Identification of Nonlinear Normal Modes of Engineering Structures under Broadband Forcing

The objective of the present paper is to develop a two-step methodology integrating system identification and numerical continuation for the experimental extraction of nonlinear normal modes (NNMs) under broadband forcing. The first step processes acquired input and output data to derive an experimental state-space model of the structure. The second step converts this state-space model into a model in modal space from which NNMs are computed using shooting and pseudo-arclength continuation. The method is demonstrated using noisy synthetic data simulated on a cantilever beam with a hardening-softening nonlinearity at its free end.Comment: Journal pape

Nonlinear normal modes, modal interactions and isolated resonance curves

The objective of the present study is to explore the connection between the nonlinear normal modes of an undamped and unforced nonlinear system and the isolated resonance curves that may appear in the damped response of the forced system. To this end, an energy balancing technique is used to predict the amplitude of the harmonic forcing that is necessary to excite a specific nonlinear normal mode. A cantilever beam with a nonlinear spring at its tip serves to illustrate the developments. The practical implications of isolated resonance curves are also discussed by computing the beam response to sine sweep excitations of increasing amplitudes.Comment: Journal pape

Connecting nonlinear normal modes to the forced response of a geometric nonlinear structure with closely spaced modes

This paper numerically and experimentally investigates the relationship between the nonlinear normal modes and the forced response of a clamped-clamped cross beam structure. The system possesses closely-spaced linear modes such that the applied force distribution across the structure plays a central role in the appropriation of the nonlinear normal modes. Numerical simulations show that the quadrature conditions of the forced response does not necessarily match the peak response nor the nonlinear normal modes of the underlying conservative system, but instead are dependent upon the applied excitation. Experimental investigations performed with a single-point excitation and control based continuation further demonstrate the necessity for appropriate forcing in order to extract the NNMs of such systems.</p

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

Searching for links between magnetic fields and stellar evolution. II. The evolution of magnetic fields as revealed by observations of Ap stars in open clusters and associations

The evolution of magnetic fields in Ap stars during the main sequence phase is presently mostly unconstrained by observation because of the difficulty of assigning accurate ages to known field Ap stars. We are carrying out a large survey of magnetic fields in cluster Ap stars with the goal of obtaining a sample of these stars with well-determined ages. In this paper we analyse the information available from the survey as it currently stands. We select from the available observational sample the stars that are probably (1) cluster or association members and (2) magnetic Ap stars. For the stars in this subsample we determine the fundamental parameters T_eff, log(L/L_o), and M/M_o. With these data and the cluster ages we assign both absolute age and fractional age (the fraction of the main sequence lifetime completed). For this purpose we have derived new bolometric corrections for Ap stars. Magnetic fields are present at the surfaces of Ap stars from the ZAMS to the TAMS. Statistically for the stars with M > 3 M_o the fields decline with advancing age approximately as expected from flux conservation together with increased stellar radius, or perhaps even faster than this rate, on a time scale of about 3 10^7 yr. In contrast, lower mass stars show no compelling evidence for field decrease even on a timescale of several times 10^8 yr. Study of magnetic cluster stars is now a powerful tool for obtaining constraints on evolution of Ap stars through the main sequence. Enlarging the sample of known cluster magnetic stars, and obtaining more precise RMS fields, will help to clarify the results obtained so far. Further field observations are in progress.Comment: Accepted by Astronomy & Astrophysic

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

Did the ancient egyptians record the period of the eclipsing binary Algol - the Raging one?

The eclipses in binary stars give precise information of orbital period changes. Goodricke discovered the 2.867 days period in the eclipses of Algol in the year 1783. The irregular orbital period changes of this longest known eclipsing binary continue to puzzle astronomers. The mass transfer between the two members of this binary should cause a long-term increase of the orbital period, but observations over two centuries have not confirmed this effect. Here, we present evidence indicating that the period of Algol was 2.850 days three millenia ago. For religious reasons, the ancient Egyptians have recorded this period into the Cairo Calendar, which describes the repetitive changes of the Raging one. Cairo Calendar may be the oldest preserved historical document of the discovery of a variable star.Comment: 26 pages, 5 figures, 11 table

Far Ultraviolet Spectra of B Stars near the Ecliptic

Spectra of B stars in the wavelength range of 911-1100 A have been obtained with the EURD spectrograph onboard the Spanish satellite MINISAT-01 with ~5 A spectral resolution. IUE spectra of the same stars have been used to normalize Kurucz models to the distance, reddening and spectral type of the corresponding star. The comparison of 8 main-sequence stars studied in detail (alpha Vir, epsilon Tau, lambda Tau, tau Tau, alpha Leo, zeta Lib, theta Oph, and sigma Sgr) shows agreement with Kurucz models, but observed fluxes are 10-40% higher than the models in most cases. The difference in flux between observations and models is higher in the wavelength range between Lyman alpha and Lyman beta. We suggest that Kurucz models underestimate the FUV flux of main-sequence B stars between these two Lyman lines. Computation of flux distributions of line-blanketed model atmospheres including non-LTE effects suggests that this flux underestimate could be due to departures from LTE, although other causes cannot be ruled out. We found the common assumption of solar metallicity for young disk stars should be made with care, since small deviations can have a significant impact on FUV model fluxes. Two peculiar stars (rho Leo and epsilon Aqr), and two emission line stars (epsilon Cap and pi Aqr) were also studied. Of these, only epsilon Aqr has a flux in agreement with the models. The rest have strong variability in the IUE range and/or uncertain reddening, which makes the comparison with models difficult.Comment: 25 pages, 6 figures, to be published in The Astrophysical Journa

The search for magnetic fields in mercury-manganese stars

We performed a highly sensitive search for magnetic fields on a large set of HgMn stars. With the aid of a new polarimeter attached to the HARPS spectrometer at the ESO 3.6m-telescope, we obtained high-quality circular polarization spectra of 41 single and double HgMn stars. Using a multi-line analysis technique on each star, we co-added information from hundreds of spectral lines resulting in significantly greater sensitivity to the presence of magnetic fields, including very weak fields. For the 47 individual objects studied, including 6 components of SB2 systems, we do not detect any magnetic fields at greater than the 3 sigma level. The lack of detection in the circular polarization profiles indicates that if strong fields are present on these stars, they must have complex surface topologies. For simple global fields, our detection limits imply upper limits to the fields present of 2-10 Gauss in the best cases. We conclude that HgMn stars lack large-scale magnetic fields, typical for spotted magnetic Ap stars, sufficient to form and sustain the chemical spots observed on HgMn stars. Our study confirms that in addition to magnetically altered atomic diffusion, there exists another differentiation mechanism operating in the atmospheres of late-B main sequence stars which can compositional inhomogeneities on their surfaces.Comment: 12 pages, 8 figures, 2 table