Oscillation threshold of a clarinet model: a numerical continuation approach

This paper focuses on the oscillation threshold of single reed instruments. Several characteristics such as blowing pressure at threshold, regime selection, and playing frequency are known to change radically when taking into account the reed dynamics and the flow induced by the reed motion. Previous works have shown interesting tendencies, using analytical expressions with simplified models. In the present study, a more elaborated physical model is considered. The influence of several parameters, depending on the reed properties, the design of the instrument or the control operated by the player, are studied. Previous results on the influence of the reed resonance frequency are confirmed. New results concerning the simultaneous influence of two model parameters on oscillation threshold, regime selection and playing frequency are presented and discussed. The authors use a numerical continuation approach. Numerical continuation consists in following a given solution of a set of equations when a parameter varies. Considering the instrument as a dynamical system, the oscillation threshold problem is formulated as a path following of Hopf bifurcations, generalizing the usual approach of the characteristic equation, as used in previous works. The proposed numerical approach proves to be useful for the study of musical instruments. It is complementary to analytical analysis and direct time-domain or frequency-domain simulations since it allows to derive information that is hardly reachable through simulation, without the approximations needed for analytical approach

Continuation of a physical model of brass instrument: application to trumpet categorization

International audienceThe system formed by the couple {player-trumpet} falls into the class of non-linear dynamical systems likely to be studied using different numerical tools such as numerical continuation methods. In this study we illustrate the interest of this approach for the categorization of Bb trumpets in the space of some performance descriptors obtained from continuation by the ANM method combined to the Harmonic Balance Method (HBM)

Structures déployables constituées de mètres rubans : modélisations et essais expérimentaux

International audienceThe study focuses on the numerical modeling and experimental characterization of the static behavior of composite tape springs. Rod models with flexible cross section have been developed and are extended in order to take into account the use of composite materials. Tape springs have been manufactured with carbon/epoxy plies to use it in an experimental setup to compare rod models to experimental results. The pure bending test highlights a complex scenario of folding that involves both bending and twisting mechanisms. The comparison between numerical and experimental results of the transverse bending of tape springs is discussed.Les travaux présentés ici portent sur la modélisation et la caractérisation expérimentale du comporte-ment en statique de rubans composites. Les modèles de poutres à section flexible précédemment développés sont étendus ici à l'utilisation de matériaux composites. Des mètres rubans ont été fabriqués à partir de plis unidirectionnels carbone/époxy pour servir d'éprouvette dans une machine d'essais conçue dans le but de confronter le modèle à des résultats expérimentaux. L'essai réalisé est la flexion transverse du ruban qui présente un scénario complexe de formation de plis faisant intervenir des phénomènes de flexion et de torsion. Une discussion est menée au sujet de la confrontation numérique/expérimental pour l'essai de flexion transverse de rubans composites

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities — which are mainly related either to nonlinear convection terms and/or some geometric variability — that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and — in the unsteady case — long-time stability of the reduced model. Moreover, we provide an extensive list of literature references

Backbone curves, Neimark-Sacker boundaries and appearance of quasi-periodicity in nonlinear oscillators: application to 1:2 internal resonance and frequency combs in MEMS

Quasi-periodic solutions can arise in assemblies of nonlinear oscillators as a consequence of Neimark-Sacker bifurcations. In this work, the appearance of Neimark-Sacker bifurcations is investigated analytically and numerically in the specific case of a system of two coupled oscillators featuring a 1:2 internal resonance. More specifically, the locus of Neimark-Sacker points is analytically derived and its evolution with respect to the system parameters is highlighted. The backbone curves, solution of the conservative system, are first investigated, showing in particular the existence of two families of periodic orbits, denoted as parabolic modes. The behaviour of these modes, when the detuning between the eigenfrequencies of the system is varied, is underlined. The non-vanishing limit value, at the origin of one solution family, allows explaining the appearance of isolated solutions for the damped-forced system. The results are then applied to a Micro-Electro-Mechanical System-like shallow arch structure, to show how the analytical expression of the Neimark-Sacker boundary curve can be used for rapid prediction of the appearance of quasiperiodic regime, and thus frequency combs, in Micro-Electro-Mechanical System dynamics

Passive control of resonances by nonlinear absorbers

A new passive technique for reducing vibration and noise using purely nonlinear absorbers is studied. Compared to classical passive systems (Frahm absorbers, Helmholtz resonator), a single nonlinear absorber works in a limited range of forcing but in a wide band of frequency. In this paper, a simple system with two degrees of freedom is used to analyze the beginning of the ‘Targeted Energy Transfer” TET phenomenon and to define the desired working zone for Nonlinear Energy Sink (NES). An analytical formula of the level of forcing for the beginning of TET is established by a simplified approach

PASSIVE SUPPRESSION OF HELICOPTER GROUND RESONANCE INSTABILITY BY MEANS OF A STRONGLY NONLINEAR ABSORBER

International audienceIn this paper, we study a problem of passive suppression of helicopter Ground Resonance (GR) using a single degree freedom Nonlinear Energy Sink (NES). GR is a dynamic instability involving the coupling of the blades motion in the rotational plane (i.e. the lag motion) and the helicopter fuselage motion. A reduced linear system reproducing GR instability is used. It is obtained using successively Coleman transformation and binormal transformation. The analysis of the steadystate responses of this model is performed when a NES is attached on the helicopter fuselage. The NES includes linear damping and essential cubic restoring force. The analysis is achieved applying complexification-averaging method and slow-fast partition of the motion. The resulting slow-flow model is finally analyzed using multiple scale approach. Four steady-state responses are highlighted and explained theoretically: complete suppression, partial suppression through strongly modulated response, partial suppression through periodic response and no suppression of the GR. An algorithm based on simple criterions is developed to predict these steady-state response regimes. Numerical simulations of the complete system confirm this analysis of the slowflow dynamics. A parametric analysis of the influence of the NES damping coefficient and the rotor speed on the response regime is finally proposed

Anatomy of an extensional shear zone leading to the exhumation of the middle crust within the Canigou dome (Eastern Pyrenees, Axial Zone)

International audienceTo investigate the mechanism of exhumation of deep crustal rocks in hot orogens, we focus on the southwestern part of the Variscan Canigou gneiss dome (Pyrenees) where the transition between the middle and upper crust can be observed. On the basis of new structural data, geological mapping, cross sections, microstructural analyses, and petrologic observations, we propose that flat-lying foliation within the gneiss dome and steep cleavage developed above it formed coevally. We note the presence of regional-scale shear zones at the boundary between the middle crust (Núria-Canigou Unit) and upper crust (Puigmal unit). At this boundary, the E-W South Canigou Shear Zone is an extensional shear zone showing top-to-the- southwest kinematics. Deformation, which is localized within the andalusite-biotite transition zone, occurred under retrogressive conditions, from high-grade ductile to brittle conditions during the main deformation stage (D2). The tectonic contact was folded during a later stage (D3). We propose that the shape of the Canigou dome resulted from the activation of extensional shear zones at the top of the orthogneiss, leading to partial exhumation of high-grade rocks. The Canigou gneiss dome can be considered an extensional dome that formed during late Variscan (ca. 310-290Ma) transpression