Travelling and standing envelope solitons in discrete non-linear cyclic structures

International audienceEnvelope solitons are demonstrated to exist in non-linear discrete structures with cyclic symmetry. The analysis is based on the Non-Linear Schrodinger Equation for the weakly non-linear limit, and on numerical simulation of the fully non-linear equations for larger amplitudes. Envelope solitons exist for parameters in which the wave equation is focussing and they have the form of shape-conserving wave packages propagating roughly with group velocity. For the limit of maximum wave number, where the group velocity vanishes, standing wave packages result and can be linked via a bifurcation to the non-localised non-linear normal modes. Numerical applications are carried out on a simple discrete system with cyclic symmetry which can be seen as a reduced model of a bladed disk as found in turbo-machinery

Frequency parametrization to numerically predict flutter in turbomachinery

In the quest for performance, modern turbomachinery designs are increasingly proner to flutter hazards. Unfortunately, their prediction is currently too expensive and inaccurate for industrial purpose. A significant step towards faster methods would consist in substituting a sequential algorithm to the classical iterative ones encountered in loose coupling strategies. The approach proposed here makes it possible through the use of a meta-model taking into account the sensitivity to design variables. This parametrized method is evaluated on a standard well referenced turbine configuration

Effect of fretting-wear on dynamic analysis. Comparison between experimental results and numerical simulations for a vibratory friction rig.

Dry friction in contact interfaces can have an important impact on the dynamic response of jointed structures subjected to vibration. It may cause frettingwear leading to a modification of the contact surface geometry by producing wear debris through material removal and dissipating energy. Consequently, the contact behaviour is modified and the worn geometry induces a change in vibrations level. Therefore, it is important to be able to simulate these complex phenomena occurring at the interfaces to predict the forced response of assembled structures and also their life-expectancy to design high confidence components. A multi-scale approach is implemented considering a slow-scale for wear phenomena and a fast-scale for the non-linear dynamic response and applied to validate an experimental test

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

Unbalance Responses of Rotor/Stator Systems with Nonlinear Bearings by the Time Finite Element Method

Since the early 1970s, major works in rotordynamics were oriented toward the calculation of critical speeds and unbalance responses. The current trend is to take into account many kinds of non-linearities in order to obtain more realistic predictions. The use of algorithms based on nonlinear methods is therefore needed. This article first describes the time finite element method. The method is then applied to nonlinear rotor/stator systems where bearings present a radial clearance. Keywords Bearing clearance, Hertz contact, Nonlinear dynamics, Stability, Time finite element Many investigations have taken place concerning the calculation of critical speeds and unbalance responses in rotor dynamics and research now tends to get more realistic predictions Engineers now have to take into account non-linearities in their models. In the aircraft engine domain, those non-linearities come from components, such as bearings or squeeze film dampers Thus, frequential methods like the incremental harmonic balance In this article, the time finite element method is described. This time-based method enables us to get steady-state solutions and to assess their stability. To prove its reliability in rotordynamics problems, two examples are addressed. Both consist of rotor/stator systems with radial clearance in the bearings. THE TIME FINITE ELEMENT METHOD Description of the Method The aim of the time finite element method is to find out the periodic solutions of forced systems. It is based on Hamilton's Law of Varying Action i.e., The principle of this method is to interpolate the displacement of all spatial degrees of freedom between given instants t i and t i+1 by polynomial

Stability Analysis of Beams Rotating on an Elastic Ring Application to Turbo machinery Rotor-Stator Contacts

Summary This paper presents a model of flexible beams rotating on the inner surface of an elastic stationary ring. The beams possesses two degrees of freedom, traction/compression and flexure. The in-plane deformations of the ring are considered and a single mode approximation is used. The model has been developed within the rotating frame by use of an energetic method. To better understand the phenomena occurring, the degrees of freedom of the beams can first be treated separately then together. Stability analysis show that even without rubbing, the radial degree of freedom of a beam rotating on an elastic ring can create divergence instabilities as well as mode couplings of the circular structure. When rubbing is considered, the system is unstable as soon as the rotational speed is non null. Moreover rubbing can couple the beams and the ring giving rise to mode coupling instabilities and locus veering phenomena. Finally, a comparison to a more complicated model of a flexible bladed-rotor in contact with an elastic casing shows a very good accordance with the phenomena occurring

