A spectral characterization of nonlinear normal modes

This paper explores the relationship that exists between nonlinear normal modes (NNMs) defined as invariant manifolds in phase space and the spectral expansion of the Koopman operator. Specifically, we demonstrate that NNMs correspond to zero level sets of specific eigenfunctions of the Koopman operator. Thanks to this direct connection, a new, global parametrization of the invariant manifolds is established. Unlike the classical parametrization using a pair of state-space variables, this parametrization remains valid whenever the invariant manifold undergoes folding, which extends the computation of NNMs to regimes of greater energy. The proposed ideas are illustrated using a two-degree-of-freedom system with cubic nonlinearity.Belgian Network DYSCO (Dynamical Systems, Control, and Optimization) funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy OfficeThis is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.jsv.2016.05.01

Shape Optimisation for Friction Dampers with Stress Constraint

International audienceFriction dampers are classically used in turbomachinery for bladed disks to control the levels of vibrations at resonance and limit the risk of fatigue failure. It consists of small metal components located under the platforms of the blades, which dissipates the vibratory energy through friction when a relative displacement between the blades and the damper appears. It is well known that the shape of such component has a strong influence on the damping properties and should be designed with a particular attention. With the arrival of additive manufacturing, new dedicated shapes for these dampers can be considered, determined with specific numerical methods as topological optimisation (TO). However, the presence of the contact nonlinearity challenges the use of traditional TO methods to minimise the vibration levels at resonance. In this work, the topology of the damper is parametrized with the Moving Morphable Components (MMC) framework, and optimised based on meta-modelling techniques: here kriging coupled with the Efficient Global Optimisation (EGO) algorithm. The level of vibration at resonance are computed based on the harmonic balanced method augmented with a constraint to aim directly for the resonant solution. It corresponds to the objective function to be minimised. Additionally, a mechanical constraint based on static stress analysis is also considered to propose reliable damper designs. Results demonstrate the efficiency of the method and show that dampers geometries that meet the engineers' requirements can be identified

Paleoproductivity of Puyehue Lake (Southern Chile) during the last millenium: climatic significance

Southern Chile is a key site for the understanding of past climatic variations since it is influenced by the El Nino Southern Oscillation (ENSO). We investigated high resolution climate changes during the last millennium by a multi-proxy analyse of short cores (60 cm long) collected in Puyehue lake (40°S): magnetic susceptibility, grain-size, mineralogy, density, gamma-density, LOI, biogenic silica content and bulk XRF geochemistry. According to age-depth model (210Pb, 137Cs and varve counting - Boës et al., this session), the cores cover the last 600 yr. The sediment is characterized by volcanic minerals and a high diatom content, due to the important lacustrine silica supply characteristic of volcanic environments. Moreover, the active volcanism of the Chilean Lake District is responsible of a high number of tephra deposits. Our main aim is to quantify biogenic particles fluxes throughout the last millennium by Na2CO3 dissolution and by normative calculation based on bulk XRF analyses. The result shows that volcanic eruptions do not influence the biogenic productivity of the lake. From 1400 to 1880 yr. AD, paleoproductivity shows a global trend from low to high biogenic production. Important paleoproductivity changes are observed over the last 120 yr. Results are compared with historical data and discussed in terms of climate changes and/or anthropic influence

Comparison between control-based continuation and phase-locked loop methods for the identification of backbone curves and nonlinear frequency responses

Control-based continuation (CBC) and phase-locked loops (PLL) are two experimental testing methods that have demonstrated great potential for the non-parametric identification of key nonlinear dynamic features such as nonlinear frequency responses and backbone curves. Both CBC and PLL exploit stabilizing feedback control to steer the dynamics of the tested system towards the responses of interest and overcome important difficulties experienced when applying conventional testing methods such as sine sweeps to nonlinear systems. For instance, if properly designed, the feedback controller can prevent the system from exhibiting untimely transitions between coexisting responses or even losing stability due to bifurcations. This contribution aims to highlight the similarities that exist between CBC and PLL and present the first thorough comparison of their capabilities. Comparisons are supported by numerical simulations as well as experimental data collected on a conceptually simple nonlinear structure primarily composed of a thin curved beam. The beam is doubly clamped and exhibits nonlinear geometric effects for moderate excitation amplitudes

Chemical composition of A and F dwarfs members of the Pleiades open cluster

Abundances of 18 chemical elements have been derived for 16 A (normal and chemically peculiar CP) and 5 F dwarfs members of the Pleiades open cluster in order to set constraints on evolutionary models. The abundances, rotational velocities and microturbulent velocities were derived by iteratively adjusting synthetic spectra to observations at high resolution (R~42000 and R~75000) and high signal-to-noise (S/N) ratios. The abundances obtained do not exhibit any clear correlation with the effective temperature nor the projected rotational velocity. Interestingly, A stars exhibit larger star-to-star variations in C, Sc, Ti, V, Cr, Mn, Sr, Y, Zr and Ba than F stars. F stars exhibit solar abundances for almost all the elements. In A stars, the abundances of Si, Ti and Cr are found to be correlated with that of Fe, the [X/Fe] ratios being solar for these three elements. The derived abundances have been compared to the predictions of published evolutionary models at the age of Pleiades (100 Myr). For the F stars, the predicted slight underabundances of light elements and overabundances of Cr, Fe and Ni are indeed confirmed by our findings. For A stars, the predicted overabundances in iron peak elements are confirmed in a few stars only. The large scatter of the abundances in A stars, already found in the Hyades, Coma Berenices and the UMa group and in field stars appears to be a characteristic property of dwarf A stars. The occurence of hydrodynamical processes competing with radiative diffusion in the radiative zones of the A dwarfs might account for the found scatter in abundances.Comment: 7 pages, 3 figures, accepted in A&

