Interaction between torsional and lateral vibrations in flexible rotor systems with discontinuous friction

In this paper, we analyze the interaction between friction-induced vibrations and self-sustained lateral vibrations caused by a mass-unbalance in an experimental rotor dynamic setup. This study is performed on the level of both numerical and experimental bifurcation analyses. Numerical analyses show that two types of torsional vibrations can appear: friction-induced torsional vibrations and torsional vibrations due to the coupling between torsional and lateral dynamics in the system. Moreover, both the numerical and experimental results show that a higher level of mass-unbalance, which generally increases the lateral vibrations, can have a stabilizing effect on the torsional dynamics, i.e. friction-induced limit cycling can disappear. Both types of analysis provide insight in the fundamental mechanisms causing self-sustained oscillations in rotor systems with flexibility, mass-unbalance and discontinuous friction which support the design of such flexible rotor systems.     

Bifurcations in Nonlinear Discontinuous Systems

This paper treats bifurcations of periodic solutions indiscontinuous systems of the Filippov type. Furthermore, bifurcations offixed points in non-smooth continuous systems are addressed. Filippov'stheory for the definition of solutions of discontinuous systems issurveyed and jumps in fundamental solution matrices are discussed. It isshown how jumps in the fundamental solution matrix lead to jumps of theFloquet multipliers of periodic solutions. The Floquet multipliers canjump through the unit circle causing discontinuous bifurcations.Numerical examples are treated which show various discontinuousbifurcations. Also infinitely unstable periodic solutions are addressed.     

An experimental investigation on vortex induced vibration of a flexible inclined cable under a shear flow

In the present study, an experimental investigation was performed to characterize the vortex induced vibration (VIV) of a flexible cable in an oncoming shear flow. The VIV tests were conducted in a wind tunnel with a flexible cable model. It was found that, under different oncoming velocity profiles, the cable model behaved in single-mode and multi-mode VIVs. The displacement amplitudes of the single mode VIVs were found to be larger than those of multi-mode VIVs, and the cross-flow (CF) response was larger than that of in-line (IL) direction for either the single mode or multi-mode VIVs. For a single mode vibration, the largest CF response occurs in the 1st mode VIV, and the motion trajectory of the 1st mode VIV was found to be an inclined figure of eight shape, while other single mode VIVs behaved in ellipse or straight line trajectories. For multi-mode VIVs, no stable vibration trajectories were found to exist since the vibration frequency bands covered two or more vibration modes. The vortex-shedding frequencies in the wake behind the inclined cable were also characterized in the present study. The shedding frequencies of the wake vortices were found to coincide well with the vibration modes: for a single mode VIV, they were close to the dominant vibration mode; for a multi-mode VIV, they could also cover the appearing vibration modes.     

An exact nonlinear hybrid-coordinate formulation for flexible multibody systems

The previous low-order approximate nonlinear formulations succeeded in capturing the stiffening terms, but failed in simulation of mechanical systems with large deformation due to the neglect of the high-order deformation terms. In this paper, a new hybrid-coordinate formulation is proposed, which is suitable for flexible multibody systems with large deformation. On the basis of exact strain–displacement relation, equations of motion for flexible multibody system are derived by using virtual work principle. A matrix separation method is put forward to improve the efficiency of the calculation. Agreement of the present results with those obtained by absolute nodal coordinate formulation (ANCF) verifies the correctness of the proposed formulation. Furthermore, the present results are compared with those obtained by use of the linear model and the low-order approximate nonlinear model to show the suitability of the proposed models. The project supported by the National Natural Science Foundation of China (10472066, 50475021).     

Dynamics of deformable flexible systems in liquid

The state-of-the-art in the investigation of nonlinear oscillations and evolution of deformable flexible systems in fluid is analyzed. Statements of problems and methods of solving them as well as results on the dynamics of flexible systems interacting with the ambient medium are briefly outlined. Important quantitative and qualitative results are presented, and conclusions of applied and fundamental importance are drawn __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 3–29, August 2007.     

Dynamic stiffness characteristics of aero-engine elastic support structure and its effects on rotor systems: mechanism and numerical and experimental studies

The support structure of a rotor system is subject to vibration excitation,which results in the stiffness of the support structure varying with the excitation frequency(i.e., the dynamic stiffness). However, the dynamic stiffness and its effect mechanism have been rarely incorporated in open studies of the rotor system. Therefore, this study theoretically reveals the effect mechanism of dynamic stiffness on the rotor system. Then,the numerical study and experimental verification are conducted on...     

