A uniqueness theorem for the determination of sources in the Germain–Lagrange plate equation

We prove a uniqueness result related to the Germain–Lagrange dynamic plate differential equation. We consider the equation {∂2u∂t2+△2u=g⊗f,in ]0,+∞)×R2,u(0)=0,∂u∂t(0)=0, where uu stands for the transverse displacement, ff is a distribution compactly supported in space, and g∈Lloc1([0,+∞)) is a function of time such that g(0)≠0g(0)≠0 and there is a T0>0T0>0 such that g∈C1[0,T0[g∈C1[0,T0[. We prove that the knowledge of uu over an arbitrary open set of the plate for any interval of time ]0,T[]0,T[, 0

Lamb mode diversity imaging fornon-destructivetesting of plate-likestructures

Several Lamb wave modes can be coupled to a particular structure, depending on its geometry and transducer used to generate the guided waves. Each Lamb mode interacts in a particular form with different types of defects, like notches, delamination, surface defects, resulting in different information which can be used to improve damage detection and characterization. An image compounding technique that uses the information obtained from different propagation modes of Lamb waves for non-destructive testing of plate-like structures is proposed. A linear array consisting of 16 piezoelectric elements is attached to a 1 mm thickness aluminum plate, coupling the fundamental A0 and SO modes at the frequencies of 100 kHz and 360 kHz, respectively. For each mode two images are obtained from amplitude and phase information: one image using the Total Focusing Method (TFM) and one phase image obtained from the Sign Coherence Factor (SCF). Each TFM image is multiplied by the SCF image of the respective mode to improve contrast and reduce side and grating lobes effects. The high dispersive characteristic of the A0 mode is compensated for adequate defect detection. The information in the SCF images is used to select one of the TFM mode images, at each pixel, to obtain the compounded image. As a result, dead zone is reduced, resolution and contrast are improved, enhancing damage detection when compared to the use of only one mode. (C) 2013 Elsevier Ltd. All rights reserved. (AU)

Stochastic gravito-inertial modes discovered by CoRoT in the hot Be star HD51452

Context. Be stars are rapidly rotating stars with a circumstellar decretion disk. They usually undergo pressure and/or gravity pulsation modes excited by the κ-mechanism, i.e. an effect of the opacity of iron-peak elements in the envelope of the star. In the Milky Way, p-modes are observed in stars that are hotter than or equal to the B3 spectral type, while g-modes are observed at the B2 spectral type and cooler. Aims. We observed a B0IVe star, HD51452, with the high-precision, high-cadence photometric CoRoT satellite and high-resolution, ground-based HARPS and SOPHIE spectrographs to study its pulsations in great detail. We also used the lower resolution spectra available in the BeSS database. Methods. We analyzed the CoRoT and spectroscopic data with several methods: Clean-NG, FreqFind, and a sliding window method. We also analyzed spectral quantities, such as the violet over red (V/R) emission variations, to obtain information about the variation in the circumstellar environment. We calculated a stellar structure model with the ESTER code to test the various interpretation of the results. Results. We detect 189 frequencies of variations in the CoRoT light curve in the range between 0 and 4.5 c d−1. The main frequencies are also recovered in the spectroscopic data. In particular we find that HD51452 undergoes gravito-inertial modes that are not in the domain of those excited by the κ-mechanism. We propose that these are stochastic modes excited in the convective zones and that at least some of them are a multiplet of r-modes (i.e. subinertial modes mainly driven by the Coriolis acceleration). Stochastically excited gravito-inertial modes had never been observed in any star, and theory predicted that their very low amplitudes would be undetectable even with CoRoT. We suggest that the amplitudes are enhanced in HD51452 because of the very rapid stellar rotation. In addition, we find that the amplitude variations of these modes are related to the occurrence of minor outbursts. Conclusions. Thanks to CoRoT data, we have detected a new kind of pulsations in HD51452, which are stochastically excited gravito-inertial modes, probably due to its very rapid rotation. These modes are probably also present in other rapidly rotating hot Be stars.