact force models are presented, both Hertzian in nature and based upon the direct-central impact of two solid particles.At low impact velocities, the energy dissipation during impact can be represented by material damping. A model is constructed based on the general trend of the Hertz contact law in conjuction with a hysteresis damping function. The unknown parameters are determined in terms of a given coefficient of restitution and the impact velocity. When local plasticity effects are the dominant factor accounting for the dissipation of energy at high impact velocities, a Hertzian contact force model with permanent indentation is constructed. Utilizing energy and momentum considerations, the unknown parameters in the model are again evaluated. The two particle models are generalized to an impact analysis between two bodies of a multibody system.     

Forces on oscillating bodies in viscous fluid

This paper describes a method for determining the fluid forces on oscillating bodies in viscous fluid when the corresponding flow problem has been solved using the finite element method. These forces are characterized by the concept of added mass, added damping and added force. Numerical results are obtained for several example body shapes. Comparison is made with exact analytical results and other finite element results for the limiting cases of Stoke's flow and inviscid flow, and good agreement is obtained. The results for finite values of the body amplitude parameter β show the appearance of added force from the steady streaming component of the flow for asymmetric bodies. Results are also obtained for the associated flow where the fluid remote from a fixed body is oscillating.     

Interface Forces in Laterally Impacted Steel Tubes

In engineering mechanisms, solid bodies frequently come to a contact with a variety of geometric and kinematic situations. There has been a trend to express the interaction of the contacted bodies in the form of equivalent interface forces. The interface force represents the level of load transferred from one body to another. In a static or quasi-static contact problem, the interface forces could be sensibly evaluated by integrating the normal and the shear stresses over the common interfaces. In a dynamic contact, the interface stresses and subsequently the interface forces happen to be more complicated. They are, furthermore, affected by other parameters such as inertia forces, stress waves propagation, the material strain rate dependency and damping. This paper reports interface forces recorded in a series of experimental impact tests on axially pre-compressed steel tubes along with those from the numerical simulations of the tests. To monitor the so called impact loads, two small steel rings as load cells have been built in the striker. Based on the experimental and numerical results, the concept of equivalent interface forces in the impacted tubes has been verified. It has been highlighted that the interface forces (or the impact loads) may vary on the striker or the specimen themselves, depending on the measuring locations. Effects of axial compressions on the interface forces picked up by the striker load cells, impact loads imparted to the specimen supports and on the impact duration have been discussed. It has been reported that the initial compression applied to the tubes does not remain constant during and after the impact event. The amount of variations also depends on the initial level of the tube compression.     

Galloping instabilities of two-dimensional triangular cross-section bodies

Galloping is a type of aeroelastic instability characterized by large amplitude, low frequency, normal to wind oscillations. It normally appears in bodies with small stiffness and structural damping when they are placed in a flow and the incident velocity is high enough. In this paper a systematic approach for the analysis of galloping of triangular cross-section bodies is reported. Wind tunnel experiments have been conducted aiming at establishing the unstable characteristics of isosceles triangular cross-section bodies when subjected to a uniform flow with angles of attack ranging from 0 to 180°. The results have been summarized in a stability map, where galloping instability zones in the angle of attack—main vertex angle plane—are identified.     

结构碰撞振动的建模与模态截断

根据弹性体碰撞理论和结构模态分析,提出一种简便方法识别两弹性结构的碰撞恢复系数和碰撞速度,进而可确定碰撞阻尼,该方法及后继的碰撞振动分析涉及到结构模态截晰,为此,文中分析了模态截断对碰撞参数识别精度的影响,讨论了不同模态截断对研究碰撞系统动力学行为的作用。     

Nonlinear dynamics of a system of rigid bodies with controlled electromagnetic dampers

A nonlinear mathematical model of a system of n rigid bodies undergoing translational vibrations under inertial loading is constructed. The system includes ball supports as a seismic-isolation mechanism and electromagnetic dampers controlled via an inertial feedback channel. A system of differential dynamic equations in normal form describing accelerative damping is derived. The frequencies of small undamped vibrations are calculated. A method for analyzing the dynamic coefficients of rigid bodies subject to accelerative damping is developed. The double phase–frequency resonance of a two-mass system is studied     

Coaxial interactions of two vortex rings or of a ring with a body

Inviscid coaxial interactions of two vortex rings, including head-on collisions and leapfrogging motions, are considered using a contour dynamics technique. Interactions of vortex rings with solid bodies are also investigated by combining the contour dynamics technique with a boundary integral equation method. Numerical results show that a clean, successful passage motion is possible for two vortex rings with not too thick cores. In both cases of head-on collisions and leapfrogging motions, very large core deformations are observed when two vortex rings get close to each other. A head-tail structure is formed in the later stage of a head-on collision of two fat vortices. Numerical results also show that a vortex ring will stretch and slow down when it moves toward a solid boundary, will shrink and speed up when it moves away from a solid boundary, and will either translate steadily or approach an oscillating asymptotic state when it is far away from any boundaries. The project supported by The National Education Commission of China and NASA under cooperative grant agreement #NCC5-34.     