Numerical continuation in nonlinear experiments using local Gaussian process regression

Control-based continuation (CBC) is a general and systematic method to probe the dynamics of nonlinear experiments. In this paper, CBC is combined with a novel continuation algorithm that is robust to experimental noise and enables the tracking of geometric features of the response surface such as folds. The method uses Gaussian process regression to create a local model of the response surface on which standard numerical continuation algorithms can be applied. The local model evolves as continuation explores the experimental parameter space, exploiting previously captured data to actively select the next data points to collect such that they maximise the potential information gain about the feature of interest. The method is demonstrated experimentally on a nonlinear structure featuring harmonically coupled modes. Fold points present in the response surface of the system are followed and reveal the presence of an isola, i.e. a branch of periodic responses detached from the main resonance peak

Effects of the seal wire on the nonlinear dynamics of the aircraft engine turbine blades

Complicated systems made of multiple components are known to be difficult to model, considering their solutions can change dramatically even with the slightest variations in conditions. Aircraft engines contain such complicated systems, and some components in aircraft engines' turbines can cause significant changes in the system's overall response. Hence, this study is focused on investigating the behavior of a turbine blade of an aircraft engine and the effects of the contact between the blade and the seal wire on the dynamics of the blade-disk system. The investigation is performed via various numerical simulations in time and frequency domains. One sector of the bladed disk is modeled using the finite element method with the lock plate and the seal wire imposing cyclic symmetry boundary conditions in the static, modal, and frequency domain forced response analyses. In time domain analyses, the cyclic symmetry is replaced with simplified displacement restricting boundary conditions. The time domain analysis contains steady-state forced responses of the system. The results show that contact with the seal wire is not a major source of nonlinearity and damping. The contacts with the lock plate contribute more to the vibration damping than the seal wire. However, compared to the contacts at the root of the blade, both components remain less significant with regard to frictional damping and nonlinearity

Deep Impact : High Resolution Optical Spectroscopy with the ESO VLT and the Keck 1 telescope

We report on observations of comet 9P/Tempel 1 carried out before, during, and after the NASA DEEP IMPACT event (UT July 4), with the optical spectrometers UVES and HIRES mounted on the telescopes Kueyen of the ESO VLT (Chile) and Keck 1 on Mauna Kea (Hawaii), respectively. A total observing time of about 60 hours, distributed over 15 nights around the impact date, allowed us (i) to find a periodic variation of 1.709 +/- 0.009 day in the CN and NH flux, explained by the presence of two major active regions; (ii) to derive a lifetime > ~ 5 x 10^4 s for the parent of the CN radical from a simple modeling of the CN light curve after the impact; (iii) to follow the gas and dust spatial profiles evolution during the 4 hours following the impact and derive the projected velocities (400 m/s and 150 m/s respectively); (iv) to show that the material released by the impact has the same carbon and nitrogen isotopic composition as the surface material (12C/13C = 95 +/- 15 and 14N/15N = 145 +/- 20).Comment: Accepted for publication in ApJ Letter

Lambda Boo stars with composite spectra

We examine the large sample of lambda Boo candidates collected in Table 1 of Gerbaldi et al. (2003) to see how many of them show composite spectra. Of the 132 lambda Boo candidates we identify 22 which definitely show composite spectra and 15 more for which there are good reasons to suspect a composite spectrum. The percentage of lambda Boo candidates with composite spectra is therefore > 17 and possibly considerably higher. For such stars the lambda Boo classification should be reconsidered taking into account the fact that their spectra are composite. We argue that some of the underabundances reported in the literature may simply be the result of the failure to consider the composite nature of the spectra. This leads to the legitimate suspicion that some, if not all, the lambda Boo candidates are not chemically peculiar at all. A thorough analysis of even a single one of the lambda Boo candidates with composite spectra, in which the composite nature of the spectrum is duly considered, which would demonstrate that the chemical peculiarities persist, would clear the doubt we presently have that the stars with composite spectra may not be lambda Boo at all.Comment: Accepted for publication by A&A on June 3rd 200

The effect of rotation on the abundances of the chemical elements of the A-type stars in the Praesepe cluster

We study how chemical abundances of late B-, A- and early F-type stars evolve with time, and we search for correlations between the abundance of chemical elements and other stellar parameters, such as effective temperature and Vsini. We have observed a large number of B-, A- and F-type stars belonging to open clusters of different ages. In this paper we concentrate on the Praesepe cluster (log t = 8.85), for which we have obtained high resolution, high signal-to-noise ratio spectra of sixteen normal A- and F-type stars and one Am star, using the SOPHIE spectrograph of the Observatoire de Haute-Provence. For all the observed stars, we have derived fundamental parameters and chemical abundances. In addition, we discuss another eight Am stars belonging to the same cluster, for which the abundance analysis had been presented in a previous paper. We find a strong correlation between peculiarity of Am stars and Vsini. The abundance of the elements underabundant in Am stars increases with Vsini, while it decreases for the overabundant elements. Chemical abundances of various elements appear correlated with the iron abundance.Comment: Accepted for publication on A&