Model and Stability Analysis of a Flexible Bladed Rotor

This paper presents a fully bladed flexible rotor and outlines the associated stability analysis. From an energetic approach based on the complete energies and potentials for Euler-Bernoulli beams, a system of equations is derived, in the rotational frame, for the rotor. This later one is made of a hollow shaft modelled by an Euler-Bernoulli beam supported by a set of bearings. It is connected to a rigid disk having a rotational inertia. A full set of flexible blades is also modelled by Euler-Bernoulli beams clamped in the disk. The flexural vibrations of the blades as well as those of the shaft are considered. The evolution of the eigenvalues of this rotor, in the corotational frame, is studied. A stability detection method, bringing coalescence and loci separation phenomena to the fore, in case of an asymmetric rotor, is undertaken in order to determine a parametric domain where turbomachinery cannot encounter damage. Finally, extensive parametric studies including the length and the stagger angle of the blades as well as their flexibility are presented in order to obtain robust criteria for stable and unstable areas prediction

Nasal Carriage of Staphylococcus Aureus and Cross-Contamination in a Surgical Intensive Care Unit: Efficacy of Mupirocin Ointment

A six month prospective study was carried out in a surgical intensive care unit (SICU) of a university hospital to assess the incidence and routes of exogenous colonization by Staphylococcus aureus. A total of 157 patients were included in the study. One thousand one hundred and eleven specimens (nasal, surgical wound swabs, tracheal secretions obtained on admission and once a week thereafter, and all clinical specimens) were collected over a four month period from patients without nasal decontamination (A). They were compared with 729 specimens collected over a two month period from patients treated with nasal mupirocin ointment (B). All S. aureus strains were typed by restriction fragment length polymorphism (RFLP) pulsed-field gel electrophoresis after SmaI macrorestriction. The nasal colonization rates on admission were 25.5 and 32.7% in groups A and B, respectively. Thirty-one untreated patients (31.3%) and three patients (5.1%) treated with nasal ointment, acquired the nasal S. aureus in the SICU (P = 0.00027). Nasal carriers were more frequently colonized in the bronchopulmonary tract (Bp) and surgical wound (Sw) (62%) than patients who were not nasal carriers (14%) (P < 0.00001). The patterns were identical for nasal, Bp and Sw strains from the same patient. RFLP analysis characterized seven epidemic strains of methicillin-resistant S. aureus (MRSA) which colonized 60% of group A and 9% of group B patients (P < 0.00001). The bronchopulmonary tract infection rate was reduced in group B (P = 0.032). In conclusion, in an SICU, nasal carriage of S. aureus appeared to be the source of endogenous and cross- colonization. The use of nasal mupirocin ointment reduced the incidence of Bp and Sw colonization, as well as the MRSA infection rate

Vibration analysis of rotating shaft on textured hydrodynamic journal bearings

The aim of this study is to analyse the influence of surface texturing on the dynamic behavior of a shaft on two hydrodynamic bearings. A prediction algorithm is presented with Fluid Structure Interaction (FSI) between the rotating shaft and the lubricant based on finite element method. Cavitation in bearings is taken into account. The hydrodynamic flow in the texturing pattern is modeled by two multi-scale algorithms. Static, modal and transient analyses are performed in order to predict the impact of several texturing patterns on the system vibrations

Stability analysis of rotating beams rubbing on an elastic circular structure

This paper presents the stability analysis of a system composed of rotating beams on a flexible, circular fixed ring, using the Routh-Hurwitz criterion. The model displayed has been fully developed within the rotating frame by use of an energy approach. The beams considered possess two degrees of freedom (dofs), a flexural motion as well as a traction/compression motion. In-plane deformations of the ring will be considered. Divergences and mode couplings have thus been underscored within the rotating frame and in order to simplify understanding of all these phenomena, the dofs of the beams will first be treated separately and then together. The dynamics of radial rotating loads on an elastic ring can create divergence instabilities as well as post-critical mode couplings. Moreover, the flexural motion of beam rubbing on the ring can also lead to mode couplings and to the locus-veering phenomenon. The presence of rubbing seems to make the system unstable as soon as the rotational speed of the beams is greater than zero. Lastly, the influence of an angle between the beams and the normal to the ring's inner surface will be studied with respect to system stability, thus highlighting a shift frequency phenomenon