Stability of motion of two rigid bodies connected by a cable in the atmosphere

The spatial motion of two rigid bodies connected by a weightless inextensible cable in the atmosphere is considered. They are assumed to be bodies of revolution with static and dynamic symmetry. The condition of static stability of the system angular motion with respect to the direction of the incident airflow velocity vector is written out and analyzed. The influence of gyroscopic terms and damping moments on the stability condition is studied. An example of analysis of motion in the atmosphere of two connected bodies that are cones with a spherical tip is given. It is shown that the stable motion in the atmosphere can always be ensured by an appropriate matched choice of the parameters of the entire system on the basis of the obtained stability conditions. A numerical example of estimating the cable tension forces arising as the system descends on a ballistic trajectory in the atmosphere is presented.     

Effects of damping on brake squeal coalescence patterns – application on a finite element model

Brake squeal is referred to, in most publications, as a flutter instability triggered by a mode coupling phenomenon. A lot of clues tend to prove that damping would be a key parameter in brake squeal modelling. This study aims at investigating the effects of damping on coalescence patterns, that is to say on the way the modes couple. A finite element model of the whole brake corner has been used to compute the brake modal behaviour. Then a complex eigenvalue analysis has been undertaken to assess the brake stability as a function of the friction coefficient. Different kinds of damping spreading over the modes have been studied. Two main effects have been noticed: a shifting effect and a smoothing effect. The first one always stabilize the brake, whereas this is not the case of the second one. The combination of the two effects may make the brake more unstable depending on the spreading of the additionnal damping.     

具有摩擦的刚体碰撞

刚体碰撞是力学上的一个经典问题，但目前大都采用给定恢复系数进行分析的方法，本文则直接从两刚体碰撞时Newton第二定律出发，建立了计及摩擦的两刚体碰撞基本理论，并指出了以往研究通过给定恢复系数方法的错误之处。文中通过利用两刚体接触相对变位加速度与碰撞力的关系，定义了法向等效质量，对二维平面碰撞，通过一些简单的比较和定义给出了各种碰撞状态的分类判别法，并给出了碰撞力和冲量的解析式。指出法向等效质量依赖于碰撞状态，在反向滑动和停止滑动这两状态下的法向等效质量是变化的，因此导致其恢复系数是变化的，这样，恢复系数不仅与接触力(接触点情况)有关，而且还与两刚体的运动和动力参数有关，同时给出各种碰撞状态下的恢复系数计算式。     

Removing Collision Singularities from Action Minimizers for the N-Body Problem with Free Boundaries

For the planar and spatial N-body problems, it has been proved by Marchal and Chenciner that solutions for the minimizing problem with fixed ends are free from interior collisions. This important result has been extended by Ferrario & Terracini to Newtonian-type problems and equivariant problems. It has also been used to construct many symmetric solutions for the N-body problem. In this paper we are interested in action minimizing solutions in function spaces with free boundaries. The function spaces are imposed with boundary conditions, such that every mass point starts and ends on two transversal proper subspaces of ℝ^d, d≥2. We will prove that solutions for this minimizing problem with free boundaries are always free from collisions, including boundary collisions. This result can be used to construct certain classes of relative periodic solutions of the N-body problem.     

Vibration of two beams connected by nonlinear isolators: analytical and experimental study

To study the coupling vibration of nonlinear isolators and flexible bodies, test rigs of two flexible beams connected by wire mesh isolators are constructed and investigated both experimentally and analytically. A five-parameter polynomial model of wire mesh isolators is derived by identifying parameters in the frequency domain with the sine-sweep test. For obtaining the parameters that are valid in a wide range of frequency, a numerically assisted identification method is developed. With this model, the vibration of two flexible beams connected by wire mesh isolators is studied. The frequency response is obtained analytically by employing the Green’s function method and harmonic balance method. Sine-sweep test results with three test rigs show good coherence with the corresponding numerical results. With obtained experimental results and numerical results, effect of connection parameters is studied in detail. It is found that traditional design rules for isolators are no longer effective and the coupling vibration must be investigated in the design phase. Another phenomenon is that the damping has a function of weakening the effect of nonlinear stiffness. Nonlinear stiffness and nonlinear damping can decrease the transmissibility along with the increase of the excitation level.