Modeling and analysis of nonlinear rotordynamics due to higher order deformations in bending

A mathematical model incorporating the higher order deformations in bending is devel- oped and analyzed to investigate the nonlinear dynamics of rotors. The rotor system con- sidered for the present work consists of a flexible shaft and a rigid disk. The shaft is modeled as a beam with a circular cross section and the Euler Bernoulli beam theory is applied with added effects such as rotary inertia, gyroscopic effect, higher order large deformations, rotor mass unbalance and dynamic axial force. The kinetic and strain (defor- mation) energies of the rotor system are derived and the Rayleigh–Ritz method is used to discretize these energy expressions. Hamilton’s principle is then applied to obtain the mathematical model consisting of second order coupled nonlinear differential equations of motion. In order to solve these equations and hence obtain the nonlinear dynamic response of the rotor system, the method of multiple scales is applied. Furthermore, this response is examined for different possible resonant conditions and resonant curves are plotted and discussed. It is concluded that nonlinearity due to higher order deformations significantly affects the dynamic behavior of the rotor system leading to resonant hard spring type curves. It is also observed that variations in the values of different parameters like mass unbalance and shaft diameter greatly influence dynamic response. These influences are also presented graphically and discussed

Couplings in parametrically excited inclined cables systems

Cables in stayed bridges are subjected to important dynamic solicitations for which dynamic model are now well established. Due to their design, such structures highlight resonance phenomena and instabilities frequently observed. Nevertheless, some structures exhibit important vibration amplitudes that can not be explained simply. Measurement recently performed on a bridge point a coupling of the cable with the deck or the pillar. The present paper suggests to consider the deck flexibility coupled to the nonlinear dynamic of the inclined cable. Results of previous study are used. The retained nonlinear model of the cable include two degrees of freedom for the in-plane motion. Considering the bridge mass and deck rigidity adds one DOF, assumed linear in a first approach. The excitation is created on the deck, which produce an external force(such as the wind or the car traffic for example). An experimental set-up uses a specific device in order to highlight expected coupling phenomena on the parametric instabilities. It is composed of a flexible blade which represents the deck, and an inclined cable. Both elements are linked to a mass forced to move vertically, and which represent the anchor point and the equivalent mass of a section of the deck. Therefore, the cable has a given initial static tension. An electrodynamic shaker applies a force close to blade clumping. The transmitted force from the shaker to the structure is measured thanks to a piezo-electric sensor. The instantaneous cable tension is measured via a Shape force sensor. And a high resolution laser sensor captures without contact the in-plane motion of the cable. Analytically, the multiple scales method is applied to solve the nonlinear equations of motion. In-plane vibration of the cable and stability in the vicinity of the primary resonance w1 and sub-harmonic resonance 2w1 are computed. The competition between the behaviour at 2w1 and w2 are of particular interest, as it is observed experimentally

Instability zones for isotropic and anisotropic multibladed rotor configurations.

Helicopter ground resonance is an unstable dynamic phenomenon which can lead to the total destruction of the aircraft during take-off or landing phases. The earliest research in this domain was carried out by Coleman and Feingold during the decade of 60s. The instability was predicted by using classical procedures once the rotor was considered as isotropic, consequently, the periodic equations of motion could be simplified to a system with constant coefficients by introducing a change of variables, known as the Coleman Variable Transformation. The goal of the present work is to further comprehend the phenomenon and the influence of the anisotropic properties of rotors by analyzing the periodic set of equations of motion. For this, Floquet's Theory (Floquet's Method — FM) is used. The analysis for predicting the ground resonance phenomenon in isotropic and anisotropic rotor configurations is explored. The conclusions lead to verify the appearance of bifurcation points depending on the anisotropic characteristic present in the rotor. The temporal response analysis in the motion of helicopter with one asymmetric blade at unstable regions highlighted the presence of non symmetric rotor deformation shapes

Cool carbon stars in the halo and in dwarf galaxies: Halpha, colours, and variabiity

The population of cool carbon (C) stars located far from the galactic plane is probably made of debris of small galaxies such as the Sagittarius dwarf spheroidal galaxy (Sgr), which are disrupted by the gravitational field of the Galaxy. We aim to know this population better through spectroscopy, 2MASS photometric colours, and variability data. When possible, we compared the halo results to C star populations in the Fornax dwarf spheroidal galaxy, Sgr, and the solar neighbourhood. We first present a few new discoveries of C stars in the halo and in Fornax. The number of spectra of halo C stars is now 125. Forty percent show Halpha in emission. The narrow location in the JHK diagram of the halo C stars is found to differ from that of similar C stars in the above galaxies. The light curves of the Catalina and LINEAR variability databases were exploited to derive the pulsation periods of 66 halo C stars. A few supplementary periods were obtained with the TAROT telescopes. We confirm that the period distribution of the halo strongly resembles that of Fornax, and we found that is it very different from the C stars in the solar neighbourhood. There is a larger proportion of short period Mira/SRa variables in the halo than in Sgr, but the survey for C stars in this dwarf galaxy is not complete, and the study of their variability needs to be continued to investigate the link between Sgr and the cool halo C stars.Comment: 11 pages, 10 figures + one appendix of 26 pages; accepted for publication in Astronomy and Astrophysic