Metastable flow in capillary tubes: An experimental evaluation

This work presents the results of an experimental study with pure refrigerants R-134a and R-600a and refrigerant–oil mixtures flowing through capillary tubes in order to analyse the metastable flow. A large number of experiments were carried out to verify the influence of several variables on the underpressure of vaporization, mainly the inlet subcooling, internal diameter and inlet pressure. Capillary tubes with internal diameter of 0.69 mm and 0.82 mm were tested for condensation temperatures between 40 °C and 50 °C and subcooling degrees between 3 °C and 12 °C. Measurements for oil concentrations of 1% and 3% were conducted and compared with those for pure refrigerant R-134a. The oil influence on the metastable flow was tested and the effect on the underpressure of vaporization is addressed for lower oil concentrations.     

The influence of crack-imbalance orientation and orbital evolution for an extended cracked Jeffcott rotor

Vibration peaks occurring at rational fractions of the fundamental rotating critical speed, here named Local Resonances, facilitate cracked shaft detection during machine shut-down. A modified Jeffcott-rotor on journal bearings accounting for gravity effects and oscillating around nontrivial equilibrium points is employed. Modal parameter selection allows this linear model to represent first mode characteristics of real machines. Orbit evolution and vibration patterns are analyzed, yielding useful results. Crack detection results indicate that, instead of 1x and 2x components, analysis of the remaining local resonances should have priority; this is due to crack-residual imbalance interaction and to 2x multiple induced origins. Therefore, local resonances and orbital evolution around 1/2, 1/3 and 1/4 of the critical speed are emphasized for various crack-imbalance orientations. To cite this article: J. Gómez-Mancilla et al., C. R. Mecanique 332 (2004).

Résumé

Les pics de vibration apparaissant au passage des fractions de la vitesse de critique de rotation des systèmes tournants, appelées résonances locales, facilitent la détection de fissures sur les machines. Dans cette étude, un modèle de rotor Jeffcott modifié avec une fissure tournante, comportant des coussinets et prenant en compte les effets de pesanteur et de balourd est présenté. Le choix modal des paramètres permet de représenter les caractéristiques liées au premier mode des machines tournantes usuelles. Les évolutions des vibrations et des orbites du système comportant une fissure sont analysées et permettent d'obtenir des résultats utiles pour la détection des fissures sur les machines tournantes. Ainsi, ces résultats indiquent que, en plus des composants 1x et 2x, l'analyse des autres résonances locales restantes doivent être regardées avec attention du fait de l'interaction possible entre les différentes orientations de la fissure et du balourd, et des origines multiples pouvant engendrer la présence des résonances 2x. Par conséquent les résonances et l'évolution des orbites obtenus autour de 1/2, 1/3 et 1/4 de la vitesse critique sont étudiées pour différentes variations d'angle entre le balourd et l'orientation de la fissure. Pour citer cet article : J. Gómez-Mancilla et al., C. R. Mecanique 332 (2004).     

Epidemiology and Self-Organized Critical Systems: An Analysis in Waiting Times and Disease Heterogeneity

The dominant paradigm in epidemiology is characterized by the absence of a theory of disease that is capable of informing epidemiologic praxis and challenging conventional linear statistical reasoning. This paper has two main objectives: first, it is a reflection over the pathologic process (transition from health to disease state) in line with the nonlinear dynamic paradigm of self-organized critical systems. According to the latter, dynamic processes are characterized by phase transitions, emergence, robustness, far-from-equilibrium dynamics, punctuated equilibria, historically-based mechanic, nonlinearity, irreversibility, and heterogeneity. Further, complex adaptive systems have outcomes with inverse power law (IPL) fits. The article second objective is to test the theory of self-organized critical systems along two paths of epidemiologic investigations. The first path takes the form of a study in waiting times (WT) and attempts to show that their distribution complies with an IPL. The second application shows that hierarchies of patients (generated by cluster analysis) with a complex disease process (diabetes) featuring coupling of their component units (biologic markers of glucose handling) also fit an IPL. The IPL fit is compared with that of a lognormal, the more likely benchmark model for WTs. It is concluded that both the WTs and hierarchies of patients can be interpreted in terms of self-organized critical systems with possible fractal significance. The paper culminates with a theory of disease emphasizing the properties of self-organized complex systems in the epidemiologic context.