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International audience; The Acoustic Black Hole (ABH) effect refers to a special vibration damping technique adapted to thin-walled structures such as beams or plates. It usually consists of a local decrease of the structure thickness profile, associated to a thin viscoelastic coating placed in the area of minimum thickness. It has been shown that such structural design acts as an efficient vibration damper in the high frequency range, but not at low frequencies. This paper investigates how different types of vibration absorbers, linear and nonlinear, added to the primary system can improve the low frequency performance of a beam ABH termination. In particular, the conjugated effects of the Acoustic Black Hole effect and a Tuned Mass Damper (TMD), a Nonlinear Energy Sink (NES), a bi-stable NES (BNES), and a vibro-impact ABH (VI-ABH) are investigated. Forced response to random excitation are computed in the time domain using a modal approach combined with an energy conserving numerical scheme. Frequency indicators are defined to characterize and compare the performance of all solutions. The simulation results clearly show that all the proposed methods are able to damp efficiently the flexural vibrations in a broadband manner. The optimal tuning of each proposed solution is then investigated through a thorough parametric study, showing how to optimize the efficiency of each solution. In particular, TMD and VI-ABH show a slight dependence on vibration amplitude, while the performance of NES and BNES have a peak of efficiency for moderate amplitudes.

International audience; Non-linear vibrations of free-edge shallow spherical shells are investigated, in order to predict the trend of non-linearity (hardening/softening behaviour) for each mode of the shell, as a function of its geometry. The analog for thin shallow shells of von Kármán's theory for large deflection of plates is used. The main difficulty in predicting the trend of non-linearity relies in the truncation used for the analysis of the partial differential equations (PDEs) of motion. Here, non-linear normal modes through real normal form theory are used. This formalism allows deriving the analytical expression of the coefficient governing the trend of non-linearity. The variation of this coefficient with respect to the geometry of the shell (radius of curvature R, thickness h and outer diameter 2 a) is then numerically computed, for axisymmetric as well as asymmetric modes. Plates (obtained as R → ∞) are known to display a hardening behaviour, whereas shells generally behave in a softening way. The transition between these two types of non-linearity is clearly studied, and the specific role of 2:1 internal resonances in this process is clarified. © 2006 Elsevier Ltd. All rights reserved.