Étude des couplages câbles-tabliers sous excitations paramétriques

Cet article concerne l’étude expérimentale et la compréhension par modèle à petit nombre de degré de liberté, des vibrations d’un câble incliné relié à une poutre - modèle simplifié d’un ouvrage d’art. L’excitation extérieure est effectuée sur la poutre. Le câble attaché à l’extrémité de celle-ci est soumis à une sollicitation verticale sinusoïdale multi-fréquentielle due à la réponse de la poutre de raideur finie. L’excitation du câble bien que plus riche est comparable à celle utilisée lors de travaux antérieurs. Un système de guidage de l’extrémité de la poutre assure cette excitation au prix d’une possible variation de la tension horizontale dans le câble introduisant une excitation paramétrique supplémentaire. L’analyse de premiers résultats expérimentaux en résonance principale et secondaire permet d’envisager des modèles explicatifs à un degré de liberté obtenus par projection du modèle continu tridimensionnel du câble sur un mode convenable d’Irvine. Le traitement de ces systèmes simples nourri des données du dispositif expérimental montre un agrément qualitatif satisfaisant des premières expérimentations et des modèles

Experimental and theoretical investigation on nonlinear behavior of cable-stayed bridges

This paper deals with experimental study and with understanding via a finite number of degrees of freedom model of the vibrations of an inclined cable linked to a continuous beam. This is a simplified version of deck and cable of a bridge. External excitation is exerted on the beam. The cable attached to the end of the beam is submitted to a vertical sinusoidal solicitation due to the response of the finite stiffness beam. The excitation of the cable though it is more complex looks similar to the excitation used in previous works. A guided device located at the end of the beam ensures the excitation with a variation of the horizontal component of the cable tension that introduces a new parametric excitation. Analysis of preliminary experimental results for main and secondary resonances permits us to consider simple modeling with one degree of freedom systems obtained by projection of the continuous three-dimensional model of the cable on adapted Irvine mode. Analytical treatment of these models involving data from the experimental devices shows a correct qualitative agreement between preliminary experiments and theoretical. Continuation techniques are used to highlight the influence of physical parameters

A parametrically excited oscillator involving coupling between inclined cable system and deck of stayed bridges

This paper is concerned with the experimental study of the dynamic behaviour of an inclined cable linked to a continuous beam modelling a simplified version of deck and cable of a bridge. External excitation is exerted on the beam. The cable attached to the end of the beam is submitted to a vertical sinusoidal solicitation due to the response of the finite stiffness beam. A guided device located at the end of the beam ensures the excitation with a variation of the horizontal component of the cable tension that introduces a new parametric excitation. Analysis of preliminary experimental results for main and secondary resonances permits us to consider simple modelling with one degree of freedom systems obtained by projection of the continuous three-dimensional model of the cable on adapted Irvine mode. Analytical treatment of these models involving data from the experimental devices shows a correct qualitative agreement between preliminary experiments and theoretical and numerical results

Multiple recombinant dengue type 1 viruses in an isolate from a dengue patient

Between 2000 and 2004, dengue virus type 1 (DENV-1) genotypes I and II from Asia were introduced into the Pacific region and co-circulated in some localities. Envelope protein gene sequences of DENV-1 from 12 patients infected on the island of New Caledonia were obtained, five of which carried genotype I viruses and six, genotype II viruses. One patient harboured a mixed infection, containing viruses assigned to both genotypes I and II, as well as a number of inter-genotypic recombinants. This is the first report of a population of dengue viruses isolated from a patient containing both parental and recombinant viruses

Analysis of a vibro-impact nonlinear energy sink: theoretical and numerical developments

Recently, it has been demonstrated that a Vibro-Impact type Nonlinear Energy Sink (VI-NES) can be used efficiently to mitigate vibration of a Linear Oscillator (LO) under transient loading and harmonic force. In this paper, a design optimization procedure of an optimal VI-NES coupled to LO for energy pumping is presented theoretically and numerically. Due to the small mass ratio between the flying mass of the VI-NES and LO, the obtained equation of motion is possible to use the method of multiple scales in the case of 1:1 resonance. It is showed that there exist different response regimes like Strongly Modulated Response (SMR) proved to be the most efficient reponse regime for vibration reduction. An optimization procedure is presented and the results are verified numerically

Modélisation dynamique d’un rotor sur base flexible.

On s’intéresse dans cette étude à la modélisation dynamique d’un rotor sur base flexible afin de mettre en évidence le phénomène de résonance du sol rencontré sur certains hélicoptères, générant des instabilités pouvant conduire à sa destruction